The type-independent resource theory of local operations and shared randomness

David Schmid1,2, Denis Rosset1, and Francesco Buscemi3

1Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, N2L 2Y5, Canada
2Institute for Quantum Computing and Dept. of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
3Graduate School of Informatics, Nagoya University, Chikusa-ku, 464-8601 Nagoya, Japan

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

Abstract

In space-like separated experiments and other scenarios where multiple parties share a classical common cause but no cause-effect relations, quantum theory allows a variety of nonsignaling resources which are useful for distributed quantum information processing. These include quantum states, nonlocal boxes, steering assemblages, teleportages, channel steering assemblages, and so on. Such resources are often studied using nonlocal games, semiquantum games, entanglement-witnesses, teleportation experiments, and similar tasks. We introduce a unifying framework which subsumes the full range of nonsignaling resources, as well as the games and experiments which probe them, into a common resource theory: that of local operations and shared randomness (LOSR). Crucially, we allow these LOSR operations to locally change the type of a resource, so that players can convert resources of $any$ type into resources of any other type, and in particular into strategies for the specific type of game they are playing. We then prove several theorems relating resources and games of different types. These theorems generalize a number of seminal results from the literature, and can be applied to lessen the assumptions needed to characterize the nonclassicality of resources. As just one example, we prove that semiquantum games are able to perfectly characterize the LOSR nonclassicality of every resource of $any$ type (not just quantum states, as was previously shown). As a consequence, we show that any resource can be characterized in a measurement-device-independent manner.

► BibTeX data

► References

[1] A. Einstein, B. Podolsky, and N. Rosen, Physical Review 47, 777 (1935).
https:/​/​doi.org/​10.1103/​PhysRev.47.777

[2] C. J. Wood and R. W. Spekkens, New J. Phys. 17, 033002 (2015).
https:/​/​doi.org/​10.1088/​1367-2630/​17/​3/​033002
http:/​/​stacks.iop.org/​1367-2630/​17/​i=3/​a=033002

[3] F. Costa and S. Shrapnel, New Journal of Physics 18, 063032 (2016).
https:/​/​doi.org/​10.1088/​1367-2630/​18/​6/​063032

[4] J.-M. A. Allen, J. Barrett, D. C. Horsman, C. M. Lee, and R. W. Spekkens, Physical Review X 7, 031021 (2017).
https:/​/​doi.org/​10.1103/​PhysRevX.7.031021

[5] J. Barrett, R. Lorenz, and O. Oreshkov, (2019), arXiv:1906.10726.
arXiv:1906.10726

[6] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).
https:/​/​doi.org/​10.1103/​RevModPhys.81.865

[7] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Rev. Mod. Phys. 86, 419 (2014a).
https:/​/​link.aps.org/​doi/​10.1103/​RevModPhys.86.419

[8] B. Coecke, T. Fritz, and R. W. Spekkens, Information and Computation 250, 59 (2016), Quantum Physics and Logic.
https:/​/​doi.org/​10.1016/​j.ic.2016.02.008

[9] J. Watrous, The theory of quantum information (Cambridge University Press, 2018).

[10] H. M. Wiseman, S. J. Jones, and A. C. Doherty, Phys. Rev. Lett. 98, 140402 (2007).
https:/​/​doi.org/​10.1103/​PhysRevLett.98.140402

[11] D. Cavalcanti and P. Skrzypczyk, Reports on Progress in Physics 80, 024001 (2017).
https:/​/​doi.org/​10.1088/​1361-6633/​80/​2/​024001

[12] M. Piani, J. Opt. Soc. Am. B 32, A1 (2015).
https:/​/​doi.org/​10.1364/​JOSAB.32.0000A1

[13] M. J. Hoban and A. B. Sainz, New Journal of Physics 20, 053048 (2018).
https:/​/​doi.org/​10.1088/​1367-2630/​aabea8

[14] D. Cavalcanti, P. Skrzypczyk, and I. Šupić, Phys. Rev. Lett. 119, 110501 (2017).
https:/​/​doi.org/​10.1103/​PhysRevLett.119.110501

[15] C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 59, 1070 (1999).
https:/​/​doi.org/​10.1103/​PhysRevA.59.1070

[16] E. G. Cavalcanti, M. J. W. Hall, and H. M. Wiseman, Phys. Rev. A 87, 032306 (2013).
https:/​/​doi.org/​10.1103/​PhysRevA.87.032306

[17] A. Belén Sainz, M. J. Hoban, P. Skrzypczyk, and L. Aolita, (2019), arXiv:1907.03705.
arXiv:1907.03705

[18] F. Buscemi, Phys. Rev. Lett. 108, 200401 (2012a).
https:/​/​doi.org/​10.1103/​PhysRevLett.108.200401

[19] D. Schmid, T. C. Fraser, R. Kunjwal, A. B. Sainz, E. Wolfe, and R. W. Spekkens, ``Why standard entanglement theory is inappropriate for the study of bell scenarios,'' (2019a), arXiv:2004.09194 [quant-ph].
arXiv:2004.09194

[20] J. I. de Vicente, J. Phys. A 47, 424017 (2014).
https:/​/​doi.org/​10.1088/​1751-8113/​47/​42/​424017

[21] R. Gallego and L. Aolita, Phys. Rev. A 95 (2017).
https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.95.032118

[22] E. Wolfe, D. Schmid, A. B. Sainz, R. Kunjwal, and R. W. Spekkens, ``Quantifying Bell: the resource theory of nonclassicality of common-cause boxes,'' (2019), arXiv:1903.06311 [quant-ph].
arXiv:1903.06311

[23] J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy (Cambridge University Press, 2004).

[24] G. Pütz, D. Rosset, T. J. Barnea, Y.-C. Liang, and N. Gisin, Physical Review Letters 113, 190402 (2014).
https:/​/​doi.org/​10.1103/​PhysRevLett.113.190402

[25] D. Rosset, R. Ferretti-Schöbitz, J.-D. Bancal, N. Gisin, and Y.-C. Liang, Physical Review A 86, 062325 (2012).
https:/​/​doi.org/​10.1103/​PhysRevA.86.062325

[26] S. Pironio, V. Scarani, and T. Vidick, New Journal of Physics 18, 100202 (2016).
https:/​/​doi.org/​10.1088/​1367-2630/​18/​10/​100202

[27] D. Cavalcanti, P. Skrzypczyk, G. H. Aguilar, R. V. Nery, P. H. S. Ribeiro, and S. P. Walborn, Nature Communications 6, 7941 (2015).
https:/​/​doi.org/​10.1038/​ncomms8941

[28] R. F. Werner, Phys. Rev. A 40, 4277 (1989).
https:/​/​doi.org/​10.1103/​PhysRevA.40.4277

[29] J. Barrett, Phys. Rev. A 65, 042302 (2002).
https:/​/​doi.org/​10.1103/​PhysRevA.65.042302

[30] P. Lipka-Bartosik and P. Skrzypczyk, (2019), arXiv:1908.05107 [quant-ph].
arXiv:1908.05107

[31] C. Branciard, D. Rosset, Y.-C. Liang, and N. Gisin, Physical Review Letters 110, 060405 (2013).
https:/​/​doi.org/​10.1103/​PhysRevLett.110.060405

[32] D. Rosset, C. Branciard, N. Gisin, and Y.-C. Liang, New Journal of Physics 15, 053025 (2013).
https:/​/​doi.org/​10.1088/​1367-2630/​15/​5/​053025

[33] F. Shahandeh, M. J. W. Hall, and T. C. Ralph, Physical Review Letters 118, 150505 (2017).
https:/​/​doi.org/​10.1103/​PhysRevLett.118.150505

[34] D. Rosset, A. Martin, E. Verbanis, C. C. W. Lim, and R. Thew, Physical Review A 98, 052332 (2018a).
https:/​/​doi.org/​10.1103/​PhysRevA.98.052332

[35] G. Vidal, J. Mod. Optic. 47, 355 (2000).
https:/​/​doi.org/​10.1080/​09500340008244048

[36] D. Rosset, D. Schmid, and F. Buscemi, ``Characterizing nonclassicality of arbitrary distributed devices,'' (2019), arXiv:1911.12462 [quant-ph].
arXiv:1911.12462

[37] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Rev. Mod. Phys. 86, 419 (2014b).
https:/​/​link.aps.org/​doi/​10.1103/​RevModPhys.86.419

[38] D. Chruściński and G. Sarbicki, Journal of Physics A: Mathematical and Theoretical 47, 483001 (2014).
https:/​/​doi.org/​10.1088/​1751-8113/​47/​48/​483001

[39] S. Popescu and D. Rohrlich, Foundations of Physics 24, 379 (1994).
https:/​/​doi.org/​10.1007/​BF02058098

[40] J. Barrett, N. Linden, S. Massar, S. Pironio, S. Popescu, and D. Roberts, Physical Review A 71, 022101 (2005).
https:/​/​doi.org/​10.1103/​PhysRevA.71.022101

[41] D. Beckman, D. Gottesman, M. A. Nielsen, and J. Preskill, Phys. Rev. A 64, 052309 (2001).
https:/​/​doi.org/​10.1103/​PhysRevA.64.052309

[42] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2010).
https:/​/​doi.org/​10.1017/​CBO9780511976667

[43] D. Schmid, K. Ried, and R. W. Spekkens, Phys. Rev. A 100, 022112 (2019b).
https:/​/​doi.org/​10.1103/​PhysRevA.100.022112

[44] K. Horodecki, A. Grudka, P. Joshi, W. Kłobus, and J. Łodyga, Physical Review A 92, 032104 (2015).
https:/​/​doi.org/​10.1103/​PhysRevA.92.032104

[45] J. I. de Vicente, Journal of Physics A: Mathematical and Theoretical 47, 424017 (2014).
https:/​/​doi.org/​10.1088/​1751-8113/​47/​42/​424017

[46] E. Schrodinger, Mathematical Proceedings of the Cambridge Philosophical Society 31, 555 (1935).
https:/​/​doi.org/​10.1017/​S0305004100013554

[47] P. Skrzypczyk, M. Navascués, and D. Cavalcanti, Physical Review Letters 112, 180404 (2014).
https:/​/​doi.org/​10.1103/​PhysRevLett.112.180404

[48] R. Gallego and L. Aolita, Physical Review X 5, 041008 (2015).
https:/​/​doi.org/​10.1103/​PhysRevX.5.041008

[49] M. Piani and J. Watrous, Physical Review Letters 114, 060404 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.114.060404

[50] R. Uola, A. C. S. Costa, H. C. Nguyen, and O. Gühne, (2019a), arXiv:1903.06663.
arXiv:1903.06663

[51] M. F. Pusey, Phys. Rev. A 88, 032313 (2013).
https:/​/​doi.org/​10.1103/​PhysRevA.88.032313

[52] I. Šupić, P. Skrzypczyk, and D. Cavalcanti, (2018), arXiv:1804.10612.
arXiv:1804.10612

[53] G. Chiribella, G. M. D'Ariano, and P. Perinotti, Phys. Rev. A 80, 022339 (2009).
https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.80.022339

[54] C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
https:/​/​doi.org/​10.1103/​PhysRevLett.70.1895

[55] P. Lipka-Bartosik and P. Skrzypczyk, ``The operational advantages provided by non-classical teleportation,'' (2019), arXiv:1908.05107 [quant-ph].
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.023029
arXiv:1908.05107

[56] I. Šupić, P. Skrzypczyk, and D. Cavalcanti, Physical Review A 95, 042340 (2017).
https:/​/​doi.org/​10.1103/​PhysRevA.95.042340

[57] T. Gonda and R. W. Spekkens, (2019), arXiv:1912.07085.
arXiv:1912.07085

[58] W. Dür, G. Vidal, and J. I. Cirac, Phys. Rev. A 62, 062314 (2000).
https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.62.062314

[59] D. Schmid, H. Du, M. Mudassar, G. Coulter-de Wit, D. Rosset, and M. J. Hoban, ``Postquantum common-cause channels: the resource theory of local operations and shared entanglement,'' (2020), arXiv:2004.06133 [quant-ph].
arXiv:2004.06133

[60] D. Mayers and A. Yao, Quantum Information & Computation 4, 273 (2004).

[61] A. Montanaro and R. de Wolf, Theory of Computing , 1 (2016).
https:/​/​doi.org/​10.4086/​toc.gs.2016.007

[62] I. Šupić and J. Bowles, (2019), arXiv:1904.10042.
arXiv:1904.10042

[63] J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).
https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.23.880

[64] I. Šupić and M. J. Hoban, New Journal of Physics 18, 075006 (2016), arXiv:1601.01552.
https:/​/​doi.org/​10.1088/​1367-2630/​18/​7/​075006
arXiv:1601.01552

[65] A. Gheorghiu, E. Kashefi, and P. Wallden, New Journal of Physics 17, 083040 (2015).
https:/​/​doi.org/​10.1088/​1367-2630/​17/​8/​083040

[66] J.-D. Bancal, N. Sangouard, and P. Sekatski, Physical Review Letters 121, 250506 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.121.250506

[67] M. O. Renou, J. Kaniewski, and N. Brunner, Physical Review Letters 121, 250507 (2018), arXiv:1807.04956.
https:/​/​doi.org/​10.1103/​PhysRevLett.121.250507
arXiv:1807.04956

[68] A. Tavakoli, J. Kaniewski, T. Vértesi, D. Rosset, and N. Brunner, Physical Review A 98, 062307 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.98.062307

[69] P. Sekatski, J.-D. Bancal, S. Wagner, and N. Sangouard, Physical Review Letters 121, 180505 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.121.180505

[70] J. Sperling and W. Vogel, Physica Scripta 83, 045002 (2011).
https:/​/​doi.org/​10.1088/​0031-8949/​83/​04/​045002

[71] F. Buscemi, Phys. Rev. Lett. 108, 200401 (2012b).
https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.108.200401

[72] F. Buscemi, Probl Inf Transm 52, 201 (2016).
https:/​/​doi.org/​10.1134/​S0032946016030017

[73] D. Rosset, F. Buscemi, and Y.-C. Liang, Phys. Rev. X 8, 021033 (2018b).
https:/​/​doi.org/​10.1103/​PhysRevX.8.021033

[74] P. Skrzypczyk and N. Linden, Phys. Rev. Lett. 122, 140403 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.122.140403

[75] P. Skrzypczyk, I. Supic, and D. Cavalcanti, Phys. Rev. Lett. 122, 130403 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.122.130403

[76] R. Takagi, B. Regula, K. Bu, Z.-W. Liu, and G. Adesso, Phys. Rev. Lett. 122, 140402 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.122.140402

[77] R. Uola, T. Kraft, J. Shang, X.-D. Yu, and O. Gühne, Phys. Rev. Lett. 122, 130404 (2019b).
https:/​/​doi.org/​10.1103/​PhysRevLett.122.130404

[78] R. Uola, T. Kraft, and A. A. Abbott, ``Quantification of quantum dynamics with input-output games,'' (2019c), arXiv:1906.09206 [quant-ph].
arXiv:1906.09206

[79] R. Takagi and B. Regula, Phys. Rev. X 9, 031053 (2019).
https:/​/​doi.org/​10.1103/​PhysRevX.9.031053

Cited by

[1] I. S. Eliëns, S. G. A. Brito, and R. Chaves, "Bell nonlocality using tensor networks and sparse recovery", Physical Review Research 2 2, 023198 (2020).

[2] Ana Belén Sainz, Matty J. Hoban, Paul Skrzypczyk, and Leandro Aolita, "Bipartite Postquantum Steering in Generalized Scenarios", arXiv:1907.03705, Physical Review Letters 125 5, 050404 (2020).

[3] Andrés F. Ducuara and Paul Skrzypczyk, "Operational Interpretation of Weight-Based Resource Quantifiers in Convex Quantum Resource Theories", Physical Review Letters 125 11, 110401 (2020).

[4] Yi-Zheng Zhen, Yingqiu Mao, Kai Chen, Francesco Buscemi, and Oscar Dahlsten, "Unified approach to witness non-entanglement-breaking quantum channels", Physical Review A 101 6, 062301 (2020).

[5] Elie Wolfe, David Schmid, Ana Belén Sainz, Ravi Kunjwal, and Robert W. Spekkens, "Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes", arXiv:1903.06311, Quantum 4, 280 (2020).

[6] Denis Rosset, David Schmid, and Francesco Buscemi, "Characterizing nonclassicality of arbitrary distributed devices", arXiv:1911.12462.

[7] Miguel Navascues, Elie Wolfe, Denis Rosset, and Alejandro Pozas-Kerstjens, "Genuine Network Multipartite Entanglement", arXiv:2002.02773.

[8] David Schmid, Thomas C. Fraser, Ravi Kunjwal, Ana Belen Sainz, Elie Wolfe, and Robert W. Spekkens, "Why standard entanglement theory is inappropriate for the study of Bell scenarios", arXiv:2004.09194.

[9] David Schmid, Haoxing Du, Maryam Mudassar, Ghi Coulter-de Wit, Denis Rosset, and Matty J. Hoban, "Postquantum common-cause channels: the resource theory of local operations and shared entanglement", arXiv:2004.06133.

[10] John H. Selby and Ciarán M. Lee, "Compositional resource theories of coherence", arXiv:1911.04513.

[11] Andrés F. Ducuara, Patryk Lipka-Bartosik, and Paul Skrzypczyk, "Multi-object operational tasks for convex quantum resource theories", arXiv:2004.12898.

[12] Patricia Contreras-Tejada, Carlos Palazuelos, and Julio I. de Vicente, "Genuine multipartite nonlocality is intrinsic to quantum networks", arXiv:2004.01722.

[13] Denis Rosset, Ämin Baumeler, Jean-Daniel Bancal, Nicolas Gisin, Anthony Martin, Marc-Olivier Renou, and Elie Wolfe, "Algebraic and geometric properties of local transformations", arXiv:2004.09405.

The above citations are from Crossref's cited-by service (last updated successfully 2020-10-21 13:58:43) and SAO/NASA ADS (last updated successfully 2020-10-21 13:58:44). The list may be incomplete as not all publishers provide suitable and complete citation data.

1 thought on “The type-independent resource theory of local operations and shared randomness

  1. Pingback: Perspective in Quantum Views by Patryk Lipka-Bartosik "Unboxing hidden correlations"