Generalized Quantum Stein's Lemma: Redeeming Second Law of Resource Theories (2401.01926v2)
Abstract: [Note: After the first version of this manuscript was uploaded, the authors of [Berta, Brand~ao, Gour, Lami, Plenio, Regula, and Tomamichel, Quantum 7, 1103 (2023)] pointed out an issue about a part of the claims in the previous version of [Bluhm, Capel, Gondolf, P\'erez-Hern\'andez, IEEE Trans. Inf. Theory 69, 5869 (2023)] used in our analysis. Due to this issue, the analysis in the previous version of this manuscript can no longer be considered complete proof of the generalized quantum Stein's lemma. This version is a temporal update to add this note. We are planning to update the manuscript further to explain the issue and what conditions we will additionally need to complete the proof of the generalized quantum Stein's lemma.]
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition, 10th ed. (Cambridge University Press, 2011).
- E. Chitambar and G. Gour, Quantum resource theories, Rev. Mod. Phys. 91, 025001 (2019).
- K. Kuroiwa and H. Yamasaki, General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures, Quantum 4, 355 (2020).
- S. Carnot, Reflections on the motive power of heat and on machines fitted to develop that power (J. Wiley, 1890).
- E. H. Lieb and J. Yngvason, The physics and mathematics of the second law of thermodynamics, Physics Reports 310, 1 (1999).
- E. H. Lieb and J. Yngvason, A Fresh Look at Entropy and the Second Law of Thermodynamics, Physics Today 53, 32 (2000).
- G. Lewis and M. Randall, Thermodynamics and the Free Energy of Chemical Substances (McGraw-Hill, 1923).
- E. Guggenheim, Modern Thermodynamics by the Methods of Willard Gibbs (Methuen & Company Limited, 1933).
- R. Landauer, Irreversibility and heat generation in the computing process, IBM Journal of Research and Development 5, 183 (1961).
- F. Meier and H. Yamasaki, Energy-consumption advantage of quantum computation, (2023), arXiv:2305.11212 [quant-ph] .
- C. E. Shannon, A mathematical theory of communication, The Bell System Technical Journal 27, 379 (1948a).
- C. E. Shannon, A mathematical theory of communication, The Bell System Technical Journal 27, 623 (1948b).
- T. Cover and J. Thomas, Elements of Information Theory (Wiley, 2012).
- G. Vidal and J. I. Cirac, Irreversibility in asymptotic manipulations of entanglement, Phys. Rev. Lett. 86, 5803 (2001).
- F. G. S. L. Brandão and M. B. Plenio, Entanglement theory and the second law of thermodynamics, Nature Physics 4, 873–877 (2008).
- F. G. Brandao and M. B. Plenio, A reversible theory of entanglement and its relation to the second law, Communications in Mathematical Physics 295, 829 (2010).
- F. G. S. L. Brandão and M. B. Plenio, A generalization of quantum stein’s lemma, Communications in Mathematical Physics 295, 791 (2010).
- F. G. S. L. Brandão and G. Gour, Reversible framework for quantum resource theories, Phys. Rev. Lett. 115, 070503 (2015).
- F. Hiai and D. Petz, The proper formula for relative entropy and its asymptotics in quantum probability, Communications in mathematical physics 143, 99 (1991).
- T. Ogawa and H. Nagaoka, Strong converse and stein’s lemma in quantum hypothesis testing, IEEE Transactions on Information Theory 46, 2428 (2000).
- M. Plenio, Problem 20 in some open problems in quantum information theory, (2005), edited by O. Krueger and R. F. Werner, arXiv:quant-ph/0504166 [quant-ph] .
- R. Renner, Security of quantum key distribution, International Journal of Quantum Information 06, 1 (2008).
- R. Renner, Symmetry of large physical systems implies independence of subsystems, Nature Physics 3, 645 (2007).
- L. Lami and B. Regula, No second law of entanglement manipulation after all, Nature Physics 19, 184 (2023).
- E. Chitambar, Dephasing-covariant operations enable asymptotic reversibility of quantum resources, Phys. Rev. A 97, 050301 (2018).
- M. Berta and C. Majenz, Disentanglement cost of quantum states, Phys. Rev. Lett. 121, 190503 (2018).
- M. Hayashi, Optimal sequence of quantum measurements in the sense of stein’s lemma in quantum hypothesis testing, Journal of Physics A: Mathematical and General 35, 10759 (2002).
- B. Regula and L. Lami, Reversibility of quantum resources through probabilistic protocols, (2023), arXiv:2309.07206 [quant-ph] .
- M. M. Wilde, Quantum Information Theory, 2nd ed. (Cambridge University Press, 2017).
- E. Carlen, Trace inequalities and quantum entropy: an introductory course, Entropy and the quantum 529, 73 (2010).
- N. Datta and R. Renner, Smooth entropies and the quantum information spectrum, IEEE Transactions on Information Theory 55, 2807 (2009).
- A. Winter, Tight uniform continuity bounds for quantum entropies: Conditional entropy, relative entropy distance and energy constraints, Communications in Mathematical Physics 347, 291 (2016).
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