A new operator extension of strong subadditivity of quantum entropy

• URL: http://arxiv.org/abs/2211.13372v3
• Date: Thu, 25 May 2023 21:24:15 GMT
• Title: A new operator extension of strong subadditivity of quantum entropy
• Authors: Ting-Chun Lin, Isaac H. Kim, Min-Hsiu Hsieh
• Abstract summary: Weak monotonicity asserts that $S(rho_AB) - S(rho_A) + S(rho_BC) - S(rho_C)geq 0$ for any tripartite density matrix $rho_ABC$. We prove an operator inequality, which, upon taking an expectation value with respect to the state $rho_ABC$, reduces to the weak monotonicity inequality.
• Score: 12.547444644243544
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Let $S(\rho)$ be the von Neumann entropy of a density matrix $\rho$. Weak monotonicity asserts that $S(\rho_{AB}) - S(\rho_A) + S(\rho_{BC}) - S(\rho_C)\geq 0$ for any tripartite density matrix $\rho_{ABC}$, a fact that is equivalent to the strong subadditivity of entropy. We prove an operator inequality, which, upon taking an expectation value with respect to the state $\rho_{ABC}$, reduces to the weak monotonicity inequality. Generalizations of this inequality to the one involving two independent density matrices, as well as their R\'enyi-generalizations, are also presented.

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