Papers
Topics
Authors
Recent
Search
2000 character limit reached

Multi-system measurements in generalized probabilistic theories and their role in information processing

Published 9 Sep 2022 in quant-ph | (2209.04474v3)

Abstract: Generalized probabilistic theories (GPTs) provide a framework in which a range of possible theories can be examined, including classical theory, quantum theory and those beyond. In general, enlarging the state space of a GPT leads to fewer possible measurements because the additional states give stronger constraints on the set of effects, the constituents of measurements. This can have implications for information processing. In boxworld, for example, a GPT in which any no-signalling distribution can be realised, there is no analogue of a measurement in the Bell basis and hence the analogue of entanglement swapping is impossible. A comprehensive study of measurements on multiple systems in boxworld has been lacking. Here we consider such measurements in detail, distinguishing those that can be performed by interacting with individual systems sequentially (termed wirings), and the more interesting set of those that cannot. We compute all the possible boxworld effects for cases with small numbers of inputs, outputs and parties, identifying those that are wirings. The large state space of boxworld leads to a small effect space and hence the effects of boxworld are widely applicable in GPTs. We also show some possible uses of non-wirings for information processing by studying state discrimination, nonlocality distillation and the boxworld analogue of nonlocality without entanglement. Finally, we connect our results to the study of logically consistent classical processes and to the composition of contextuality scenarios. By enhancing understanding of measurements in boxworld, our results could be useful in studies of possible underlying principles on which quantum theory can be based.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (55)
  1. S. Popescu and D. Rohrlich, ‘‘Quantum nonlocality as an axiom,” Foundations of Physics 24, 379–385 (1994).
  2. L. Hardy, “Quantum theory from five reasonable axioms,” e-print quant-ph/0101012 (2001).
  3. C. A. Fuchs, “Quantum mechanics as quantum information (and only a little more),” e-print arXiv:quant-ph/0205039 (2002).
  4. L. Masanes and M. P. Müller, “A derivation of quantum theory from physical requirements,” New Journal of Physics 13, 063001 (2011).
  5. B. Dakić and C. Brukner, “Quantum theory and beyond: Is entanglement special?” in Deep Beauty: Understanding the Quantum World through Mathematical Innovation, edited by H. Halvorson (Cambridge University Press, 2011) p. 365–392.
  6. G. Chiribella, G. M. D’Ariano,  and P. Perinotti, “Informational derivation of quantum theory,” Phys. Rev. A 84, 012311 (2011).
  7. J. S. Bell, “On the Einstein-Podolsky-Rosen paradox,” Physics Physique Fizika 1, 195–200 (1964).
  8. J. Barrett, “Information processing in generalized probabilistic theories,” Physical Review A 75, 032304 (2007).
  9. J. Barrett, R. Colbeck,  and A. Kent, “Unconditionally secure device-independent quantum key distribution with only two devices,” Physical Review A 86, 062326 (2012).
  10. R. Colbeck and R. Renner, “Free randomness can be amplified,” Nature Physics 8, 450–454 (2012).
  11. R. Gallego, L. Masanes, G. De La Torre, C. Dhara, L. Aolita,  and A. Acin, “Full randomness from arbitrarily deterministic events,” Nature Communications 4, 3654 (2013).
  12. W. Van Dam, “Implausible consequences of superstrong nonlocality,” Natural Computing 12, 9–12 (2013).
  13. M. Navascués and H. Wunderlich, “A glance beyond the quantum model,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, 881–890 (2010).
  14. M. Pawlowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter,  and M. Zukowski, “Information causality as a physical principle,” Nature 461, 1101–1104 (2009).
  15. T. Fritz, A. Sainz, R. Augusiak, J. B. Brask, R. Chaves, A. Leverrier,  and A. Acin, “Local orthogonality as a multipartite principle for quantum correlations,” Nature Communications 4, 2263 (2013).
  16. C. Branciard, N. Gisin,  and S. Pironio, “Characterizing the nonlocal correlations created via entanglement swapping,” Physical Review Letters 104, 170401 (2010).
  17. T. Fritz, “Beyond Bell’s theorem: correlation scenarios,” New Journal of Physics 14, 103001 (2012).
  18. J. H. Selby, A. B. Sainz, V. Magron, Ł. Czekaj,  and M. Horodecki, “Correlations constrained by composite measurements,” Quantum 7, 1080 (2023).
  19. A. Pozas-Kerstjens, N. Gisin,  and A. Tavakoli, “Full network nonlocality,” Physical Review Letters 128, 010403 (2022).
  20. I. Šupić, J.-D. Bancal, Y. Cai,  and N. Brunner, “Genuine network quantum nonlocality and self-testing,” Physical Review A 105, 022206 (2022).
  21. M. Weilenmann and R. Colbeck, “Self-testing of physical theories, or, is quantum theory optimal with respect to some information-processing task?” Physical Review Letters 125, 060406 (2020a).
  22. Ä. Baumeler and S. Wolf, “The space of logically consistent classical processes without causal order,” New Journal of Physics 18, 013036 (2016).
  23. A. Acín, T. Fritz, A. Leverrier,  and A. B. Sainz, “A combinatorial approach to nonlocality and contextuality,” Communications in Mathematical Physics 334, 533–628 (2015).
  24. A. B. Sainz and E. Wolfe, “Multipartite composition of contextuality scenarios,” Foundations of Physics 48, 925–953 (2018).
  25. A. J. Short and J. Barrett, “Strong nonlocality: A trade-off between states and measurements,” New Journal of Physics 12, 033034 (2010).
  26. A. J. Short, S. Popescu,  and N. Gisin, “Entanglement swapping for generalized nonlocal correlations,” Physical Review A 73, 012101 (2006).
  27. C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin,  and W. K. Wootters, “Quantum nonlocality without entanglement,” Physical Review A 59, 1070 (1999).
  28. E. Chitambar, D. Leung, L. Mančinska, M. Ozols,  and A. Winter, “Everything you always wanted to know about LOCC (but were afraid to ask),” Communications in Mathematical Physics 328, 303–326 (2014).
  29. A. Chefles, “Condition for unambiguous state discrimination using local operations and classical communication,” Physical Review A 69, 050307 (2004).
  30. E. Chitambar, W. Cui,  and H.-K. Lo, “Increasing entanglement monotones by separable operations,” Physical Review Letters 108, 240504 (2012).
  31. A. M. Childs, D. Leung, L. Mančinska,  and M. Ozols, “A framework for bounding nonlocality of state discrimination,” Communications in Mathematical Physics 323, 1121–1153 (2013).
  32. G. Chiribella, G. M. D’Ariano,  and P. Perinotti, “Probabilistic theories with purification,” Physical Review A 81, 062348 (2010).
  33. L. Hardy, “Foliable operational structures for general probabilistic theories,” in Deep Beauty: Understanding the Quantum World through Mathematical Innovation, edited by H. Halvorson (Cambridge University Press, 2011) p. 409–442.
  34. B. S. Tsirelson, “Some results and problems on quantum Bell-type inequalities,” Hadronic Journal Supplement 8, 329–345 (1993).
  35. D. Rosset, J.-D. Bancal,  and N. Gisin, “Classifying 50 years of Bell inequalities,” Journal of Physics A: Mathematical and Theoretical 47, 424022 (2014).
  36. Supplementary data files are available to download from www-users.york.ac.uk/~rc973/effects.zip.
  37. T. Christof and A. Loebel, “POlyhedron Representation Transformation Algorithm (PORTA),”  (2008).
  38. C. W. Helstrom, Quantum Detection and Estimation Theory (Academic Press, London, 1976).
  39. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).
  40. A. J. Short and S. Wehner, “Entropy in general physical theories,” New Journal of Physics 12, 033023 (2010).
  41. J. Löfberg, “YALMIP : A toolbox for modeling and optimization in Matlab,” in IEEE International Conference on Robotics and Automation (2004) pp. 284–289.
  42. The MOSEK optimization toolbox for MATLAB manual. Version 9.0. (2019).
  43. S. S. Bhattacharya, S. Saha, T. Guha,  and M. Banik, “Nonlocality without entanglement: Quantum theory and beyond,” Phys. Rev. Research 2, 012068 (2020).
  44. B. Groisman and L. Vaidman, “Nonlocal variables with product-state eigenstates,” Journal of Physics A: Mathematical and General 34, 6881 (2001).
  45. G. Eftaxias, M. Weilenmann,  and R. Colbeck, “Advantages of multi-copy nonlocality distillation and its application to minimizing communication complexity,” Physical Review Letters 130, 100201 (2023).
  46. J. Allcock, N. Brunner, N. Linden, S. Popescu, P. Skrzypczyk,  and T. Vértesi, “Closed sets of nonlocal correlations,” Physical Review A 80, 062107 (2009).
  47. P. Høyer and J. Rashid, “Optimal protocols for nonlocality distillation,” Physical Review A 82, 042118 (2010).
  48. M. Forster, S. Winkler,  and S. Wolf, “Distilling nonlocality,” Physical Review Letters 102, 120401 (2009).
  49. M. Weilenmann and R. Colbeck, “Toward correlation self-testing of quantum theory in the adaptive Clauser-Horne-Shimony-Holt game,” Physical Review A 102, 022203 (2020b).
  50. S. Kochen and E. P. Specker, “The problem of hidden variables in quantum mechanics,” Journal of Mathematics and Mechanics 17, 59–87 (1967).
  51. D. J. Foulis and C. H. Randall, “Empirical logic and tensor products,” in Interpretations and foundations of quantum theory (1981).
  52. P. Skrzypczyk and N. Brunner, “Couplers for non-locality swapping,” New Journal of Physics 11, 073014 (2009).
  53. R. Kunjwal and Ämin Baumeler, “Trading causal order for locality,”  (2022), arXiv:2202.00440 [quant-ph] .
  54. S. Akibue, M. Owari, G. Kato,  and M. Murao, “Entanglement-assisted classical communication can simulate classical communication without causal order,” Phys. Rev. A 96, 062331 (2017).
  55. D. Gross, M. Müller, R. Colbeck,  and O. C. O. Dahlsten, “All reversible dynamics in maximally nonlocal theories are trivial,” Physical Review Letters 104, 080402 (2010).
Citations (4)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up