Papers
Topics
Authors
Recent
Search
2000 character limit reached

Complete Characterization of Entanglement Embezzlement

Published 31 Mar 2023 in quant-ph | (2303.17749v3)

Abstract: Using local operations and classical communication (LOCC), entanglement can be manipulated but not created. However, entanglement can be embezzled. In this work, we completely characterize universal embezzling families and demonstrate how this singles out the original family introduced by van Dam and Hayden. To achieve this, we first give a full characterization of pure to mixed state LOCC-conversions. Then, we introduce a new conversion distance and derive a closed-form expression for it. These results might be of independent interest.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (70)
  1. M. A. Nielsen, Conditions for a class of entanglement transformations, Phys. Rev. Lett. 83, 436 (1999).
  2. M. B. Plenio and S. Virmani, An introduction to entanglement measures, Quantum Inf. Comput. 7, 1 (2007).
  3. A. Einstein, B. Podolsky, and N. Rosen, Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev. 47, 777 (1935).
  4. C. H. Bennet and G. Brassard, Quantum cryptography: Public key distribution and coin tossing, in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Vol. 1 (IEEE Bangalore, 1984) pp. 175–179.
  5. C. H. Bennett and G. Brassard, Quantum cryptography: Public key distribution and coin tossing, Theor. Comput. Sci. 560, 7 (2014), Theoretical Aspects of Quantum Cryptography – celebrating 30 years of BB84.
  6. C. H. Bennett and S. J. Wiesner, Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states, Phys. Rev. Lett. 69, 2881 (1992).
  7. S. Popescu, Bell’s inequalities versus teleportation: What is nonlocality?, Phys. Rev. Lett. 72, 797 (1994).
  8. M. Berta, M. Christandl, and R. Renner, The quantum reverse shannon theorem based on one-shot information theory, Commun. Math. Phys. 306, 579 (2011).
  9. E. Chitambar and G. Gour, Quantum resource theories, Rev. Mod. Phys. 91, 025001 (2019).
  10. B. Coecke, T. Fritz, and R. W. Spekkens, A mathematical theory of resources, Inf. Comput. 250, 59 (2016).
  11. D. Jonathan and M. B. Plenio, Minimal conditions for local pure-state entanglement manipulation, Phys. Rev. Lett. 83, 1455 (1999a).
  12. G. Vidal, D. Jonathan, and M. A. Nielsen, Approximate transformations and robust manipulation of bipartite pure-state entanglement, Phys. Rev. A 62, 012304 (2000).
  13. A. Uhlmann, The “transition probability” in the state space of a *-algebra, Rep. Math. Phys. 9, 273 (1976).
  14. R. Jozsa, Fidelity for mixed quantum states, J. Mod. Opt 41, 2315 (1994).
  15. C. Fuchs and J. van de Graaf, Cryptographic distinguishability measures for quantum-mechanical states, IEEE Trans. Inf. Theory 45, 1216 (1999).
  16. M. Tomamichel, R. Colbeck, and R. Renner, Duality between smooth min- and max-entropies, IEEE Trans. Inf. Theory 56, 4674 (2010).
  17. G. Gour and M. Tomamichel, Optimal extensions of resource measures and their applications, Phys. Rev. A 102, 062401 (2020).
  18. X. Wang and M. M. Wilde, Resource theory of asymmetric distinguishability, Phys. Rev. Res. 1, 033170 (2019).
  19. G. Saxena, E. Chitambar, and G. Gour, Dynamical resource theory of quantum coherence, Phys. Rev. Res. 2, 023298 (2020).
  20. G. Saxena and G. Gour, Quantifying multiqubit magic channels with completely stabilizer-preserving operations, Phys. Rev. A 106, 042422 (2022).
  21. G. Gour, Role of quantum coherence in thermodynamics, PRX Quantum 3, 040323 (2022).
  22. W. van Dam and P. Hayden, Universal entanglement transformations without communication, Phys. Rev. A 67, 060302 (2003).
  23. D. Leung and B. Wang, Characteristics of universal embezzling families, Phys. Rev. A 90, 042331 (2014).
  24. R. Cleve, L. Liu, and V. I. Paulsen, Perfect embezzlement of entanglement, J. Math. Phys. 58, 012204 (2017).
  25. D. Jonathan and M. B. Plenio, Entanglement-assisted local manipulation of pure quantum states, Phys. Rev. Lett. 83, 3566 (1999b).
  26. L. Lami, B. Regula, and A. Streltsov, Catalysis cannot overcome bound entanglement (2023), arXiv:2305.03489 [quant-ph] .
  27. R. Ganardi, T. V. Kondra, and A. Streltsov, Catalytic and asymptotic equivalence for quantum entanglement (2023), arXiv:2305.03488 [quant-ph] .
  28. J. Son and N. H. Y. Ng, A hierarchy of thermal processes collapses under catalysis (2023), arXiv:2303.13020 [quant-ph] .
  29. S. H. Lie and N. H. Y. Ng, Catalysis always degrades external quantum correlations (2023), arXiv:2303.02376 [quant-ph] .
  30. L. van Luijk, R. F. Werner, and H. Wilming, Covariant catalysis requires correlations and good quantum reference frames degrade little (2023), arXiv:2301.09877 [quant-ph] .
  31. J. Son and N. H. Y. Ng, Catalysis in action via elementary thermal operations (2022), arXiv:2209.15213 [quant-ph] .
  32. P. Lipka-Bartosik, M. Perarnau-Llobet, and N. Brunner, Operational definition of the temperature of a quantum state, Phys. Rev. Lett. 130, 040401 (2023a).
  33. K. Korzekwa and M. Lostaglio, Optimizing thermalization, Phys. Rev. Lett. 129, 040602 (2022).
  34. P. Lipka-Bartosik and P. Skrzypczyk, Catalytic quantum teleportation, Phys. Rev. Lett. 127, 080502 (2021a).
  35. T. V. Kondra, C. Datta, and A. Streltsov, Catalytic transformations of pure entangled states, Phys. Rev. Lett. 127, 150503 (2021).
  36. M. Karvonen, Neither contextuality nor nonlocality admits catalysts, Phys. Rev. Lett. 127, 160402 (2021).
  37. H. Wilming, Entropy and reversible catalysis, Phys. Rev. Lett. 127, 260402 (2021).
  38. S. H. Lie and H. Jeong, Randomness for quantum channels: Genericity of catalysis and quantum advantage of uniformness, Phys. Rev. Res. 3, 013218 (2021).
  39. P. Lipka-Bartosik and P. Skrzypczyk, All states are universal catalysts in quantum thermodynamics, Phys. Rev. X 11, 011061 (2021b).
  40. N. Shiraishi and T. Sagawa, Quantum thermodynamics of correlated-catalytic state conversion at small scale, Phys. Rev. Lett. 126, 150502 (2021).
  41. P. Lipka-Bartosik, H. Wilming, and N. H. Y. Ng, Catalysis in quantum information theory (2023b), arXiv:2306.00798 [quant-ph] .
  42. A. W. Marshall, I. Olkin, and B. C. Arnold, Inequalities: Theory of Majorization and Its Applications, Springer Series in Statistics (Springer, 2011).
  43. G. Vidal, Entanglement of pure states for a single copy, Phys. Rev. Lett. 83, 1046 (1999).
  44. H.-K. Lo and S. Popescu, Concentrating entanglement by local actions: Beyond mean values, Phys. Rev. A 63, 022301 (2001).
  45. C. W. Helstrom, Quantum detection and estimation theory, J. Stat. Phys. 1, 231 (1969).
  46. A. S. Holevo, Statistical decision theory for quantum systems, J. Multivariate Anal. 3, 337 (1973).
  47. J. Watrous, Similarity and distance among states and channels, in The Theory of Quantum Information (Cambridge University Press, 2018) p. 124–200.
  48. E. N. Torgersen, Comparison of experiments when the parameter space is finite, Probab. Theory Relat. Fields 16, 219 (1970).
  49. E. Torgersen, Comparison of Statistical Experiments, Encyclopedia of Mathematics and its Applications (Cambridge University Press, Cambridge, 1991).
  50. J. M. Renes, Relative submajorization and its use in quantum resource theories, J. Math. Phys 57, 122202 (2016).
  51. M. Horodecki, J. Oppenheim, and C. Sparaciari, Extremal distributions under approximate majorization, J. Phys. A 51, 305301 (2018).
  52. T. Baumgratz, M. Cramer, and M. B. Plenio, Quantifying Coherence, Phys. Rev. Lett. 113, 140401 (2014).
  53. S. Du, Z. Bai, and Y. Guo, Conditions for coherence transformations under incoherent operations, Phys. Rev. A 91, 052120 (2015).
  54. R. Takagi and N. Shiraishi, Correlation in catalysts enables arbitrary manipulation of quantum coherence, Phys. Rev. Lett. 128, 240501 (2022).
  55. M. Horodecki and J. Oppenheim, Fundamental limitations for quantum and nanoscale thermodynamics, Nat. Commun. 4, 2059 (2013).
  56. P. Lipka-Bartosik and P. Skrzypczyk, All states are universal catalysts in quantum thermodynamics, Phys. Rev. X 11, 011061 (2021c).
  57. R. Rubboli and M. Tomamichel, Fundamental limits on correlated catalytic state transformations, Phys. Rev. Lett. 129, 120506 (2022).
  58. O. Regev and T. Vidick, Elementary proofs of Grothendieck theorems for completely bounded norms, J. Operat. Theor. 71, 491 (2014).
  59. A. Grothendieck, Résumé de la théorie métrique des produits tensoriels topologiques, Boll. Soc. Mat. São-Paulo 8, 1 (1953), reprinted in Resenhas 4, 401 (1996).
  60. G. Pisier, Grothendieck’s theorem, past and present, Bull. Amer. Math. Soc. 49, 237 (2012).
  61. D. Leung, B. Toner, and J. Watrous, Coherent state exchange in multi-prover quantum interactive proof systems, Chic. J. Theoret. Comput. Sci. 2013, 11 (2013).
  62. I. Dinur, D. Steurer, and T. Vidick, A parallel repetition theorem for entangled projection games, Comput. Complex. 24, 201 (2015).
  63. O. Regev and T. Vidick, Quantum xor games, ACM Trans. Comput. Theory 7, 15 (2015).
  64. Z. Ji, D. Leung, and T. Vidick, A three-player coherent state embezzlement game, Quantum 4, 349 (2020).
  65. G. Chiribella and C. M. Scandolo, Entanglement and thermodynamics in general probabilistic theories, New J. Phys 17, 103027 (2015).
  66. A. W. Roberts and D. E. Varberg, Convex Functions, edited by P. A. Smith and S. Ellenberg, Pure and Applied Mathemathics; A Series of Monographs and Textbooks, Vol. 57 (ACADEMIC PRESS New York and London, 1973).
  67. L. Mirsky, A trace inequality of John von Neumann, Monatsh. Math 79, 303 (1975).
  68. T. S. Ferguson, Mathematical statistics: A decision theoretic approach, Probability and Mathematical Statistics: A Series of Monographs and Textbooks (Academic Press, 1967).
  69. W. Rudin, Real and Complex Analysis, Higher Mathematics Series (McGraw-Hill Education, 1987).
  70. R. A. Wijsman, A useful inequality on ratios of integrals, with application to maximum likelihood estimation, J. Am. Stat. Assoc 80, 472 (1985).
Citations (8)
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

Tweets

Sign up for free to view the 1 tweet with 0 likes about this paper.

Sign Up for Free