Asymptotic Equipartition Theorems in von Neumann Algebras

Alberti, P.M., Uhlmann, A.: On bures-distance and *-algebraic transition probability between inner derived positive linear forms over \(\text^* \)-algebra. Acta Appl. Math. 60, 1–37 (2000)

Article  MathSciNet  MATH  Google Scholar 

Anshu, A., Berta, M., Jain, R., Tomamichel, M.: A minimax approach to one-shot entropy inequalities. J. Math. Phys. 60(12), 122201 (2019)

Article  ADS  MathSciNet  MATH  Google Scholar 

Araki, H.: Relative entropy for states of von Neumann algebras II. Publ. Res. Inst. Math. Sci. 13, 173 (1977)

Article  MathSciNet  MATH  Google Scholar 

Arnon-Friedman, R., Dupuis, F., Fawzi, O., Renner, R., Viddic, T.: Practical device independent quantum cryptography via entropy accumulation. Nat. Comm. 9(459), 459 (2018)

Article  ADS  MATH  Google Scholar 

Audenaert, K.M.R., Calsamiglia, J., Muñoz-Tapia, R., Bagan, E., Masanes, L., Acin, A., Verstraete, F.: Discriminating states: the quantum Chernoff bound. Phys. Rev. Lett. 98(16), 160501 (2007)

Article  ADS  MATH  Google Scholar 

Bergh, B., Kochanowski, J., Salzmann, R., Datta, N.: Infinite dimensional asymmetric quantum channel discrimination. arXiv preprint arXiv:2308.12959 (2023)

Berta, M., Furrer, F., Scholz, V.B.: The smooth entropy formalism for von Neumann algebras. J. Math. Phys. 57(1), 015213 (2016)

Article  ADS  MathSciNet  MATH  Google Scholar 

Berta, M., Scholz, V.B., Tomamichel, M.: Rényi divergences as weighted non-commutative vector-valued \(L_p\)-spaces. Ann. Henri Poincaré 19(6), 1843 (2018)

Article  ADS  MathSciNet  MATH  Google Scholar 

Berta, M., Tomamichel, M.: Chain rules for quantum channels. arXiv preprint arXiv:2204.11153 (2022)

Cooney, T., Mosonyi, M., Wilde, M.M.: Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication. Commun. Math. Phys. 344, 797 (2016)

Article  ADS  MathSciNet  MATH  Google Scholar 

Cover, T.M.: Elements of Information Theory, 2nd edn. Wiley, Hoboken (1999)

MATH  Google Scholar 

Datta, N., Mosonyi, M., Hsieh, M.-H., Brandao, F.G.S.L.: A smooth entropy approach to quantum hypothesis testing and the classical capacity of quantum channels. IEEE Trans. Inf. Theory 59(12), 8014 (2013)

Article  MathSciNet  MATH  Google Scholar 

Datta, N., Pautrat, Y., Rouzé, C.: Second-order asymptotics for quantum hypothesis testing in settings beyond iid-quantum lattice systems and more. J. Math. Phys. 57(6), 062207 (2016)

Article  ADS  MathSciNet  MATH  Google Scholar 

Datta, N., Renner, R.: Smooth entropies and the quantum information spectrum. IEEE Trans. Inform. Theory 55(6), 2807–2815 (2009)

Article  MathSciNet  MATH  Google Scholar 

Devetak, I., Junge, M., King, C., Ruskai, M.B.: Multiplicativity of completely bounded p-norms implies a new additivity result. Commun. Math. Phys. 266(1), 37 (2006)

Article  ADS  MathSciNet  MATH  Google Scholar 

Dupuis, F., Fawzi, O.: Entropy accumulation with improved second-order term. IEEE Trans. Inf. Theory 65, 7596 (2019)

Article  MathSciNet  MATH  Google Scholar 

Dupuis, F., Fawzi, O., Renner, R.: Entropy accumulation. Commun. Math. Phys. 379, 867 (2020)

Article  ADS  MathSciNet  MATH  Google Scholar 

Fang, K., Fawzi, O., Renner, R., Sutter, D.: A chain rule for the quantum relative entropy. Phys. Rev. Lett. 124, 100501 (2020)

Article  ADS  MathSciNet  MATH  Google Scholar 

Faulkner, T., Hollands, S., Swingle, B., Wang, Y.: Approximate recovery and relative entropy \(\text\): General von Neumann subalgebras. Commun. Math. Phys. 389(1), 349–397 (2022)

Article  ADS  MathSciNet  MATH  Google Scholar 

Fawzi, H., Fawzi, O.: Defining quantum divergences via convex optimization. Quantum 5, 387 (2021)

Article  MATH  Google Scholar 

Fawzi, O., Renner, R.: Quantum conditional mutual information and approximate Markov chains. Commun. Math. Phys. 340, 576 (2015)

Article  ADS  MathSciNet  MATH  Google Scholar 

Furrer, F., Aberg, J., Renner, R.: Min- and max-entropy in infinite dimensions. Comm. Math. Phys. 306(1), 165–186 (2011)

Article  ADS  MathSciNet  MATH  Google Scholar 

Furuya, K., Lashkari, N.: Real-space RG, error correction and Petz map. J. High Energy Phys. 1, 2022 (2022)

MathSciNet  MATH  Google Scholar 

Ganesan, P., Gao, L., Pandey, P.S.K., Plosker, S.: Quantum majorization on semi-finite von Neumann algebras. J. Funct. Anal. 279(7), 108650 (2020)

Article  MathSciNet  MATH  Google Scholar 

Gao, L., Junge, M., LaRacuente, N., Li, H.: Complete order and relative entropy decay rates. arXiv preprint arXiv:2209.11684 (2022)

Gao, L., Wilde, M.M.: Recoverability for optimized quantum f-divergences. J. Phys. A: Math. Theor. 54(28), 385302 (2021)

Article  MathSciNet  MATH  Google Scholar 

Haagerup, U., Junge, M., Xu, Q.: A reduction method for noncommutative \(l_p\)-spaces and applications. Trans. Am. Math. Soc. 362, 2125 (2010)

Article  MATH  Google Scholar 

Hayashi, M.: Optimal sequence of quantum measurements in the sense of Stein’s lemma in quantum hypothesis testing. J. Phys. A: Math. Gen. 35, 10759 (2002)

Article  ADS  MathSciNet  MATH  Google Scholar 

Hiai, F.: Quantum \(f\)-Divergences in von Neumann Algebras-Reversibility of Quantum Operations. Mathematical Physics Studies. Springer, Singapore (2021)

Book  MATH  Google Scholar 

Hiai, F.: Quantum rényi divergences and the strong converse exponent of state discrimination in operator algebras. Ann. Henri Poincaré 24, 1681–1724 (2023)

Article  ADS  MathSciNet  MATH  Google Scholar 

Hiai, F., Petz, D.: The proper formula for relative entropy and its asymptotics in quantum probability. Commun. Math. Phys. 143(1), 99 (1991)

Article  ADS  MathSciNet  MATH  Google Scholar 

Hollands, S., Sanders, K.: Entanglement measures and their properties in quantum field theory. Springer Briefs in Mathematical Physics. 34 (2018)

Jakšić, V., Ogata, Y., Pillet, C.A., Seiringer, R.: Quantum hypothesis testing and non-equilibrium statistical mechanics. Rev. Math. Phys. 24(6), 1230002 (2012)

Article  MathSciNet  MATH  Google Scholar 

Jenčová, A.: Rényi relative entropies and noncommutative \(\text_p\)-spaces. Annales Henri Poincaré, 19(8), (2018)

Jenčová, A.: Rényi relative entropies and noncommutative \(\text_p\)-spaces II. Annales Henri Poincaré, 22 (2021)

Junge, M., Parcet, J.: Mixed-norm inequalities and operator space Lp embedding theory, volume 203. Memoirs of American Mathematical Society (2010)

Kadison, Richard: On representations of finite type. Proc. Natl. Acad. Sci. USA 95(23), 13392 (1998)

Article  ADS  MathSciNet  MATH  Google Scholar 

Khatri, S., Kaur, E., Guha, S., Wilde, M.: Second-order coding rates for key distillation in quantum key distribution. arXiv e-prints (2019)

Kosaki, H.: Relative entropy of states: a variational expression. J. Oper. Theory 16, 335 (1986)

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