The generalized strong subadditivity of the von Neumann entropy for bosonic quantum systems

We prove a generalization of the strong subadditivity of the von Neumann entropy for bosonic quantum Gaussian systems. Such generalization determines the minimum values of linear combinations of the entropies of subsystems associated to arbitrary linear functions of the quadratures, and holds for ar...

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Bibliographic Details
Published in:Journal of mathematical physics 2024-06, Vol.65 (6)
Main Authors: De Palma, Giacomo, Trevisan, Dario
Format: Article
Language:English
Subjects:
Entropy
Hamiltonian functions
Linear functions
Quadratures
Quantum entanglement
Quantum phenomena
Quantum theory
Subsystems
Online Access:Get full text
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Summary:We prove a generalization of the strong subadditivity of the von Neumann entropy for bosonic quantum Gaussian systems. Such generalization determines the minimum values of linear combinations of the entropies of subsystems associated to arbitrary linear functions of the quadratures, and holds for arbitrary quantum states including the scenario where the entropies are conditioned on a memory quantum system. We apply our result to prove new entropic uncertainty relations with quantum memory, a generalization of the quantum Entropy Power Inequality, and the linear time scaling of the entanglement entropy produced by quadratic Hamiltonians.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0131431