Connect with us


Law without law: from observer states to physics via algorithmic information theory




Markus P. Müller

Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


According to our current conception of physics, any valid physical theory is supposed to describe the objective evolution of a unique external world. However, this condition is challenged by quantum theory, which suggests that physical systems should not always be understood as having objective properties which are simply revealed by measurement. Furthermore, as argued below, several other conceptual puzzles in the foundations of physics and related fields point to limitations of our current perspective and motivate the exploration of an alternative: to start with the first-person (the observer) rather than the third-person perspective (the world).
In this work, I propose a rigorous approach of this kind on the basis of algorithmic information theory. It is based on a single postulate: that $textit{universal induction}$ determines the chances of what any observer sees next. That is, instead of a world or physical laws, it is the local state of the observer alone that determines those probabilities. Surprisingly, despite its solipsistic foundation, I show that the resulting theory recovers many features of our established physical worldview: it predicts that it appears to observers $textit{as if there was an external world}$ that evolves according to simple, computable, probabilistic laws. In contrast to the standard view, objective reality is not assumed on this approach but rather provably emerges as an asymptotic statistical phenomenon. The resulting theory dissolves puzzles like cosmology’s Boltzmann brain problem, makes concrete predictions for thought experiments like the computer simulation of agents, and suggests novel phenomena such as “probabilistic zombies” governed by observer-dependent probabilistic chances. It also suggests that some basic phenomena of quantum theory (Bell inequality violation and no-signalling) might be understood as consequences of this framework.

► BibTeX data

► References

[1] A. Aguirre and M. Tegmark, Born in an Infinite Universe: a Cosmological Interpretation of Quantum Mechanics, Phys. Rev. D 84, 105002 (2011).

[2] A. Linde and M. Noorbala, Measure problem for eternal and non-eternal inflation, J. Cosmol. Astropart. Phys. 1009 (2010).

[3] A. Albrecht, Cosmic Inflation and the Arrow of Time, in J. D. Barrow, P. C. W. Davies, and C. L. Harper (eds.), Science and Ultimate Reality: Quantum Theory, Cosmology, and Complexity, Cambridge University Press, 2004.

[4] A. Albrecht and L. Sorbo, Can the universe afford inflation?, Phys. Rev. D 70, 063528 (2004).

[5] Y. Nomura, Physical theories, eternal inflation, and the quantum universe, J. High Energ. Phys. 11, 063 (2011).

[6] A. Peres, Unperformed experiments have no results, Am. J. Phys. 46, 745–747 (1978).

[7] C. A. Fuchs and R. Schack, Quantum-Bayesian coherence, Rev. Mod. Phys. 85, 1693–1715 (2013).

[8] C. Fuchs, Quantum Foundations in the Light of Quantum Information, in A. Gonis and P. E. A. Turchi, Decoherence and its Implications in Quantum Computation and Information Transfer: Proceedings of the NATO Advanced Research Workshop, Mykonos, Greece, June 25–30, 2000, IOS Press, Amsterdam, arXiv:quant-ph/​0106166.

[9] Č. Brukner, A no-go theorem for observer-independent facts, Entropy 20, 350 (2018).

[10] K.-W. Bong, A. Utreras-Alarcón, F. Ghafari, Y.-C. Liang, N. Tischler, E. G. Cavalcanti, G. F. Pryde, and H. M. Wiseman, Testing the reality of Wigner’s friend’s observations, arXiv:1907.05607.

[11] N. Bostrom, Are You Living In a Computer Simulation?, Philosophical Quarterly 53(211), 243–255 (2003).

[12] D. R. Hofstadter and D. C. Dennett, The Mind’s I — Fantasies and Reflections on Self and Soul, Basic Books, 1981.

[13] D. Parfit, Reasons and Persons, Clarendon Press, Oxford, 1984.

[14] C. Rovelli, Relational Quantum Mechanics, Int. J. Theor. Phys. 35(8), 1637–1678 (1996).

[15] J. A. Wheeler, Information, physics, quantum: the search for links, Proceedings of the 3rd International Symposium on Quantum Mechanics, 354–368, Tokyo, 1989.

[16] J. S. Bell, On the Einstein Podolsky Rosen Paradox, Physics 1(3), 195–200 (1964).

[17] J. S. Bell, On the problem of hidden variables in quantum mechanics, Rev. Mod. Phys. 38(3), 447–452 (1966).

[18] D. Deutsch, Quantum theory, the Church-Turing principle and the universal quantum computer, Proceedings of the Royal Society of London A 400, pp. 97-117 (1985).

[19] L. Hardy, Quantum Theory From Five Reasonable Axioms, arXiv:quant-ph/​0101012.

[20] B. Dakić and Č. Brukner, Quantum Theory and Beyond: Is Entanglement Special?, in H. Halvorson (ed.), “Deep Beauty: Understanding the Quantum World through Mathematical Innovation”, Cambridge University Press, 2011.

[21] Ll. Masanes and M. P. Müller, A derivation of quantum theory from physical requirements, New J. Phys. 13, 063001 (2011).

[22] G. Chiribella, G. M. D’Ariano, and P. Perinotti, Informational derivation of quantum theory, Phys. Rev. A 84, 012311 (2011).

[23] L. Hardy, Reformulating and Reconstructing Quantum Theory, arXiv:1104.2066.

[24] Ll. Masanes, M. P. Müller, R. Augusiak, and D. Pérez-García, Existence of an information unit as a postulate of quantum theory, Proc. Natl. Acad. Sci. USA 110(41), 16373 (2013).

[25] H. Barnum, M. P. Müller, and C. Ududec, Higher-order interference and single-system postulates characterizing quantum theory, New J. Phys. 16, 123029 (2014).

[26] P. A. Höhn, Quantum theory from rules on information acquisition, Entropy 19(3), 98 (2017).

[27] P. A. Höhn and C. S. P. Wever, Quantum theory from questions, Phys. Rev. A 95, 012102 (2017).

[28] A. Wilce, A Royal Road to Quantum Theory (or Thereabouts), Entropy 20(4), 227 (2018).

[29] A. Peres, Quantum Theory: Concepts and Methods, Kluwer Academic Publishers, 2002.

[30] W. Myrvold, Beyond Chance and Credence, unpublished manuscript (2017).

[31] M. Hutter, Universal Artificial Intelligence – Sequential Decisions Based on Algorithmic Probability, Springer, 2005.

[32] R. Kirk, Zombies, The Stanford Encyclopedia of Philosophy, E. N. Zalta (ed.), URL=http:/​/​​archives/​win2012/​entries/​zombies (2011).

[33] J. A. Wheeler, Law Without Law, in J. A. Wheeler and W. H. Zurek (eds.), “Quantum Theory and Measurement”, Princeton Series in Physics, Princeton University Press, 1983.

[34] A. M. Turing, On computable numbers, with an application to the Entscheidungsproblem, Proc. London Maths. Soc. Ser. 2 42, 230–265 (1936).

[35] S. B. Cooper, Computability Theory, Chapman & Hall/​CRC, 2004.

[36] S. Wolfram, A New Kind of Science, Champaign, Illinois, 2002.

[37] R. Gandy, Church’s thesis and principles for mechanisms, in J. Barwise, H. Jerome Keisler, and K. Kunen (eds.), The Kleene Symposium, North Holland Publishing, Amsterdam, 1980.

[38] P. Arrighi and G. Dowek, The physical Church-Turing thesis and the principles of quantum theory, Int. J. Found. Comput. S. 23(5), 1131–1145 (2012).

[39] D. R. Hofstadter, Gödel, Escher, Bach: an eternal golden braid, Basic Books, New York, 1979.

[40] G. Piccinini, Computationalism, The Church-Turing Thesis, and the Church-Turing Fallacy, Synthese 154(1), 97–120 (2007).

[41] M. Davis, Why there is no such discipline as hypercomputation, Appl. Math. Comput. 178, 4–7 (2006).

[42] M. Tegmark, Does the universe in fact contain almost no information?, Found. Phys. Lett. 9 25-42 (1996).

[43] R. W. Spekkens, Evidence for the epistemic view of quantum states: A toy theory, Phys. Rev. A 75, 032110 (2007).

[44] H. Everett, The Theory of the Universal Wave Function, in B. S. Dewitt and N. Graham (eds.), The Many Worlds Interpretation of Quantum Mechanics, Princeton University Press, 1973.

[45] B. Marchal, Mechanism and personal identity, in Proceedings of the 1st World Conference on the Fundamentals of Artificial Intelligence (WOCFAI’91), 461–475, Paris, 1991.

[46] I. Wood, P. Sunehag, and M. Hutter, (Non-)Equivalence of Universal Priors, in D. L. Dowe (ed.), Algorithmic Probability and Friends – Bayesian Prediction and Artificial Intelligence, Springer Lecture Notes in Artificial Intelligence, 2013.

[47] M. Li and P. Vitányi, An Introduction to Kolmogorov Complexity and Its Applications, Springer, 1997.

[48] G. J. Chaitin, Algorithmic Information Theory, Cambridge University Press, Cambridge, 1987.

[49] T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd edition, John Wiley & Sons, 2006.

[50] M. Hutter, Open Problems in Universal Induction & Intelligence, Algorithms 2(3), 879–906 (2009).

[51] R. Schack, Algorithmic information and simplicity in statistical physics, Int. J. Theor. Phys. 36(1), 209–226 (1997).

[52] M. Müller, Stationary algorithmic probability, Theoretical Computer Science 411, 113–130 (2010).

[53] P. Walley, Statistical Reasoning with Imprecise Probabilities, Monographs on Statistics and Applied Probability, Springer Science and Business Media, 1991.

[54] R. Lima, Equivalence of ensembles in quantum lattice systems, Annales de l’I.H.P. 15(1), 61–68 (1971).

[55] R. Lima, Equivalence of ensembles in quantum lattice systems: states, Commun. Math. Phys. 24, 180–192 (1972).

[56] M. P. Müller, E. Adlam, Ll. Masanes, and N. Wiebe, Thermalization and canonical typicality in translation-invariant quantum lattice systems, Commun. Math. Phys. 340(2), 499–561 (2015).

[57] R. Colbeck, Quantum And Relativistic Protocols For Secure Multi-Party Computation, PhD Thesis, University of Cambridge (2006), arXiv:0911.3814.

[58] S. Pironio, A. Acín, S. Massar, A. Boyer de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and C. Monroe, Random numbers certified by Bell’s theorem, Nature 464, 1021 (2010).

[59] A. K. Zvonkin and L. A. Levin, The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms, Russian Math. Surveys 25(6), 83–124 (1970).

[60] A. A. Brudno, Entropy and the complexity of the trajectories of a dynamical system, Trans. Moscow Math. Sec. 2, 127–151 (1983).

[61] M. Hutter, On universal prediction and Bayesian confirmation, Theoret. Comput. Sci. 384, 33–48 (2007).

[62] M. Hutter and A. Muchnik, On semimeasures predicting Martin-Löf random sequences, Theor. Comput. Sci. 382(3), 247–261 (2007).

[63] J. M. Bernardo and A. F. M. Smith, Bayesian theory, Wiley Series in Probability and Statistics, Toronto, 1993.

[64] C. Glymour, Why I am not a Bayesian, in H. Arló-Costa, V. F. Hendricks, and J. van Benthem (eds.), Readings in Formal Epistemology, Springer Graduate Texts in Philosophy, Springer, 2016.

[65] B. Eva and S. Hartmann, On the Origins of Old Evidence, Australas. J. Philos. 1–14 (2019).

[66] N. Goodman, Fact, Fiction, and Forecast, Harvard University Press, Cambridge, MA, 1955.

[67] T. F. Sterkenburg, A Generalized Characterization of Algorithmic Probability, Theory Comput. Syst. 1–16 (2017).

[68] T. F. Sterkenburg, Universal Prediction – A Philosophical Investigation, PhD thesis, University of Groningen, 2018.

[69] S. Wolf, Second Thoughts on the Second Law, in H. J. Böckenhauer, D. Komm, and W. Unger (eds.), Adventures Between Lower Bounds and Higher Altitudes, Lecture Notes in Computer Science, Springer, Cham, 2018.

[70] T. Zeugmann and S. Zilles, Learning recursive functions: A survey, Theor. Comput. Sci. 397, 4–56 (2008).

[71] N. Harrigan and R. W. Spekkens, Einstein, Incompleteness, and the Epistemic View of Quantum States, Found. Phys. 40(2), 125–157 (2010).

[72] R. W. Spekkens, Contextuality for Preparations, Transformations, and Unsharp Measurements, Phys. Rev. A 71, 052108 (2005).

[73] G. Piccinini, Computation in Physical Systems, The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.), URL =https:/​/​​archives/​sum2017/​entries/​computation-physicalsystems/​ (2017).

[74] K. Zuse, Rechnender Raum, Friedrich Vieweg u. Sohn, Wiesbaden, 1969.

[75] J. Schmidhuber, Algorithmic Theories of Everything, Instituto Dalle Molle Di Studi Sull Intelligenza Artificiale (2000), arXiv:quant-ph/​0011122.

[76] G. ‘t Hooft, Quantum Mechanics and Determinism, in P. Frampton and J. Ng (eds.), Proceedings of the Eighth International Conference on Particles, Strings and Cosmology, Univ. of North Carolina, Chapel Hill, 275–285, 2001.

[77] S. Lloyd, Programming the Universe: A Quantum Computer Scientist Takes on the Cosmos, Random House, New York, 2006.

[78] M. Hutter, A Complete Theory of Everything (will be subjective), Algorithms 3(4), 329–350 (2010).

[79] P. Diaconis and D. Freedman, On the consistency of Bayes estimates, Ann. Statist. 14, 1–26 (1986).

[80] H. Moravec, The Doomsday Device, in Mind Children: The Future of Robot and Human Intelligence, Harvard University Press, London, 1988.

[81] B. Marchal, Informatique théorique et philosophie de l’esprit, in Acte du 3ème colloque international Cognition et Connaissance, 193–227, Toulouse, 1988.

[82] M. Tegmark, The Interpretation of Quantum Mechanics: Many Worlds or Many Words?.

[83] A. Linde, Inflationary Cosmology, in M. Lemoine, J. Martin, and P. Peter (eds), Inflationary Cosmology, Lecture Notes in Physics 738, Springer, Berlin/​Heidelberg, 2008.

[84] D. N. Page, Cosmological Measures without Volume Weighting, J. Cosmol. Astropart. P. 10, (2008).

[85] D. N. Page, Is our Universe likely to decay within 20 billion years?, Phys. Rev. D 78, 063535 (2008).

[86] L. Dyson, M. Kleban, and L. Susskind, Disturbing Implications of a Cosmological Constant, JHEP 0210 (2002).

[87] W. H. Zurek, Thermodynamic cost of computation, algorithmic complexity and the information metric, Nature 341, 119–124 (1989).

[88] F. Benatti, T. Krüger, M. Müller, Ra. Siegmund-Schultze, and A. Skoła, Entropy and quantum Kolmogorov complexity: a quantum Brudno’s theorem, Commun. Math. Phys. 265(2), 437–461 (2006).

[89] Č. Brukner, On the quantum measurement problem, in R. Bertlmann and A. Zeilinger (eds.), Quantum (Un)Speakables II — Half a Century of Bell’s Theorem, Springer International Publishing Switzerland, 2017.

[90] A. Zeilinger, A Foundational Principle for Quantum Mechanics, Found. Phys. 29(4), 631–643 (1999).

[91] C. A. Fuchs and A. Peres, Quantum Theory Needs No ‘Interpretation’, Phys. Today 53(3), 70 (2000).

[92] C. A. Fuchs, Quantum Bayesianism at the Perimeter, Physics in Canada 66(2), 77–82 (2010).

[93] C. Timpson, Quantum information theory & the Foundations of Quantum Mechanics, Oxford University Press, Oxford, 2013.

[94] D. N. Page and W. K. Wootters, Evolution without evolution: Dynamics described by stationary observables, Phys. Rev. D 27(12), 2885–2892 (1983).

[95] D. M. Appleby, Concerning Dice and Divinity, AIP Conference Proceedings 889, 30 (2007).

[96] C. J. Wood and R. W. Spekkens, The lesson of causal discovery algorithms for quantum correlations: causal explanations of Bell-inequality violations require fine-tuning, New J. Phys. 17, 033002 (2015).

[97] E. Schrödinger, Discussion of Probability Relations between Separated Systems, Proc. Camb. Phil. Soc. 31, 555 (1935).

[98] J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23, 880 (1969).

[99] C. H. Bennett and G. Brassard, Quantum cryptography: Public key distribution and coin tossing, in Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, IEEE, New York, 1984.

[100] J. Barrett, L. Hardy, and A. Kent, No Signaling and Quantum Key Distribution, Phys. Rev. Lett. 95, 010503 (2005).

[101] M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-Å. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, Significant-loophole-free test of Bell’s theorem with entangled photons, Phys. Rev. Lett. 115, 250401 (2015).

[102] R. Colbeck and R. Renner, A system’s wave function is uniquely determined by its underlying physical state, New J. Phys. 19, 013016 (2017).

[103] R. Colbeck and R. Renner, A short note on the concept of free choice, arXiv:1302.4446.

[104] M. Navascués, Y. Guryanova, M. J. Hoban, and A. Acín, Almost quantum correlations, Nat. Comm. 6, 6288 (2015).

[105] L. A. Khalfin and B. S. Tsirelson, Quantum and quasi-classical analogs of Bell inequalities, in P. Lahti and P. Mittelstaedt (eds.), Symposium on the Foundations of Modern Physics, World Scientific, Singapore, 1985.

[106] B. S. Tsirelson, Some results and problems on quantum Bell-type inequalities, Hadronic J. Suppl. 8, 329 (1993).

[107] S. Popescu and D. Rohrlich, Quantum Nonlocality as an Axiom, Found. Phys. 24(3), 379–385 (1994).

[108] J. Barrett, N. Linden, S. Massar, S. Pironio, S. Popescu, and D. Roberts, Nonlocal correlations as an information-theoretic resource, Phys. Rev. A 71, 022101 (2005).

[109] A. Garg and N. D. Mermin, Detector inefficiencies in the Einstein-Podolsky-Rosen experiment, Phys. Rev. D 35(12), 3831 (1987).

[110] C. Branciard, Detection loophole in Bell experiments: How postselection modifies the requirements to observe nonlocality, Phys. Rev. A 83, 032123 (2011).

[111] P. M. Pearle, Hidden-Variable Example Based upon Data Rejection, Phys. Rev. D 2(8), 1418–1425 (1970).

[112] J. Berkson, Limitations of the Application of Fourfold Table Analysis to Hospital Data, Biometrics Bulletin 2(3), 47–53 (1946).

[113] J.-P. W. MacLean, K. Ried, R. W. Spekkens, and K. Resch, Quantum-coherent mixtures of causal relations, Nat. Comm. 8, 15149 (2017).

[114] G. Brassard and R. Raymond-Robichaud, Can Free Will Emerge from Determinism in Quantum Theory?, in A. Suarez and P. Adams (eds.), Is Science Compatible with Free Will? Exploring Free Will and Consciousness in the Light of Quantum Physics and Neuroscience, Springer, 2013; arXiv:1204.2128.

[115] G. Brassard and P. Raymond-Robichaud, Parallel Lives: A local realistic interpretation of “nonlocal” boxes, poster (2015), available at http:/​/​​tests/​poster_revsmall.jpg.

[116] G. Brassard and P. Raymond-Robichaud, Parallel lives: A local-realistic interpretation of “nonlocal” boxes, Entropy 21(1), 87 (2019).

[117] W. van Dam, Implausible consequences of superstrong nonlocality, Natural Computing 12(1), 9–12 (2013).

[118] G. Brassard, H. Buhrman, N. Linden, A. A. Méthot, A. Tapp, and F. Unger, Limit on Nonlocality in Any World in Which Communication Complexity Is Not Trivial, Phys. Rev. Lett. 96, 250401 (2006).

[119] M. Pawlowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, and M. Zukowski, Information causality as a physical principle, Nature 461, 1101–1104 (2009).

[120] M. Navascués and H. Wunderlich, A glance beyond the quantum model, Proc. R. Soc. A 466, 881–890 (2009).

[121] A. Cabello, Simple Explanation of the Quantum Violation of a Fundamental Inequality, Phys. Rev. Lett. 110, 060402 (2013).

[122] A. Cabello, Quantum correlations from simple assumptions, Phys. Rev. A 100, 032120 (2019).

[123] G. Chiribella, A. Cabello, M. Kleinmann, and M. P. Müller, General Bayesian theories and the emergence of the exclusivity principle, arXiv:1901.11412.

[124] S. Armstrong, A. Sandberg, and N. Bostrom, Thinking inside the box: using and controlling an Oracle AI, Minds and Machines 22(4), 299–324 (2012).

[125] N. Bostrom, Superintelligence: Paths, Dangers, Strategies, Oxford University Press, Oxford, 2014.

[126] N. Bostrom and A. Salamon, The Intelligence Explosion (extended abstract), retrieved April 2015 from http:/​/​​2011/​01/​intelligence-explosion-extended.html (2011).

[127] D. C. Dennett, Freedom evolves, Viking Books, 2003.

[128] S. Wolfram, Cellular automata as models of complexity, Nature 311, 419–424 (1984).

[129] S. Wolfram, Undecidability and Intractability in Theoretical Physics, Phys. Rev. Lett. 54, 735–738 (1985).

[130] N. Israeli and N. Goldenfeld, Computational Irreducibility and the Predictability of Complex Physical Systems, Phys. Rev. Lett. 92, 074105 (2004).

[131] E. Bernstein and U. Vazirani, Quantum Complexity Theory, SIAM J. Comput. 26(5), 1411–1473 (1997).

[132] M. Müller, Strongly Universal Quantum Turing Machines and Invariance of Kolmogorov Complexity, IEEE Trans. Inf. Th. 54(2), 763–780 (2008).

Cited by

[1] Augustin Vanrietvelde, Philipp A Hoehn, Flaminia Giacomini, and Esteban Castro-Ruiz, “A change of perspective: switching quantum reference frames via a perspective-neutral framework”, arXiv:1809.00556.

[2] Arne Hansen and Stefan Wolf, “The Measurement Problem Is the “Measurement” Problem”, arXiv:1810.04573.

[3] Markus P. Mueller, “Mind before matter: reversing the arrow of fundamentality”, arXiv:1812.08594.

[4] John Realpe-Gómez, “Modeling observers as physical systems representing the world from within: Quantum theory as a physical and self-referential theory of inference”, arXiv:1705.04307.

[5] Arne Hansen and Stefan Wolf, “Wigner’s Isolated Friend”, arXiv:1912.03248.

[6] Ali Barzegar, “QBism Is Not So Simply Dismissed”, Foundations of Physics 50 7, 693 (2020).

[7] John Realpe-Gomez, “Embodied observations from an intrinsic perspective can entail quantum dynamics”, arXiv:2005.03653.

The above citations are from SAO/NASA ADS (last updated successfully 2020-07-21 23:33:52). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2020-07-21 23:33:51).



On maximum-likelihood decoding with circuit-level errors




Leonid P. Pryadko

Department of Physics & Astronomy, University of California, Riverside, California 92521, USA

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


Error probability distribution associated with a given Clifford measurement circuit is described exactly in terms of the circuit error-equivalence group, or the circuit subsystem code previously introduced by Bacon, Flammia, Harrow, and Shi. This gives a prescription for maximum-likelihood decoding with a given measurement circuit. Marginal distributions for subsets of circuit errors are also analyzed; these generate a family of related asymmetric LDPC codes of varying degeneracy. More generally, such a family is associated with any quantum code. Implications for decoding highly-degenerate quantum codes are discussed.

► BibTeX data

► References

[1] P. W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Phys. Rev. A 52, R2493 (1995).

[2] C. G. Almudever, L. Lao, X. Fu, N. Khammassi, I. Ashraf, D. Iorga, S. Varsamopoulos, C. Eichler, A. Wallraff, L. Geck, A. Kruth, J. Knoch, H. Bluhm, and K. Bertels, “The engineering challenges in quantum computing,” in Design, Automation Test in Europe Conference Exhibition (DATE), 2017 (2017) pp. 836–845.

[3] P. Aliferis, D. Gottesman, and J. Preskill, “Quantum accuracy threshold for concatenated distance-3 codes,” Quantum Inf. Comput. 6, 97–165 (2006), quant-ph/​0504218.

[4] David S. Wang, Austin G. Fowler, and Lloyd C. L. Hollenberg, “Surface code quantum computing with error rates over $1%$,” Phys. Rev. A 83, 020302 (2011).

[5] Christopher T. Chubb and Steven T. Flammia, “Statistical mechanical models for quantum codes with correlated noise,” (2018), unpublished, 1809.10704.

[6] E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, “Topological quantum memory,” J. Math. Phys. 43, 4452 (2002).

[7] Austin G. Fowler, Adam C. Whiteside, and Lloyd C. L. Hollenberg, “Towards practical classical processing for the surface code,” Phys. Rev. Lett. 108, 180501 (2012a).

[8] A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, “Surface codes: Towards practical large-scale quantum computation,” Phys. Rev. A 86, 032324 (2012b).

[9] Austin G. Fowler, Adam C. Whiteside, Angus L. McInnes, and Alimohammad Rabbani, “Topological code autotune,” Phys. Rev. X 2, 041003 (2012c).

[10] Christopher Chamberland, Guanyu Zhu, Theodore J. Yoder, Jared B. Hertzberg, and Andrew W. Cross, “Topological and subsystem codes on low-degree graphs with flag qubits,” Phys. Rev. X 10, 011022 (2020a).

[11] Christopher Chamberland, Aleksander Kubica, Theodore J Yoder, and Guanyu Zhu, “Triangular color codes on trivalent graphs with flag qubits,” New Journal of Physics 22, 023019 (2020b).

[12] Christophe Vuillot, Lingling Lao, Ben Criger, Carmen García Almudéver, Koen Bertels, and Barbara M. Terhal, “Code deformation and lattice surgery are gauge fixing,” New Journal of Physics 21, 033028 (2019).

[13] Giacomo Torlai and Roger G. Melko, “Neural decoder for topological codes,” Phys. Rev. Lett. 119, 030501 (2017).

[14] S. Krastanov and L. Jiang, “Deep neural network probabilistic decoder for stabilizer codes,” Scientific Reports 7, 11003 (2017), 1705.09334.

[15] N. P. Breuckmann and X. Ni, “Scalable neural network decoders for higher dimensional quantum codes,” Quantum 2, 68 (2018), 1710.09489.

[16] Zhih-Ahn Jia, Yuan-Hang Zhang, Yu-Chun Wu, Liang Kong, Guang-Can Guo, and Guo-Ping Guo, “Efficient machine-learning representations of a surface code with boundaries, defects, domain walls, and twists,” Phys. Rev. A 99, 012307 (2019).

[17] Paul Baireuther, Thomas E. O’Brien, Brian Tarasinski, and Carlo W. J. Beenakker, “Machine-learning-assisted correction of correlated qubit errors in a topological code,” Quantum 2, 48 (2018).

[18] Christopher Chamberland and Pooya Ronagh, “Deep neural decoders for near term fault-tolerant experiments,” Quantum Science and Technology 3, 044002 (2018).

[19] P. Baireuther, M. D. Caio, B. Criger, C. W. J. Beenakker, and T. E. O’Brien, “Neural network decoder for topological color codes with circuit level noise,” New Journal of Physics 21, 013003 (2019).

[20] Nishad Maskara, Aleksander Kubica, and Tomas Jochym-O’Connor, “Advantages of versatile neural-network decoding for topological codes,” Phys. Rev. A 99, 052351 (2019).

[21] D. Bacon, S. T. Flammia, A. W. Harrow, and J. Shi, “Sparse quantum codes from quantum circuits,” in Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing, STOC ’15 (ACM, New York, NY, USA, 2015) pp. 327–334, 1411.3334.

[22] D. Bacon, S. T. Flammia, A. W. Harrow, and J. Shi, “Sparse quantum codes from quantum circuits,” IEEE Transactions on Information Theory 63, 2464–2479 (2017).

[23] Jozef Strečka, “Generalized algebraic transformations and exactly solvable classical-quantum models,” Physics Letters A 374, 3718 – 3722 (2010).

[24] Christopher Chamberland and Michael E. Beverland, “Flag fault-tolerant error correction with arbitrary distance codes,” Quantum 2, 53 (2018), 1708.02246.

[25] C. Chamberland and A. W. Cross, “Fault-tolerant magic state preparation with flag qubits,” Quantum 3, 143 (2019), 1811.00566.

[26] Rui Chao and Ben W. Reichardt, “Quantum error correction with only two extra qubits,” Phys. Rev. Lett. 121, 050502 (2018).

[27] Héctor Bombín, “Single-shot fault-tolerant quantum error correction,” Phys. Rev. X 5, 031043 (2015).

[28] Benjamin J. Brown, Naomi H. Nickerson, and Dan E. Browne, “Fault-tolerant error correction with the gauge color code,” Nature Communications 7, 12302 (2016).

[29] Earl T. Campbell, “A theory of single-shot error correction for adversarial noise,” Quantum Science and Technology 4, 025006 (2019), 1805.09271.

[30] I. Dumer, A. A. Kovalev, and L. P. Pryadko, “Thresholds for correcting errors, erasures, and faulty syndrome measurements in degenerate quantum codes,” Phys. Rev. Lett. 115, 050502 (2015), 1412.6172.

[31] A. A. Kovalev, S. Prabhakar, I. Dumer, and L. P. Pryadko, “Numerical and analytical bounds on threshold error rates for hypergraph-product codes,” Phys. Rev. A 97, 062320 (2018), 1804.01950.

[32] David Poulin, “Stabilizer formalism for operator quantum error correction,” Phys. Rev. Lett. 95, 230504 (2005).

[33] Dave Bacon, “Operator quantum error-correcting subsystems for self-correcting quantum memories,” Phys. Rev. A 73, 012340 (2006).

[34] Daniel Gottesman, Stabilizer Codes and Quantum Error Correction, Ph.D. thesis, Caltech (1997).

[35] A. R. Calderbank, E. M. Rains, P. M. Shor, and N. J. A. Sloane, “Quantum error correction via codes over GF(4),” IEEE Trans. Info. Theory 44, 1369–1387 (1998).

[36] Jeroen Dehaene and Bart De Moor, “Clifford group, stabilizer states, and linear and quadratic operations over GF(2),” Phys. Rev. A 68, 042318 (2003).

[37] Scott Aaronson and Daniel Gottesman, “Improved simulation of stabilizer circuits,” Phys. Rev. A 70, 052328 (2004).

[38] Bin Dai, Shilin Ding, and Grace Wahba, “Multivariate Bernoulli distribution,” Bernoulli 19, 1465–1483 (2013).

[39] F. Wegner, “Duality in generalized Ising models and phase transitions without local order parameters,” J. Math. Phys. 2259, 12 (1971).

[40] A. J. Landahl, J. T. Anderson, and P. R. Rice, “Fault-tolerant quantum computing with color codes,” (2011), presented at QIP 2012, December 12 to December 16, arXiv:1108.5738.

[41] A. A. Kovalev and L. P. Pryadko, “Spin glass reflection of the decoding transition for quantum error-correcting codes,” Quantum Inf. & Comp. 15, 0825 (2015), arXiv:1311.7688.

[42] Lars Onsager, “Crystal statistics. I. a two-dimensional model with an order-disorder transition,” Phys. Rev. 65, 117–149 (1944).

[43] Shigeo Naya, “On the spontaneous magnetizations of honeycomb and Kagomé Ising lattices,” Progress of Theoretical Physics 11, 53–62 (1954).

[44] Michael E. Fisher, “Transformations of Ising models,” Phys. Rev. 113, 969–981 (1959).

[45] Sergey Bravyi, Martin Suchara, and Alexander Vargo, “Efficient algorithms for maximum likelihood decoding in the surface code,” Phys. Rev. A 90, 032326 (2014).

[46] Markus Hauru, Clement Delcamp, and Sebastian Mizera, “Renormalization of tensor networks using graph-independent local truncations,” Phys. Rev. B 97, 045111 (2018).

[47] M. de Koning, Wei Cai, A. Antonelli, and S. Yip, “Efficient free-energy calculations by the simulation of nonequilibrium processes,” Computing in Science Engineering 2, 88–96 (2000).

[48] Charles H. Bennett, “Efficient estimation of free energy differences from Monte Carlo data,” Journal of Computational Physics 22, 245–268 (1976).

[49] Tobias Preis, Peter Virnau, Wolfgang Paul, and Johannes J. Schneider, “GPU accelerated monte carlo simulation of the 2d and 3d ising model,” Journal of Computational Physics 228, 4468 – 4477 (2009).

[50] A. Gilman, A. Leist, and K. A. Hawick, “3D lattice Monte Carlo simulations on FPGAs,” in Proceedings of the International Conference on Computer Design (CDES) (The Steering Committee of The World Congress in Computer Science, Computer Engineering and Applied Computing (WorldComp), 2013).

[51] Kun Yang, Yi-Fan Chen, Georgios Roumpos, Chris Colby, and John Anderson, “High performance Monte Carlo simulation of Ising model on TPU clusters,” (2019), unpublished, 1903.11714.

[52] D. Poulin and Y. Chung, “On the iterative decoding of sparse quantum codes,” Quant. Info. and Comp. 8, 987 (2008), arXiv:0801.1241.

[53] Ye-Hua Liu and David Poulin, “Neural belief-propagation decoders for quantum error-correcting codes,” Phys. Rev. Lett. 122, 200501 (2019), 1811.07835.

[54] Alex Rigby, J. C. Olivier, and Peter Jarvis, “Modified belief propagation decoders for quantum low-density parity-check codes,” Phys. Rev. A 100, 012330 (2019), 1903.07404.

[55] A. A. Kovalev, I. Dumer, and L. P. Pryadko, “Design of additive quantum codes via the code-word-stabilized framework,” Phys. Rev. A 84, 062319 (2011).

[56] Pavithran Iyer and David Poulin, “Hardness of decoding quantum stabilizer codes,” IEEE Transactions on Information Theory 61, 5209–5223 (2015), arXiv:1310.3235.

[57] E. A. Kruk, “Decoding complexity bound for linear block codes,” Probl. Peredachi Inf. 25, 103–107 (1989), (In Russian).

[58] J. T. Coffey and R. M. Goodman, “The complexity of information set decoding,” IEEE Trans. Info. Theory 36, 1031 –1037 (1990).

[59] Andrew J. Viterbi, “Error bounds for convolutional codes and an asymptotically optimum decoding algorithm,” IEEE Transactions on Information Theory 13, 260–269 (1967).

[60] R. G. Gallager, Low-Density Parity-Check Codes (M.I.T. Press, Cambridge, Mass., 1963).

[61] M. P. C. Fossorier, “Iterative reliability-based decoding of low-density parity check codes,” IEEE Journal on Selected Areas in Communications 19, 908–917 (2001).

[62] Thomas J. Richardson and Rüdiger L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” Information Theory, IEEE Transactions on 47, 599–618 (2001).

[63] David Declerq, Marc Fossorier, and Ezio Biglieri, eds., Channel Coding. Theory, Algorithms, and Applications (Academic Press Library in Mobile and Wireless Communications, San Francisco, 2014).

[64] Weilei Zeng and Leonid P. Pryadko, “Iterative decoding of row-reduced quantum LDPC codes,” (2020), unpublished.

[65] F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes (North-Holland, Amsterdam, 1981).

[66] Omar Fawzi, Antoine Grospellier, and Anthony Leverrier, “Efficient decoding of random errors for quantum expander codes,” (2017), unpublished, 1711.08351.

[67] Omar Fawzi, Antoine Grospellier, and Anthony Leverrier, “Constant overhead quantum fault-tolerance with quantum expander codes,” in 59th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2018, Paris, France, October 7-9, 2018 (2018) pp. 743–754.

[68] A. Grospellier and A. Krishna, “Numerical study of hypergraph product codes,” (2018), unpublished, 1810.03681.

[69] Pavel Panteleev and Gleb Kalachev, “Degenerate quantum LDPC codes with good finite length performance,” (2019), unpublished, 1904.02703.

[70] Antoine Grospellier, Lucien Grouès, Anirudh Krishna, and Anthony Leverrier, “Combining hard and soft decoders for hypergraph product codes,” (2020), unpublished, arXiv:2004.11199.

Cited by

[1] Nicolas Delfosse, Ben W. Reichardt, and Krysta M. Svore, “Beyond single-shot fault-tolerant quantum error correction”, arXiv:2002.05180.

The above citations are from SAO/NASA ADS (last updated successfully 2020-08-07 05:01:01). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2020-08-07 05:01:00).


Continue Reading


A robust W-state encoding for linear quantum optics




Madhav Krishnan Vijayan1, Austin P. Lund2, and Peter P. Rohde1

1Centre for Quantum Software & Information (UTS:QSI), University of Technology Sydney, Sydney NSW, Australia
2Centre for Quantum Computation & Communications Technology, School of Mathematics & Physics, The University of Queensland, St Lucia QLD, Australia

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


Error-detection and correction are necessary prerequisites for any scalable quantum computing architecture. Given the inevitability of unwanted physical noise in quantum systems and the propensity for errors to spread as computations proceed, computational outcomes can become substantially corrupted. This observation applies regardless of the choice of physical implementation. In the context of photonic quantum information processing, there has recently been much interest in $textit{passive}$ linear optics quantum computing, which includes boson-sampling, as this model eliminates the highly-challenging requirements for feed-forward via fast, active control. That is, these systems are $textit{passive}$ by definition. In usual scenarios, error detection and correction techniques are inherently $textit{active}$, making them incompatible with this model, arousing suspicion that physical error processes may be an insurmountable obstacle. Here we explore a photonic error-detection technique, based on W-state encoding of photonic qubits, which is entirely passive, based on post-selection, and compatible with these near-term photonic architectures of interest. We show that this W-state redundant encoding techniques enables the suppression of dephasing noise on photonic qubits via simple fan-out style operations, implemented by optical Fourier transform networks, which can be readily realised today. The protocol effectively maps dephasing noise into heralding failures, with zero failure probability in the ideal no-noise limit. We present our scheme in the context of a single photonic qubit passing through a noisy communication or quantum memory channel, which has not been generalised to the more general context of full quantum computation.

► BibTeX data

► References

[1] Scott Aaronson and Alex Arkhipov. The computational complexity of linear optics. In Proceedings of the Forty-third Annual ACM Symposium on Theory of Computing, STOC ’11, page 333, 2011. 10.1364/​qim.2014.qth1a.2.

[2] Scott Aaronson and Alex Arkhipov. Bosonsampling is far from uniform. Quantum Information and Computation, 14: 1383, 2014.

[3] Scott Aaronson and Daniel J. Brod. BosonSampling with lost photons. Physical Review A, 93, 2016. 10.1103/​physreva.93.012335.

[4] Alex Arkhipov. BosonSampling is robust against small errors in the network matrix. Physical Review A, 92, 2015. 10.1103/​physreva.92.062326.

[5] Michael J. Bremner, Richard Jozsa, and Dan J. Shepherd. Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 467: 459, 2011. 10.1098/​rspa.2010.0301.

[6] Daniel E. Browne, Jens Eisert, Stefan Scheel, and Martin B. Plenio. Driving non-gaussian to gaussian states with linear optics. Physical Review A, 67, 2003. 10.1103/​physreva.67.062320.

[7] L-M Duan, Mikhail D. Lukin, J. Ignacio Cirac, and Peter Zoller. Long-distance quantum communication with atomic ensembles and linear optics. Nature, 414: 413, 2001. 10.1038/​35106500.

[8] Wolfgang Dür, Guifre Vidal, and J. Ignacio Cirac. Three qubits can be entangled in two inequivalent ways. Physical Review A, 62: 062314, 2000. 10.1103/​physreva.62.062314.

[9] Jens Eisert, Stefan Scheel, and Martin B. Plenio. Distilling gaussian states with gaussian operations is impossible. Physical Review Letters, 89: 137903, 2002. 10.1103/​physrevlett.89.137903.

[10] Fabian Ewert and Peter van Loock. Ultrafast fault-tolerant long-distance quantum communication with static linear optics. Phys. Rev. A, 95: 012327, Jan 2017. 10.1103/​PhysRevA.95.012327.

[11] Nicolas Gisin, Noah Linden, Serge Massar, and S Popescu. Error filtration and entanglement purification for quantum communication. Physical Review A, 72: 012338, 2005. 10.1103/​physreva.72.012338.

[12] Aram W. Harrow and Ashley Montanaro. Quantum computational supremacy. Nature, 549: 203, 2017. 10.1038/​nature23458.

[13] YuXiao Jiang, PengLiang Guo, ChengYan Gao, HaiBo Wang, Faris Alzahrani, Aatef Hobiny, and FuGuo Deng. Self-error-rejecting photonic qubit transmission in polarization-spatial modes with linear optical elements. Science China Physics, Mechanics & Astronomy, 60: 120312, 2017. 10.1007/​s11433-017-9091-0.

[14] Gil Kalai and Guy Kindler. Gaussian Noise Sensitivity and BosonSampling, 2014. https:/​/​​abs/​1409.3093.

[15] Emanuel Knill, Raymond Laflamme, and Gerald Milburn. A scheme for efficient quantum computation with linear optics. Nature, 409: 46, 2001. 10.1038/​35051009.

[16] Anthony Leverrier and Raúl García-Patrón. Analysis of circuit imperfections in bosonsampling. Quantum Information and Computation, 15: 489, 2015. ISSN 1533.

[17] Xi-Han Li, Fu-Guo Deng, and Hong-Yu Zhou. Faithful qubit transmission against collective noise without ancillary qubits. Applied Physics Letters, 91: 144101, 2007. 10.1063/​1.2794433.

[18] Austin P. Lund, Michael J. Bremner, and Timothy C. Ralph. Quantum sampling problems, bosonsampling and quantum supremacy. NPJ Quantum Information, 3: 15, 2017. 10.1038/​s41534-017-0018-2.

[19] Ryan J. Marshman, Austin P. Lund, Peter P. Rohde, and Timothy Cameron Ralph. Passive quantum error correction of linear optics networks through error averaging. Physical Review A, 97: 22324, 2018. 10.1103/​PhysRevA.97.022324.

[20] Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, 2000. 10.1017/​cbo9780511976667.

[21] John Preskill. Fault-Tolerant Quantum Computation, chapter 8, page 213. World Scientific, 1998. 10.1142/​9789812385253_0008.

[22] Saleh Rahimi-Keshari, Timothy C. Ralph, and Carlton M. Caves. Sufficient conditions for efficient classical simulation of quantum optics. Physical Review X, 6: 21039, 2016. 10.1103/​PhysRevX.6.021039.

[23] Timothy C. Ralph and Austin P. Lund. Nondeterministic noiseless linear amplification of quantum systems. In AIP Conference Proceedings. AIP, 2009. 10.1063/​1.3131295.

[24] R. Raussendorf and H. J. Briegel. A one-way quantum computer. Physical Review Letters, 86: 5188, 2001. 10.1103/​physrevlett.86.5188.

[25] R. Raussendorf, D. E. Browne, and H. J. Briegel. Measurement-based quantum computation on cluster states. Physical Review A, 68: 022312, 2003. 10.1103/​physreva.68.022312.

[26] Peter P. Rohde and Timothy C. Ralph. Error models for mode-mismatch in linear optics quantum computing. Physical Review A, 73: 062312, 2006. 10.1103/​physreva.73.062312.

[27] Peter P. Rohde and Timothy C. Ralph. Error tolerance of the boson-sampling model for linear optics quantum computing. Physical Review A, 85: 022332, 2012. 10.1103/​physreva.85.022332.

[28] V. S. Shchesnovich. Sufficient condition for the mode mismatch of single photons for scalability of the boson-sampling computer. Physical Review A, 89, 2014. 10.1103/​PhysRevA.89.022333.

[29] Dan Shepherd and Michael J. Bremner. Temporally unstructured quantum computation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 465: 1413, 2009. 10.1098/​rspa.2008.0443.

[30] Peter W. Shor. Scheme for reducing decoherence in quantum computer memory. Physical Review A, 52: R2493, 1995. 10.1103/​physreva.52.r2493.

[31] Peter W. Shor. Fault-tolerant quantum computation. In 37th Symposium on Foundations of Computing, page 56. IEEE Computer Society Press, 1996. 10.1007/​978-1-4939-2864-4_143.

[32] Malte C. Tichy. Sampling of partially distinguishable bosons and the relation to the multidimensional permanent. Physical Review A, 91, 2015. 10.1103/​PhysRevA.91.022316.

[33] Nathan Walk, Austin P. Lund, and Timothy C. Ralph. Nondeterministic noiseless amplification via non-symplectic phase space transformations. New Journal of Physics, 15: 73014, 2013. 10.1088/​1367-2630/​15/​7/​073014.

[34] G. Y. Xiang, Timothy C. Ralph, Austin P. Lund, Nathan Walk, and Geoff J. Pryde. Heralded noiseless linear amplification and distillation of entanglement. Nature Photonics, 4: 316, 2010. 10.1038/​nphoton.2010.35.

[35] Anton Zeilinger, Michael A. Horne, and D. M. Greenberger. Publ. no. 3135. In NASA Conference, National Aeronautics and Space Administration, Code NTT, 1997.

Cited by


Continue Reading


Sum-of-squares decompositions for a family of noncontextuality inequalities and self-testing of quantum devices




Debashis Saha, Rafael Santos, and Remigiusz Augusiak

Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


Violation of a noncontextuality inequality or the phenomenon referred to `quantum contextuality’ is a fundamental feature of quantum theory. In this article, we derive a novel family of noncontextuality inequalities along with their sum-of-squares decompositions in the simplest (odd-cycle) sequential-measurement scenario capable to demonstrate Kochen-Specker contextuality. The sum-of-squares decompositions allow us to obtain the maximal quantum violation of these inequalities and a set of algebraic relations necessarily satisfied by any state and measurements achieving it. With their help, we prove that our inequalities can be used for self-testing of three-dimensional quantum state and measurements. Remarkably, the presented self-testing results rely on weaker assumptions than the ones considered in Kochen-Specker contextuality.

► BibTeX data

► References

[1] B. Amaral and M. T. Cunha. Contextuality: The Compatibility-Hypergraph Approach, pages 13–48. Springer Briefs in Mathematics. Springer, Cham, 2018. DOI: 10.1007/​978-3-319-93827-1_2.

[2] M. Araújo, M. T. Quintino, C. Budroni, M. T. Cunha, and A. Cabello. All noncontextuality inequalities for the $n$-cycle scenario. Phys. Rev. A, 88: 022118, 2013. DOI: 10.1103/​PhysRevA.88.022118.

[3] R. Augusiak, A. Salavrakos, J. Tura, and A. Acín. Bell inequalities tailored to the Greenberger-Horne-Zeilinger states of arbitrary local dimension. New J. Phys., 21(11): 113001, 2019. DOI: 10.1088/​1367-2630/​ab4d9f.

[4] J. S. Bell. On the Einstein Podolsky Rosen paradox. Physics Physique Fizika, 1: 195–200, 1964. DOI: 10.1103/​PhysicsPhysiqueFizika.1.195.

[5] C. Bamps and S. Pironio. Sum-of-squares decompositions for a family of Clauser-Horne-Shimony-Holt-like inequalities and their application to self-testing. Phys. Rev. A, 91: 052111, 2015. DOI: 10.1103/​PhysRevA.91.052111.

[6] K. Bharti, M. Ray, A. Varvitsiotis, A. Cabello, and L. Kwek. Local certification of programmable quantum devices of arbitrary high dimensionality. 2019. https:/​/​​abs/​1911.09448.

[7] K. Bharti, M. Ray, A. Varvitsiotis, N. Warsi, A. Cabello, and L. Kwek. Robust Self-Testing of Quantum Systems via Noncontextuality Inequalities. Phys. Rev. Lett., 122: 250403, 2019. DOI: 10.1103/​PhysRevLett.122.250403.

[8] P. Busch and J. Singh. Lüders theorem for unsharp quantum measurements. Physics Letters A, 249(1): 10–12, 1998. DOI: 10.1016/​S0375-9601(98)00704-X.

[9] P. Busch. Unsharp reality and joint measurements for spin observables. Phys. Rev. D, 33: 2253–2261, 1986. DOI: 10.1103/​PhysRevD.33.2253.

[10] A. Cabello. Experimentally Testable State-Independent Quantum Contextuality. Phys. Rev. Lett., 101: 210401, 2008. DOI: 10.1103/​PhysRevLett.101.210401.

[11] A. Cabello. Simple Explanation of the Quantum Violation of a Fundamental Inequality. Phys. Rev. Lett., 110: 060402, 2013. DOI: 10.1103/​PhysRevLett.110.060402.

[12] A. Coladangelo, K. Goh, and V. Scarani. All pure bipartite entangled states can be self-tested. Nature Communications, 8(1): 15485, 2017. DOI: 10.1038/​ncomms15485.

[13] D. Cui, A. Mehta, H. Mousavi, and S. Nezhadi. A generalization of CHSH and the algebraic structure of optimal strategies. 2019.

[14] A. Cabello, S. Severini, and A. Winter. Graph-Theoretic Approach to Quantum Correlations. Phys. Rev. Lett., 112: 040401, 2014. DOI: 10.1103/​PhysRevLett.112.040401.

[15] M. Farkas and J. Kaniewski. Self-testing mutually unbiased bases in the prepare-and-measure scenario. Phys. Rev. A, 99: 032316, 2019. DOI: 10.1103/​PhysRevA.99.032316.

[16] O. Gühne, C. Budroni, A. Cabello, M. Kleinmann, and J. Larsson. Bounding the quantum dimension with contextuality. Phys. Rev. A, 89: 062107, 2014. DOI: 10.1103/​PhysRevA.89.062107.

[17] A. Grudka, K. Horodecki, M. Horodecki, P. Horodecki, R. Horodecki, P. Joshi, W. Kłobus, and A. Wójcik. Quantifying Contextuality. Phys. Rev. Lett., 112: 120401, 2014. DOI: 10.1103/​PhysRevLett.112.120401.

[18] M. Howard, J. Wallman, V. Veitch, and J. Emerson. Contextuality supplies the “magic” for quantum computation. Nature, 510(7505): 351–355, 2014. DOI: 10.1038/​nature13460.

[19] A. Irfan, K. Mayer, G. Ortiz, and E. Knill. Certified quantum measurement of Majorana fermions. Phys. Rev. A, 101: 032106, 2020. DOI: 10.1103/​PhysRevA.101.032106.

[20] J. Kaniewski. A weak form of self-testing. 2019. https:/​/​​abs/​1910.00706.

[21] P. Kurzyński, A. Cabello, and D. Kaszlikowski. Fundamental Monogamy Relation between Contextuality and Nonlocality. Phys. Rev. Lett., 112: 100401, 2014. DOI: 10.1103/​PhysRevLett.112.100401.

[22] A. Klyachko, M. Can, S. Binicioğlu, and A. Shumovsky. Simple Test for Hidden Variables in Spin-1 Systems. Phys. Rev. Lett., 101: 020403, 2008. DOI: 10.1103/​PhysRevLett.101.020403.

[23] S. Kochen and E. Specker. The Problem of Hidden Variables in Quantum Mechanics. In The Logico-Algebraic Approach to Quantum Mechanics, The Western Ontario Series in Philosophy of Science, pages 293–328. Springer Netherlands, 1975. DOI: 10.1007/​978-94-010-1795-4.

[24] J. Kaniewski, I. Šupić, J. Tura, F. Baccari, A. Salavrakos, and R. Augusiak. Maximal nonlocality from maximal entanglement and mutually unbiased bases, and self-testing of two-qutrit quantum systems. Quantum, 3: 198, 2019. DOI: 10.22331/​q-2019-10-24-198.

[25] Y. Liang, R. Spekkens, and H. Wiseman. Specker$’$s parable of the overprotective seer: A road to contextuality, nonlocality and complementarity. Phys. Rep., 506(1): 1–39, 2011. DOI: 10.1016/​j.physrep.2011.05.001.

[26] D. Mayers and A. Yao. Self testing quantum apparatus. Quantum Inf. Comput., 4(4): 273–286, 2004. DOI:​10.26421/​QIC4.4.

[27] M. B. Plenio and P. L. Knight. The quantum-jump approach to dissipative dynamics in quantum optics. Rev. Mod. Phys., 70: 101–144, 1998. DOI: 10.1103/​RevModPhys.70.101.

[28] R. Raussendorf. Contextuality in measurement-based quantum computation. Phys. Rev. A, 88: 022322, 2013. DOI: 10.1103/​PhysRevA.88.022322.

[29] I. Šupić, R. Augusiak, A. Salavrakos, and A. Acín. Self-testing protocols based on the chained bell inequalities. New J. Phys., 18(3): 035013, 2016. DOI: 10.1088/​1367-2630/​18/​3/​035013.

[30] A. Salavrakos, R. Augusiak, J. Tura, P. Wittek, A. Acín, and S. Pironio. Bell Inequalities Tailored to Maximally Entangled States. Phys. Rev. Lett., 119: 040402, 2017. DOI: 10.1103/​PhysRevLett.119.040402.

[31] J. Singh, K. Bharti, and Arvind. Quantum key distribution protocol based on contextuality monogamy. Phys. Rev. A, 95: 062333, 2017. DOI: 10.1103/​PhysRevA.95.062333.

[32] D. Saha, P. Horodecki, and M. Pawłowski. State independent contextuality advances one-way communication. New J. Phys., 21(9): 093057, 2019. DOI: 10.1088/​1367-2630/​ab4149.

[33] D. Saha and R. Ramanathan. Activation of monogamy in nonlocality using local contextuality. Phys. Rev. A, 95: 030104, 2017. DOI: 10.1103/​PhysRevA.95.030104.

[34] S. Sarkar, D. Saha, J. Kaniewski, and R. Augusiak. Self-testing quantum systems of arbitrary local dimension with minimal number of measurements. 2019. https:/​/​​abs/​1909.12722v2.

[35] A. Tavakoli, J. Kaniewski, T. Vértesi, D. Rosset, and N. Brunner. Self-testing quantum states and measurements in the prepare-and-measure scenario. Phys. Rev. A, 98: 062307, 2018. DOI: 10.1103/​PhysRevA.98.062307.

[36] Z. Xu, D. Saha, H. Su, M. Pawłowski, and J. Chen. Reformulating noncontextuality inequalities in an operational approach. Phys. Rev. A, 94: 062103, 2016. DOI: 10.1103/​PhysRevA.94.062103.

[37] T. Yang, T. Vértesi, J. Bancal, V. Scarani, and M. Navascués. Robust and Versatile Black-Box Certification of Quantum Devices. Phys. Rev. Lett., 113: 040401, 2014. DOI: 10.1103/​PhysRevLett.113.040401.

Cited by


Continue Reading
AI3 hours ago

Impacts of Artificial Intelligence in Content Writing

Publications5 hours ago

Hong Kong media tycoon Jimmy Lai arrested under security law

Cannabis5 hours ago

How to make a cannabis-infused canna-grapefruit spritz

Cannabis5 hours ago

Could Joe Biden budge on cannabis legalization?

Cannabis5 hours ago

4 weed products Weldon Angelos can’t live without

Blockchain6 hours ago

A $15K Bitcoin Likely As Price Breaks Above “Multi-Year Bullish Triangle”

Blockchain6 hours ago

Ethereum Classic Under Multiple 51% Attacks | Bitcoin News Summary Aug 10, 2020

Publications6 hours ago

Chinese Tesla rival Xpeng Motors files for New York IPO

Publications7 hours ago

U.S. health chief offers Taiwan ‘strong’ support in landmark visit

Publications7 hours ago

Stock futures mixed after Trump signs orders extending coronavirus relief

Blockchain7 hours ago

Number of Bitcoin Cash Whales Drop Following 39% Price Surge

Blockchain7 hours ago

Bitcoin Price Tackles $12,000 After Breaking Through a Key Resistance Zone

Blockchain8 hours ago

Japanese Messaging Giant LINE’s LN Token Trading on BitMax

Blockchain9 hours ago

Bitcoin Erupts Past $12,000: Here’s What Analysts Think Comes Next

Publications10 hours ago

Some office space could get permanently cut during the pandemic. Here’s how companies will cope

Blockchain10 hours ago

Here’s Why Analysts Are Expecting For Ethereum To Drop Back Towards $370

Publications11 hours ago

Pelosi slams Trump’s executive actions on coronavirus relief: ‘Absurdly unconstitutional’

Automotive12 hours ago

Hyundai launches Ioniq as a standalone brand to exclusively make electric cars

Blockchain12 hours ago

How Miners Can Hedge Their Inventory to Increase Return on Investment

Blockchain13 hours ago

Analysts Expect Chainlink (LINK) Reversal After 50% Eruption to $14

Blockchain13 hours ago

BAND Token is Now Available for Trading on Huobi Global

Publications14 hours ago

Amazon reportedly discussing using former J.C. Penney and Sears stores as fulfillment centers

Blockchain14 hours ago

DeFi has more than just yield farming to thank for the recent surge

Automotive14 hours ago

Judge denies bail for men accused of sneaking Carlos Ghosn out of Japan

Blockchain15 hours ago

What Hope Do Bears Have If Bitcoin Holds $11,500? Analyst Asks

Blockchain16 hours ago

Cardano short/medium-term price analysis: August 09

Publications16 hours ago

U.S. tops 5 million coronavirus cases as outbreak threatens America’s Midwest

Automotive17 hours ago

School buses are another coronavirus question mark

Blockchain17 hours ago

Will Bitcoin be the go-to asset during the incoming stagflation?

Cannabis17 hours ago

5 Thing You Can Do To Make Your Weeks Run Smoother

Automotive18 hours ago

Max Verstappen wins 70th Anniversary Grand Prix at Silverstone

Blockchain18 hours ago

Economic Crisis Leaves US Government Officials in State of Confusion

Blockchain18 hours ago

Litecoin short-term price analysis: 09 August

Automotive18 hours ago

This ‘Hoverboard’ can transform into a rideable 4-wheeler

Blockchain19 hours ago

Bitcoin: What to expect during institutional ‘land grab’ phase?

Blockchain20 hours ago

LINK Trading Volume Surpasses Bitcoin on Coinbase

Publications20 hours ago

While some techies flee Silicon Valley, this Waymo engineer is doubling down and running for office

Blockchain20 hours ago

Bitcoin’s price surge has depleted long-term hodlings

Blockchain21 hours ago

The Top Dice Strategies That Actually Make You Money

Cannabis21 hours ago

Stanley Brothers Face Another Setback with Final Refusal of “CW” Trademark