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Catalytic transformations with finite-size environments: applications to cooling and thermometry

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Ivan Henao and Raam Uzdin

Fritz Haber Research Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel

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Abstract

The laws of thermodynamics are usually formulated under the assumption of infinitely large environments. While this idealization facilitates theoretical treatments, real physical systems are always finite and their interaction range is limited. These constraints have consequences for important tasks such as cooling, not directly captured by the second law of thermodynamics. Here, we study catalytic transformations that cannot be achieved when a system exclusively interacts with a finite environment. Our core result consists of constructive conditions for these transformations, which include the corresponding global unitary operation and the explicit states of all the systems involved. From this result we present various findings regarding the use of catalysts for cooling. First, we show that catalytic cooling is always possible if the dimension of the catalyst is sufficiently large. In particular, the cooling of a qubit using a hot qubit can be maximized with a catalyst as small as a three-level system. We also identify catalytic enhancements for tasks whose implementation is possible without a catalyst. For example, we find that in a multiqubit setup catalytic cooling based on a three-body interaction outperforms standard (non-catalytic) cooling using higher order interactions. Another advantage is illustrated in a thermometry scenario, where a qubit is employed to probe the temperature of the environment. In this case, we show that a catalyst allows to surpass the optimal temperature estimation attained only with the probe.

Catalysts are a key component of the modern chemical industry, with an impact in increased production rates, energy saving, and reduction of waste material. Concomitant with these advantages is the fact that catalysts remain ideally unaltered, thereby providing an extremely efficient method to assist diverse chemical reactions. This appealing feature has inspired the study of catalysts for applications in Quantum Information and Quantum Thermodynamics. Despite important progress, a crucial step towards a deeper understanding of the mechanisms that underpin catalysis is the derivation of explicit catalytic transformations, where information about the state of the catalyst and the corresponding evolution is available. In contrast, the current paradigm emphasizes the existence of a given transformation over the details of its implementation.

In this work we introduce a framework for the construction of explicit catalytic transformations. Focusing on cooling, we derive sufficient conditions for catalytic cooling when this is otherwise impossible. A key result in this respect is that a catalyst of sufficiently large dimension allows cooling regardless of the environment dimension, as long as the later does not start in a fully mixed state. In addition, we demonstrate cooling enhancements where a catalyst can increase cooling and at the same time reduce the complexity of the interactions with the environment.

Beyond the thermodynamic scenario, our results unveil catalytic transformations that no coupling between the system and the environment can achieve. We illustrate this finding in a thermometry setting. Here, we show that a catalyst can reduce the error in estimating the temperature of a thermal environment. On top of these applications, we hope that the technical aspects of our work also help to shed light on the fascinating phenomenon of catalysis.

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[1] D. Jonathan and M. B. Plenio, Entanglement-Assisted Local Manipulation of Pure Quantum States, Phys. Rev. Lett. 83, 3566 (1999). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.83.3566.
https:/​/​doi.org/​10.1103/​PhysRevLett.83.3566

[2] M. Klimesh, Inequalities that Collectively Completely Characterize the Catalytic Majorization Relation, arXiv:0709.3680v1 (2007).
arXiv:0709.3680

[3] S. Daftuar and M. Klimesh, Mathematical structure of entanglement catalysis, Phys. Rev. A 64, 042314 (2001). DOI: https:/​/​doi.org/​10.1103/​PhysRevA.64.042314.
https:/​/​doi.org/​10.1103/​PhysRevA.64.042314

[4] S. Turgut, Catalytic transformations for bipartite pure states, J. Phys. A: Math. Theor. 40 12185 (2007). DOI: https:/​/​doi.org/​10.1088/​1751-8113/​40/​40/​012.
https:/​/​doi.org/​10.1088/​1751-8113/​40/​40/​012

[5] Y. R. Sanders and G. Gour, Necessary conditions for entanglement catalysts, Phys. Rev. A 79, 054302 (2009). DOI: https:/​/​doi.org/​10.1103/​PhysRevA.79.054302.
https:/​/​doi.org/​10.1103/​PhysRevA.79.054302

[6] J. Aberg, Catalytic Coherence, Phys. Rev. Lett. 113, 150402 (2014). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.113.150402.
https:/​/​doi.org/​10.1103/​PhysRevLett.113.150402

[7] K. Bu, U. Singh, and J. Wu, Catalytic coherence transformations, Phys. Rev. A 93, 042326 (2016). DOI: https:/​/​doi.org/​10.1103/​PhysRevA.93.042326.
https:/​/​doi.org/​10.1103/​PhysRevA.93.042326

[8] A. Anshu, M.-H. Hsieh, and R. Jain, Quantifying Resources in General Resource Theory with Catalysts, Phys. Rev. Lett. 121, 190504 (2018). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.121.190504.
https:/​/​doi.org/​10.1103/​PhysRevLett.121.190504

[9] P. Boes, J. Eisert, R. Gallego, M. P. Müller, and H. Wilming, Von Neumann Entropy from Unitarity, Phys. Rev. Lett. 122, 210402 (2019). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.122.210402.
https:/​/​doi.org/​10.1103/​PhysRevLett.122.210402

[10] S. Rethinasamy and M. M. Wilde, Relative entropy and catalytic relative majorization, Phys. Rev. Research 2, 033455 (2020). DOI: https:/​/​doi.org/​10.1103/​PhysRevResearch.2.033455.
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.033455

[11] P. Boes, H. Wilming, R. Gallego, and J. Eisert, Catalytic Quantum Randomness, Phys. Rev. X 8, 041016 (2018). DOI: https:/​/​doi.org/​10.1103/​PhysRevX.8.041016.
https:/​/​doi.org/​10.1103/​PhysRevX.8.041016

[12] C. Majenz, M. Berta, F. Dupuis, R. Renner, and M. Christandl, Catalytic Decoupling of Quantum Information, Phys. Rev. Lett. 118, 080503 (2017). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.118.080503.
https:/​/​doi.org/​10.1103/​PhysRevLett.118.080503

[13] F. Ding, X. Hu, and H. Fan, Amplifying asymmetry with correlated catalysts, Phys. Rev. A 103, 022403 (2020). DOI: https:/​/​doi.org/​10.1103/​PhysRevA.103.022403.
https:/​/​doi.org/​10.1103/​PhysRevA.103.022403

[14] H. Wilming, Entropy and reversible catalysis, arXiv:2012.05573 (2020).
arXiv:2012.05573

[15] F. Brandao, M. Horodecki, N. Ng, J. Oppenheim, and S. Wehner, The second laws of quantum thermodynamics, PNAS 112, 3275 (2015). DOI: https:/​/​doi.org/​10.1073/​pnas.1411728112.
https:/​/​doi.org/​10.1073/​pnas.1411728112

[16] N. Ng, L. Mancinska, C. Cirstoiu, J. Eisert, and S. Wehner, Limits to catalysis in quantum thermodynamics, New J. Phys. 17, 085004 (2015). DOI: https:/​/​doi.org/​10.1088/​1367-2630/​17/​8/​085004.
https:/​/​doi.org/​10.1088/​1367-2630/​17/​8/​085004

[17] C. Sparaciari, D. Jennings, and J. Oppenheim, Energetic instability of passive states in thermodynamics, Nat. Commun. 8, 1895 (2017). DOI: https:/​/​doi.org/​10.1038/​s41467-017-01505-4.
https:/​/​doi.org/​10.1038/​s41467-017-01505-4

[18] H. Wilming and R. Gallego, Third Law of Thermodynamics as a Single Inequality, Phys. Rev. X 7, 041033 (2017). DOI: https:/​/​doi.org/​10.1103/​PhysRevX.7.041033.
https:/​/​doi.org/​10.1103/​PhysRevX.7.041033

[19] M. P. Muller, Correlating Thermal Machines and the Second Law at the Nanoscale, Phys. Rev. X 8, 041051 (2018). DOI: https:/​/​doi.org/​10.1103/​PhysRevX.8.041051.
https:/​/​doi.org/​10.1103/​PhysRevX.8.041051

[20] P. Lipka-Bartosik and P. Skrzypczyk, All states are universal catalysts in quantum thermodynamics, Phys. Rev. X 11, 011061 (2021). DOI: https:/​/​doi.org/​10.1103/​PhysRevX.11.011061.
https:/​/​doi.org/​10.1103/​PhysRevX.11.011061

[21] M. Lostaglio, M. P. Muller, and M. Pastena, Stochastic Independence as a Resource in Small-Scale Thermodynamics, Phys. Rev. Lett. 115, 150402 (2015). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.115.150402.
https:/​/​doi.org/​10.1103/​PhysRevLett.115.150402

[22] P. Boes, R. Gallego, N. H. Y. Ng, J. Eisert, and H. Wilming, By-passing fluctuation theorems, Quantum 4, 231 (2020). DOI: https:/​/​doi.org/​10.22331/​q-2020-02-20-231.
https:/​/​doi.org/​10.22331/​q-2020-02-20-231

[23] A. E. Allahverdyan and K. V. Hovhannisyan, Work extraction from microcanonical bath, EPL 95, 60004 (2011). DOI: https:/​/​doi.org/​10.1209/​0295-5075/​95/​60004.
https:/​/​doi.org/​10.1209/​0295-5075/​95/​60004

[24] N. Shiraishi and T. Sagawa, Quantum thermodynamics of correlated-catalytic state conversion at small-scale, Phys. Rev. Lett. 126, 150502 (2021). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.126.150502.
https:/​/​doi.org/​10.1103/​PhysRevLett.126.150502

[25] M. P. Muller and M. Pastena, A Generalization of Majorization that Characterizes Shannon Entropy, IEEE Transactions on Information Theory 62, 1711 (2016). DOI: https:/​/​doi.org/​10.1109/​TIT.2016.2528285.
https:/​/​doi.org/​10.1109/​TIT.2016.2528285

[26] M. Horodecki and J. Oppenheim, Fundamental limitations for quantum and nanoscale thermodynamics, Nat. Commun. 4, 2059 (2013). DOI: https:/​/​doi.org/​10.1038/​ncomms3059.
https:/​/​doi.org/​10.1038/​ncomms3059

[27] F. Brandao, M. Horodecki, J. Oppenheim, J. M. Renes, and R. W. Spekkens, Resource Theory of Quantum States Out of Thermal Equilibrium, Phys. Rev. Lett. 111, 250404 (2013). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.111.250404.
https:/​/​doi.org/​10.1103/​PhysRevLett.111.250404

[28] M. Lostaglio, D. Jennings, and T. Rudolph, Description of quantum coherence in thermodynamic processes requires constraints beyond free energy, Nat. Commun. 6, 6383 (2015). DOI: https:/​/​doi.org/​10.1038/​ncomms7383.
https:/​/​doi.org/​10.1038/​ncomms7383

[29] K. Korzekwa, M. Lostaglio, J. Oppenheim, and D. Jennings, The extraction of work from quantum coherence, New J. Phys. 18, 023045 (2016). DOI: https:/​/​doi.org/​10.1088/​1367-2630/​18/​2/​023045.
https:/​/​doi.org/​10.1088/​1367-2630/​18/​2/​023045

[30] M. Lostaglio, A. M. Alhambra, and C. Perry, Elementary Thermal Operations, Quantum 2, 52 (2018). DOI: https:/​/​doi.org/​10.22331/​q-2018-02-08-52.
https:/​/​doi.org/​10.22331/​q-2018-02-08-52

[31] M. Lostaglio, An introductory review of the resource theory approach to thermodynamics, Rep. Prog. Phys. 82, 114001 (2019). DOI: https:/​/​doi.org/​10.1088/​1361-6633/​ab46e5.
https:/​/​doi.org/​10.1088/​1361-6633/​ab46e5

[32] J. Goold, M. Huber, A. Riera, L. del Rio, and P. Skrzypczyk, The role of quantum information in thermodynamics— a topical review, J. Phys. A: Math. Theor. 49, 143001 (2016). DOI: https:/​/​doi.org/​10.1088/​1751-8113/​49/​14/​143001.
https:/​/​doi.org/​10.1088/​1751-8113/​49/​14/​143001

[33] S. Vinjanampathy and J. Anders, Quantum thermodynamics, Contemporary Physics 57, 545 (2016). DOI: https:/​/​doi.org/​10.1080/​00107514.2016.1201896.
https:/​/​doi.org/​10.1080/​00107514.2016.1201896

[34] A. M. Alhambra, M. Lostaglio, and C. Perry, Heat-Bath Algorithmic Cooling with optimal thermalization strategies, Quantum 3, 188 (2019). DOI: https:/​/​doi.org/​10.22331/​q-2019-09-23-188.
https:/​/​doi.org/​10.22331/​q-2019-09-23-188

[35] J. Scharlau and M. P. Muller, Quantum Horn’s lemma, finite heat baths, and the third law of thermodynamics, Quantum 2, 54 (2018). DOI: https:/​/​doi.org/​10.22331/​q-2018-02-22-54.
https:/​/​doi.org/​10.22331/​q-2018-02-22-54

[36] Freitas N., Gallego R., Masanes L., Paz J.P. (2018) Cooling to Absolute Zero: The Unattainability Principle. In: Binder F., Correa L., Gogolin C., Anders J., Adesso G. (eds) Thermodynamics in the Quantum Regime. Fundamental Theories of Physics, vol 195. Springer, Cham. DOI: http:/​/​doi.org/​10.1007/​978-3-319-99046-0-25.
https:/​/​doi.org/​10.1007/​978-3-319-99046-0-25

[37] M. Kolar, D. Gelbwaser-Klimovsky, R. Alicki, and G. Kurizki, Quantum Bath Refrigeration towards Absolute Zero: Challenging the Unattainability Principle, Phys. Rev. Lett. 109, 090601 (2012). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.109.090601.
https:/​/​doi.org/​10.1103/​PhysRevLett.109.090601

[38] L. Masanes and J. Oppenheim, A general derivation and quantification of the third law of thermodynamics, Nat. Commun. 8, 14538 (2017). DOI: https:/​/​doi.org/​10.1038/​ncomms14538.
https:/​/​doi.org/​10.1038/​ncomms14538

[39] A. Levy, R. Alicki, and R. Kosloff, Quantum refrigerators and the third law of thermodynamics, Phys. Rev. E 85, 061126 (2012). DOI: https:/​/​doi.org/​10.1103/​PhysRevE.85.061126.
https:/​/​doi.org/​10.1103/​PhysRevE.85.061126

[40] N. A. Rodríguez-Briones, and R. Laflamme, Achievable Polarization for Heat-Bath Algorithmic Cooling, Phys. Rev. Lett. 116, 170501 (2016). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.116.170501.
https:/​/​doi.org/​10.1103/​PhysRevLett.116.170501

[41] L. J. Schulman, T. Mor, and Y. Weinstein, Physical Limits of Heat-Bath Algorithmic Cooling, Phys. Rev. Lett. 94, 120501 (2005). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.94.120501.
https:/​/​doi.org/​10.1103/​PhysRevLett.94.120501

[42] N. Freitas and J. P. Paz, Fundamental limits for cooling of linear quantum refrigerators, Phys. Rev. E 95 012146 (2017). DOI: https:/​/​doi.org/​10.1103/​PhysRevE.95.012146.
https:/​/​doi.org/​10.1103/​PhysRevE.95.012146

[43] F. Clivaz, R. Silva, G. Haack, J. Bohr Brask, N. Brunner, and M. Huber, Unifying Paradigms of Quantum Refrigeration: A Universal and Attainable Bound on Cooling, Phys. Rev. Lett. 123, 170605 (2019). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.123.170605.
https:/​/​doi.org/​10.1103/​PhysRevLett.123.170605

[44] S. Raeisi, and M. Mosca, Asymptotic Bound for Heat-Bath Algorithmic Cooling, Phys. Rev. Lett. 114, 100404 (2015). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.114.100404.
https:/​/​doi.org/​10.1103/​PhysRevLett.114.100404

[45] N. A. Rodríguez-Briones, J. Li, X. Peng, T. Mor, Y. Weinstein, and R. Laflamme, Heat-bath algorithmic cooling with correlated qubit-environment interactions, New J. Phys. 19, 113047 (2017). DOI: https:/​/​doi.org/​10.1088/​1367-2630/​aa8fe0.
https:/​/​doi.org/​10.1088/​1367-2630/​aa8fe0

[46] F. Clivaz, R. Silva, G. Haack, J. Bohr Brask, N. Brunner, and M. Huber, Unifying paradigms of quantum refrigeration: Fundamental limits of cooling and associated work costs, Phys. Rev. E 100, 042130 (2019). DOI: https:/​/​doi.org/​10.1103/​PhysRevE.100.042130.
https:/​/​doi.org/​10.1103/​PhysRevE.100.042130

[47] A. Serafini, M. Lostaglio, S. Longden, U. Shackerley-Bennett, C.-Y. Hsieh, and G. Adesso, Gaussian Thermal Operations and The Limits of Algorithmic Cooling, Phys. Rev. Lett. 124, 010602 (2020). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.124.010602.
https:/​/​doi.org/​10.1103/​PhysRevLett.124.010602

[48] P. Taranto, F. Bakhshinezhad, P. Schuttelkopf, F. Clivaz, and M. Huber, Exponential improvement for quantum cooling through finite memory effects, Phys. Rev. Applied 14, 054005 (2020). DOI: https:/​/​doi.org/​10.1103/​PhysRevApplied.14.054005.
https:/​/​doi.org/​10.1103/​PhysRevApplied.14.054005

[49] R. Silva, G. Manzano, P. Skrzypczyk, and N. Brunner, Performance of autonomous quantum thermal machines: Hilbert space dimension as a thermodynamical resource, Phys. Rev. E 94, 032120 (2020). DOI: https:/​/​doi.org/​10.1103/​PhysRevE.94.032120.
https:/​/​doi.org/​10.1103/​PhysRevE.94.032120

[50] N. Linden, S. Popescu, and P. Skrzypczyk, How Small Can Thermal Machines Be? The Smallest Possible Refrigerator, Phys. Rev. Lett. 105, 130401 (2010). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.105.130401.
https:/​/​doi.org/​10.1103/​PhysRevLett.105.130401

[51] M. T. Mitchison, M. P. Woods, J. Prior, and Marcus Huber, Coherence-assisted single-shot cooling by quantum absorption refrigerators, New J. Phys. 17, 115013 (2015). DOI: https:/​/​doi.org/​10.1088/​1367-2630/​17/​11/​115013.
https:/​/​doi.org/​10.1088/​1367-2630/​17/​11/​115013

[52] N. Brunner, M. Huber, N. Linden, S. Popescu, R. Silva, and P. Skrzypczyk, Entanglement enhances cooling in microscopic quantum refrigerators, Phys. Rev. E 89, 032115 (2014). DOI: https:/​/​doi.org/​10.1103/​PhysRevE.89.032115.
https:/​/​doi.org/​10.1103/​PhysRevE.89.032115

[53] A. E. Allahverdyan, K. V. Hovhannisyan, D. Janzing, and G. Mahler, Thermodynamic limits of dynamic cooling, Phys. Rev. E 84, 041109 (2011). DOI: https:/​/​doi.org/​10.1103/​PhysRevE.84.041109.
https:/​/​doi.org/​10.1103/​PhysRevE.84.041109

[54] Lian-Ao Wu, Dvira Segal, and Paul Brumer, No-go theorem for ground state cooling given initial system-thermal bath factorization, Scientific Reports 3, 1824 (2013). DOI: https:/​/​doi.org/​10.1038/​srep01824.
https:/​/​doi.org/​10.1038/​srep01824

[55] F. Ticozzi and L. Viola, Quantum resources for purification and cooling: fundamental limits and opportunities, Scientific Reports 4, 5192 (2014). DOI: https:/​/​doi.org/​10.1038/​srep05192.
https:/​/​doi.org/​10.1038/​srep05192

[56] D. Reeb and M. M. Wolf, An improved Landauer principle with finite-size corrections, New J. Phys. 16, 103011 (2014). https:/​/​doi.org/​10.1088/​1367-2630/​16/​10/​103011.
https:/​/​doi.org/​10.1088/​1367-2630/​16/​10/​103011

[57] R. Uzdin and S. Rahav, The Passivity Deformation Approach for the Thermodynamics of Isolated Quantum Setups, PRX Quantum 2, 010336 (2020). DOI: https:/​/​doi.org/​10.1103/​PRXQuantum.2.010336.
https:/​/​doi.org/​10.1103/​PRXQuantum.2.010336

[58] W. Pusz and S. L. Woronowicz, Passive states and KMS states for general quantum systems, Commun. Math. Phys. 58, 273 (1978). DOI: https:/​/​doi.org/​10.1007/​BF01614224.
https:/​/​doi.org/​10.1007/​BF01614224

[59] A. E. Allahverdyan, R. Balian, and Th. M. Nieuwenhuizen, Maximal work extraction from finite quantum systems, Europhys. Lett. 67, 565 (2004). DOI: https:/​/​doi.org/​10.1209/​epl/​i2004-10101-2.
https:/​/​doi.org/​10.1209/​epl/​i2004-10101-2

[60] P. Skrzypczyk, R. Silva, and N. Brunner, Passivity, complete passivity, and virtual temperatures, Phys. Rev. E 91, 052133 (2015). DOI: https:/​/​doi.org/​10.1103/​PhysRevE.91.052133.
https:/​/​doi.org/​10.1103/​PhysRevE.91.052133

[61] R. Uzdin and S. Rahav, Global Passivity in Microscopic Thermodynamics, Phys. Rev. X 8, 021064 (2018). DOI: https:/​/​doi.org/​10.1103/​PhysRevX.8.021064.
https:/​/​doi.org/​10.1103/​PhysRevX.8.021064

[62] M. Mehboudi, A. Sanpera, and L. A. Correa, Thermometry in the quantum regime: recent theoretical progress, J. Phys. A: Math. Theor. 52, 30 (2019). DOI: https:/​/​doi.org/​10.1088/​1751-8121/​ab2828.
https:/​/​doi.org/​10.1088/​1751-8121/​ab2828

[63] V. Giovannetti, S. Lloyd, and L. Maccone, Quantum Metrology, Phys. Rev. Lett. 96, 010401 (2006). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.96.010401.
https:/​/​doi.org/​10.1103/​PhysRevLett.96.010401

[64] V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nat. Phot. 5, 222 (2011). DOI: https:/​/​doi.org/​10.1038/​nphoton.2011.35.
https:/​/​doi.org/​10.1038/​nphoton.2011.35

[65] M. G. A. Paris, Quantum Estimation For Quantum Technology, Int. J. Quantum. Inform. 7, 125 (2009). DOI: https:/​/​doi.org/​10.1142/​S0219749909004839.
https:/​/​doi.org/​10.1142/​S0219749909004839

[66] C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017). DOI: https:/​/​doi.org/​10.1103/​RevModPhys.89.035002.
https:/​/​doi.org/​10.1103/​RevModPhys.89.035002

[67] M. Brunelli, S. Olivares, and M. G. A. Paris, Qubit thermometry for micromechanical resonators, Phys. Rev. A 84, 032105 (2011). DOI: https:/​/​doi.org/​10.1103/​PhysRevA.84.032105.
https:/​/​doi.org/​10.1103/​PhysRevA.84.032105

[68] M. Brunelli, S. Olivares, M. Paternostro, and M. G. A. Paris, Qubit-assisted thermometry of a quantum harmonic oscillator, Phys. Rev. A 86, 012125 (2012). DOI: https:/​/​doi.org/​10.1103/​PhysRevA.86.012125.
https:/​/​doi.org/​10.1103/​PhysRevA.86.012125

[69] S. Jevtic, D. Newman, T. Rudolph, and T. M. Stace, Single-qubit thermometry, Phys. Rev. A 91, 012331 (2015). DOI: https:/​/​doi.org/​10.1103/​PhysRevA.91.012331.
https:/​/​doi.org/​10.1103/​PhysRevA.91.012331

[70] A. De Pasquale, K. Yuasa, and V. Giovannetti, Estimating temperature via sequential measurements, Phys. Rev. A 96, 012316 (2017). DOI: https:/​/​doi.org/​10.1103/​PhysRevA.96.012316.
https:/​/​doi.org/​10.1103/​PhysRevA.96.012316

[71] V. Cavina, L. Mancino, A. De Pasquale, I. Gianani, M. Sbroscia, R. I. Booth, E. Roccia, R. Raimondi, V. Giovannetti, and M. Barbieri, Bridging thermodynamics and metrology in nonequilibrium quantum thermometry, Phys. Rev. A 98, 050101(R) (2018). DOI: https:/​/​doi.org/​10.1103/​PhysRevA.98.050101.
https:/​/​doi.org/​10.1103/​PhysRevA.98.050101

[72] L. A. Correa, M. Mehboudi, G. Adesso, and A. Sanpera, Individual Quantum Probes for Optimal Thermometry, Phys. Rev. Lett. 114, 220405 (2015). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.114.220405.
https:/​/​doi.org/​10.1103/​PhysRevLett.114.220405

[73] M. T. Mitchison, T. Fogarty, G. Guarnieri, S. Campbell, T. Busch, and J. Goold, In Situ Thermometry of a Cold Fermi Gas via Dephasing Impurities, Phys. Rev. Lett. 125, 080402 (2020). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.125.080402.
https:/​/​doi.org/​10.1103/​PhysRevLett.125.080402

[74] L. A. Correa, M. Perarnau-Llobet, K. V. Hovhannisyan, S. Hernandez-Santana, M. Mehboudi, and A. Sanpera, Enhancement of low-temperature thermometry by strong coupling, Phys. Rev. A 96, 062103 (2017). DOI: https:/​/​doi.org/​10.1103/​PhysRevA.96.062103.
https:/​/​doi.org/​10.1103/​PhysRevA.96.062103

[75] A. H. Kiilerich, A. De Pasquale, and V. Giovannetti, Dynamical approach to ancilla-assisted quantum thermometry, Phys. Rev. A 98, 042124 (2018). DOI: https:/​/​doi.org/​10.1103/​PhysRevA.98.042124.
https:/​/​doi.org/​10.1103/​PhysRevA.98.042124

[76] S. Seah, S. Nimmrichter, D. Grimmer, J. P. Santos, V. Scarani, and G. T. Landi, Collisional Quantum Thermometry, Phys. Rev. Lett. 123, 180602 (2019). DOI: https:/​/​doi.org/​10.1103/​PhysRevLett.123.180602.
https:/​/​doi.org/​10.1103/​PhysRevLett.123.180602

[77] K. V. Hovhannisyan, M. R. Jorgensen, G. T. Landi, A. M. Alhambra, J. B. Brask, and Marti Perarnau-Llobet, Optimal Quantum Thermometry with Coarse-grained Measurements, PRX Quantum 2, 020322 (2021). DOI: https:/​/​doi.org/​10.1103/​PRXQuantum.2.020322.
https:/​/​doi.org/​10.1103/​PRXQuantum.2.020322

[78] R. Alicki and M. Fannes, Entanglement boost for extractable work from ensembles of quantum batteries, Phys. Rev. E 87, 042123 (2013). DOI: https:/​/​doi.org/​10.1103/​PhysRevE.87.042123.
https:/​/​doi.org/​10.1103/​PhysRevE.87.042123

[79] M. Perarnau-Llobet, K. V. Hovhannisyan, M. Huber, P. Skrzypczyk, N. Brunner, and A. Acin, Extractable Work from Correlations, Phys. Rev. X 5, 041011 (2015). DOI: https:/​/​doi.org/​10.1103/​PhysRevX.5.041011.
https:/​/​doi.org/​10.1103/​PhysRevX.5.041011

[80] M. Perarnau-Llobet, K. V. Hovhannisyan, M. Huber, P. Skrzypczyk, J. Tura, and A. Acin, Most energetic passive states, Phys. Rev. E 92, 042147 (2015). DOI: https:/​/​doi.org/​10.1103/​PhysRevE.92.042147.
https:/​/​doi.org/​10.1103/​PhysRevE.92.042147

[81] E. G. Brown, N. Friis, and M. Huber, Passivity and practical work extraction using Gaussian operations, New J. Phys. 18, 113028 (2016). DOI: https:/​/​doi.org/​10.1088/​1367-2630/​18/​11/​113028.
https:/​/​doi.org/​10.1088/​1367-2630/​18/​11/​113028

[82] For a graphical characterization of this condition see the diagrams developed in Ref. p40.1Raam-PD.

[83] K. M. R. Audenaert, and S. Scheel, On random unitary channels, New J. Phys. 10, 023011 (2008). DOI: https:/​/​doi.org/​10.1088/​1367-2630/​10/​2/​023011.
https:/​/​doi.org/​10.1088/​1367-2630/​10/​2/​023011

[84] M. A. Nielsen, An introduction to majorization and its applications to quantum mechanics, Lecture Notes, Department of Physics, Univesity of Queensland, Queensland 4072, Australia (2002).

[85] J. Watrous, The Theory of Quantum Information (Cambridge University Press, 2018). DOI: https:/​/​doi.org/​10.1017/​9781316848142.
https:/​/​doi.org/​10.1017/​9781316848142

[86] J. Kolodyński, Precision bounds in noisy quantum metrology, Ph.D. thesis, University of Warsaw (2015), arXiv:1409.0535v2.
arXiv:1409.0535

[87] We note that although $mathrm{max}_{U_{Pe}}|partial_{beta}q_{1}^{P}|=mathrm{max}left{ bigl|mathrm{min}_{U_{Pe}}partial_{beta}q_{1}^{P}bigr|,mathrm{max}_{U_{Pe}}partial_{beta}q_{1}^{P}right}$ we can restrict ourselves to the maximization of $partial_{beta}q_{1}^{P}$. First, probability conservation $partial_{beta}q_{1}^{P}=-partial_{beta}q_{2}^{P}$ implies that $bigl|mathrm{min}_{U_{Pe}}partial_{beta}q_{1}^{P}bigr|=mathrm{max}_{U_{Pe}}partial_{beta}q_{2}^{P}$. Since the maximum $mathrm{max}_{U_{Pe}}partial_{beta}q_{2}^{P}$ is taken over all the unitaries $U_{Pe}$, it is equivalent to first apply the local permutation $|1_{P}rangleleftrightarrow|2_{P}rangle$ and then maximize over $U_{Pe}$. However, this permutation is also equivalent to the label exchange $q_{1}^{P}leftrightarrow q_{2}^{P}$, which yields $mathrm{max}_{U_{Pe}}partial_{beta}q_{2}^{P}=mathrm{max}_{U_{Pe}}partial_{beta}q_{1}^{P}$. Accordingly, $mathrm{max}_{U_{Pe}}|partial_{beta}q_{1}^{P}|=mathrm{max}_{U_{Pe}}partial_{beta}q_{1}^{P}$.

[88] A. W. Marshall, I. Olkin, and B. C. Arnold, Inequalities: theory of majorization and its applications (Springer, 1979). DOI: https:/​/​doi.org/​10.1007/​978-0-387-68276-1.
https:/​/​doi.org/​10.1007/​978-0-387-68276-1

[89] A. Horn, Doubly stochastic matrices and the diagonal of a rotation matrix, Am. J. Math.76, 620 (1954). DOI: https:/​/​doi.org/​10.2307/​2372705.
https:/​/​doi.org/​10.2307/​2372705

Cited by

[1] Karen V. Hovhannisyan, Mathias R. Jørgensen, Gabriel T. Landi, Álvaro M. Alhambra, Jonatan B. Brask, and Martí Perarnau-Llobet, “Optimal Quantum Thermometry with Coarse-Grained Measurements”, PRX Quantum 2 2, 020322 (2021).

[2] Patryk Lipka-Bartosik and Paul Skrzypczyk, “Catalytic Quantum Teleportation”, Physical Review Letters 127 8, 080502 (2021).

[3] Pavel Sekatski and Martí Perarnau-Llobet, “Optimal nonequilibrium thermometry in finite time”, arXiv:2107.04425.

[4] Julia Boeyens, Stella Seah, and Stefan Nimmrichter, “Non-informative Bayesian Quantum Thermometry”, arXiv:2108.07025.

[5] Ivan Henao, Karen V. Hovhannisyan, and Raam Uzdin, “Thermometric machine for ultraprecise thermometry of low temperatures”, arXiv:2108.10469.

The above citations are from SAO/NASA ADS (last updated successfully 2021-09-21 16:26:55). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2021-09-21 16:26:52: Could not fetch cited-by data for 10.22331/q-2021-09-21-547 from Crossref. This is normal if the DOI was registered recently.

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Source: https://quantum-journal.org/papers/q-2021-09-21-547/

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