1School of Computational Sciences, Korea Institute for Advanced Study, Seoul 02455, Korea
2LIP6, CNRS, Université Pierre et Marie Curie, Sorbonne Universités, 75005 Paris, France
3JFLI, CNRS, National Institute of Informatics, University of Tokyo, Tokyo, Japan
4Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria
5Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
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Abstract
This work analyzes correlations arising from quantum systems subject to sequential projective measurements to certify that the system in question has a quantum dimension greater than some $d$. We refine previous known methods and show that dimension greater than two can be certified in scenarios which are considerably simpler than the ones presented before and, for the first time in this sequential projective scenario, we certify quantum systems with dimension strictly greater than three. We also perform a systematic numerical analysis in terms of robustness and conclude that performing random projective measurements on random pure qutrit states allows a robust certification of quantum dimensions with very high probability.
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► References
[1] J. Eisert, D. Hangleiter, N. Walk, I. Roth, D. Markham, R. Parekh, U. Chabaud, and E. Kashefi, Nature Reviews Physics 2, 382 (2020).
https://doi.org/10.1038/s42254-020-0186-4
[2] M. Kliesch and I. Roth, Theory of quantum system certification – a tutorial (2020), arXiv:2010.05925 [quant-ph].
https://doi.org/10.1103/PRXQuantum.2.010201
arXiv:2010.05925
[3] I. Šupić and J. Bowles, Quantum 4, 337 (2020).
https://doi.org/10.22331/q-2020-09-30-337
[4] K. Bharti, M. Ray, A. Varvitsiotis, N. A. Warsi, A. Cabello, and L.-C. Kwek, Phys. Rev. Lett. 122, 250403 (2019).
https://doi.org/10.1103/PhysRevLett.122.250403
[5] A. Tavakoli, J. m. k. Kaniewski, T. Vértesi, D. Rosset, and N. Brunner, Phys. Rev. A 98, 062307 (2018).
https://doi.org/10.1103/PhysRevA.98.062307
[6] A. Sohbi and J. Kim, Phys. Rev. A 100, 022117 (2019).
https://doi.org/10.1103/PhysRevA.100.022117
[7] D. Saha, R. Santos, and R. Augusiak, Quantum 4, 302 (2020).
https://doi.org/10.22331/q-2020-08-03-302
[8] D. G. Marangon, G. Vallone, and P. Villoresi, Phys. Rev. Lett. 118, 060503 (2017).
https://doi.org/10.1103/PhysRevLett.118.060503
[9] A. Acín and L. Masanes, Nature 540, 213 (2016).
https://doi.org/10.1038/nature20119
[10] T. Lunghi, J. B. Brask, C. C. W. Lim, Q. Lavigne, J. Bowles, A. Martin, H. Zbinden, and N. Brunner, Phys. Rev. Lett. 114, 150501 (2015).
https://doi.org/10.1103/PhysRevLett.114.150501
[11] N. Brunner, S. Pironio, A. Acin, N. Gisin, A. A. Méthot, and V. Scarani, Physical Review Letters 100, 10.1103/physrevlett.100.210503 (2008).
https://doi.org/10.1103/physrevlett.100.210503
[12] R. Gallego, N. Brunner, C. Hadley, and A. Acín, Phys. Rev. Lett. 105, 230501 (2010).
https://doi.org/10.1103/PhysRevLett.105.230501
[13] N. Brunner, M. Navascués, and T. Vértesi, Phys. Rev. Lett. 110, 150501 (2013).
https://doi.org/10.1103/PhysRevLett.110.150501
[14] O. Gühne, C. Budroni, A. Cabello, M. Kleinmann, and J.-A. Larsson, Phys. Rev. A 89, 062107 (2014).
https://doi.org/10.1103/PhysRevA.89.062107
[15] A. Sohbi, I. Zaquine, E. Diamanti, and D. Markham, Phys. Rev. A 94, 032114 (2016).
https://doi.org/10.1103/PhysRevA.94.032114
[16] Y. Cai, J.-D. Bancal, J. Romero, and V. Scarani, Journal of Physics A: Mathematical and Theoretical 49, 305301 (2016).
https://doi.org/10.1088/1751-8113/49/30/305301
[17] H.-W. Li, Y.-S. Zhang, X.-B. An, Z.-F. Han, and G.-C. Guo, Communications Physics 1, 10 (2018).
https://doi.org/10.1038/s42005-018-0011-x
[18] D. Saha, P. Horodecki, and M. Pawłowski, New Journal of Physics 21, 093057 (2019).
https://doi.org/10.1088/1367-2630/ab4149
[19] E. T. Campbell, H. Anwar, and D. E. Browne, Phys. Rev. X 2, 041021 (2012).
https://doi.org/10.1103/PhysRevX.2.041021
[20] E. T. Campbell, Phys. Rev. Lett. 113, 230501 (2014).
https://doi.org/10.1103/PhysRevLett.113.230501
[21] A. Krishna and J.-P. Tillich, Phys. Rev. Lett. 123, 070507 (2019).
https://doi.org/10.1103/PhysRevLett.123.070507
[22] B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, Nature Physics 5, 134 (2009).
https://doi.org/10.1038/nphys1150
[23] H. S. Tonchev and N. V. Vitanov, Phys. Rev. A 94, 042307 (2016).
https://doi.org/10.1103/PhysRevA.94.042307
[24] A. Bocharov, M. Roetteler, and K. M. Svore, Phys. Rev. A 96, 012306 (2017).
https://doi.org/10.1103/PhysRevA.96.012306
[25] G. Duclos-Cianci and D. Poulin, Phys. Rev. A 87, 062338 (2013).
https://doi.org/10.1103/PhysRevA.87.062338
[26] M. H. Michael, M. Silveri, R. T. Brierley, V. V. Albert, J. Salmilehto, L. Jiang, and S. M. Girvin, Phys. Rev. X 6, 031006 (2016).
https://doi.org/10.1103/PhysRevX.6.031006
[27] M. Grassl, L. Kong, Z. Wei, Z. Yin, and B. Zeng, IEEE Transactions on Information Theory 64, 4674 (2018).
https://doi.org/10.1109/TIT.2018.2790423
[28] M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. D. O’Connell, D. Sank, H. Wang, J. Wenner, A. N. Cleland, M. R. Geller, and J. M. Martinis, Science 325, 722 (2009).
https://doi.org/10.1126/science.1173440
[29] M. Y. Niu, I. L. Chuang, and J. H. Shapiro, Phys. Rev. Lett. 120, 160502 (2018).
https://doi.org/10.1103/PhysRevLett.120.160502
[30] D. Cozzolino, B. Da Lio, D. Bacco, and L. K. Oxenløwe, Advanced Quantum Technologies 2, 1900038 (2019).
https://doi.org/10.1002/qute.201900038
[31] Y.-H. Luo, H.-S. Zhong, M. Erhard, X.-L. Wang, L.-C. Peng, M. Krenn, X. Jiang, L. Li, N.-L. Liu, C.-Y. Lu, A. Zeilinger, and J.-W. Pan, Phys. Rev. Lett. 123, 070505 (2019).
https://doi.org/10.1103/PhysRevLett.123.070505
[32] A. Marin and D. Markham, Phys. Rev. A 88, 042332 (2013).
https://doi.org/10.1103/PhysRevA.88.042332
[33] J. Hoffmann, C. Spee, O. Gühne, and C. Budroni, New Journal of Physics 20, 102001 (2018).
https://doi.org/10.1088/1367-2630/aae87f
[34] C. Spee, H. Siebeneich, T. F. Gloger, P. Kaufmann, M. Johanning, M. Kleinmann, C. Wunderlich, and O. Gühne, New Journal of Physics 22, 023028 (2020).
https://doi.org/10.1088/1367-2630/ab6d42
[35] Y. Mao, C. Spee, Z.-P. Xu, and O. Gühne, Structure of dimension-bounded temporal correlations (2020), arXiv:2005.13964 [quant-ph].
arXiv:2005.13964
[36] A. Sohbi, R. Ohana, I. Zaquine, E. Diamanti, and D. Markham, Experimental approach to demonstrating contextuality for qudits (2020), arXiv:2010.13278 [quant-ph].
arXiv:2010.13278
[37] M. Ray, N. G. Boddu, K. Bharti, L.-C. Kwek, and A. Cabello, Graph-theoretic approach to dimension witnessing (2020), arXiv:2007.10746 [quant-ph].
arXiv:2007.10746
[38] M. Navascués, S. Pironio, and A. Acín, New Journal of Physics 10, 073013 (2008).
https://doi.org/10.1088/1367-2630/10/7/073013
[39] S. Pironio, M. Navascués, and A. Acín, SIAM Journal on Optimization 20, 2157 (2010).
https://doi.org/10.1137/090760155
[40] M. Navascués and T. Vértesi, Phys. Rev. Lett. 115, 020501 (2015).
https://doi.org/10.1103/PhysRevLett.115.020501
[41] M. Navascués, A. Feix, M. Araújo, and T. Vértesi, Phys. Rev. A 92, 042117 (2015).
https://doi.org/10.1103/PhysRevA.92.042117
[42] H. H. Jee, C. Sparaciari, O. Fawzi, and M. Berta, Characterising quantum correlations of fixed dimension (2020), arXiv:2005.08883 [quant-ph].
arXiv:2005.08883
[43] G. Lüders, Annalen der Physik 15, 663–670 (2006).
https://doi.org/10.1002/andp.200610207
[44] C. Budroni and C. Emary, Physical Review Letters 113, 10.1103/physrevlett.113.050401 (2014).
https://doi.org/10.1103/physrevlett.113.050401
[45] G. Schild and C. Emary, Physical Review A 92, 10.1103/physreva.92.032101 (2015).
https://doi.org/10.1103/physreva.92.032101
[46] Guth, Monatshefte für Mathematik und Physik 40, A31 (1933).
https://doi.org/10.1007/BF01708937
[47] A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985).
https://doi.org/10.1103/PhysRevLett.54.857
[48] C. Budroni, T. Moroder, M. Kleinmann, and O. Gühne, Phys. Rev. Lett. 111, 020403 (2013).
https://doi.org/10.1103/PhysRevLett.111.020403
[49] N. D. Mermin, Phys. Rev. Lett. 65, 3373 (1990).
https://doi.org/10.1103/PhysRevLett.65.3373
[50] A. Peres, Physics Letters A 151, 107 (1990).
https://doi.org/10.1016/0375-9601(90)90172-K
[51] M. L. Almeida, J.-D. Bancal, N. Brunner, A. Acín, N. Gisin, and S. Pironio, Phys. Rev. Lett. 104, 230404 (2010).
https://doi.org/10.1103/PhysRevLett.104.230404
[52] A. Sohbi, Online repository: Bounding the dimension of quantum systems via sequential measurements (2021).
https://doi.org/10.5281/zenodo.4460759
[53] M. Navascués, G. de la Torre, and T. Vértesi, Phys. Rev. X 4, 011011 (2014).
https://doi.org/10.1103/PhysRevX.4.011011
[54] J. M. Donohue and E. Wolfe, Phys. Rev. A 92, 062120 (2015).
https://doi.org/10.1103/PhysRevA.92.062120
[55] G. Vidal and R. Tarrach, Phys. Rev. A 59, 141 (1999), arXiv:quant-ph/9806094 [quant-ph].
https://doi.org/10.1103/PhysRevA.59.141
arXiv:quant-ph/9806094
[56] D. Cavalcanti and P. Skrzypczyk, Reports on Progress in Physics 80, 024001 (2017), arXiv:1604.00501 [quant-ph].
https://doi.org/10.1088/1361-6633/80/2/024001
arXiv:1604.00501
[57] J. Bavaresco, M. T. Quintino, L. Guerini, T. O. Maciel, D. Cavalcanti, and M. T. Cunha, Physical Review A 96, 10.1103/physreva.96.022110 (2017).
https://doi.org/10.1103/physreva.96.022110
[58] S. Designolle, M. Farkas, and J. Kaniewski, New Journal of Physics 21, 113053 (2019), arXiv:1906.00448 [quant-ph].
https://doi.org/10.1088/1367-2630/ab5020
arXiv:1906.00448
[59] M. Araújo, C. Branciard, F. Costa, A. Feix, C. Giarmatzi, and C. Brukner, New Journal of Physics 17, 102001 (2015).
https://doi.org/10.1088/1367-2630/17/10/102001
[60] M. Oszmaniec and T. Biswas, Quantum 3, 133 (2019).
https://doi.org/10.22331/q-2019-04-26-133
[61] K. Baek, A. Sohbi, J. Lee, J. Kim, and H. Nha, New Journal of Physics 22, 093019 (2020).
https://doi.org/10.1088/1367-2630/abad7e
[62] S. Diamond and S. Boyd, Journal of Machine Learning Research 17, 1 (2016).
[63] A. Agrawal, R. Verschueren, S. Diamond, and S. Boyd, Journal of Control and Decision 5, 42 (2018).
https://doi.org/10.1080/23307706.2017.1397554
[64] M. ApS, MOSEK Optimizer API for Python 9.2.28 (2020).
https://docs.mosek.com/9.2/pythonapi/index.html
[65] J. Bertrand, Calcul des probabilités (Editions Jacques Gabay, 2006).
[66] I. Šupić and J. Bowles, Quantum 4, 337 (2020).
https://doi.org/10.22331/q-2020-09-30-337
[67] A. A. Klyachko, M. A. Can, S. Binicioğlu, and A. S. Shumovsky, Phys. Rev. Lett. 101, 020403 (2008).
https://doi.org/10.1103/PhysRevLett.101.020403
[68] F. Mezzadri, Notices of the American Mathematical Society 54, 592 (2007).
arXiv:math-ph/0609050
[69] M. Matsumoto and T. Nishimura, ACM Trans. Model. Comput. Simul. 8, 3–30 (1998).
https://doi.org/10.1145/272991.272995
[70] S. Boyd, S. P. Boyd, and L. Vandenberghe, Convex optimization (Cambridge university press, 2004).
Cited by
[1] Lucas B. Vieira and Costantino Budroni, “Temporal correlations in the simplest measurement sequences”, arXiv:2104.02467.
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