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arXiv · 2211.13372

A new operator extension of strong subadditivity of quantum entropy

Ting-Chun Lin·Isaac H. Kim·Min-Hsiu Hsieh
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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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Ting-Chun Lin, Isaac H. Kim, Min-Hsiu Hsieh. 2022-11-24. A new operator extension of strong subadditivity of quantum entropy. https://doi.org/10.1007/s11005-023-01688-6

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