The property of superadditivity of the quantum relative entropy states that, in a bipartite system HAB=HA⊗HB , for every density operator ΡAB , one has D(ΡAB||σA⊗σB)=D(ΡA||σA)+D(ΡB||σB) . In this paper, we provide an extension of this inequality for arbitrary density operators σAB . More specifically, we prove that a(σAB)D(ΡAB||σAB)=D(ΡA||σA)+D(ΡB||σB) holds for all bipartite states ΡAB and σAB , where a(σAB)=1+2?σ-1/2A⊗σ-1/2BσABσ-1/2A⊗σ-1/2B-1AB?∞.
Superadditivity of Quantum Relative Entropy for General States
Lucia A.;
2018-01-01
Abstract
The property of superadditivity of the quantum relative entropy states that, in a bipartite system HAB=HA⊗HB , for every density operator ΡAB , one has D(ΡAB||σA⊗σB)=D(ΡA||σA)+D(ΡB||σB) . In this paper, we provide an extension of this inequality for arbitrary density operators σAB . More specifically, we prove that a(σAB)D(ΡAB||σAB)=D(ΡA||σA)+D(ΡB||σB) holds for all bipartite states ΡAB and σAB , where a(σAB)=1+2?σ-1/2A⊗σ-1/2BσABσ-1/2A⊗σ-1/2B-1AB?∞.File in questo prodotto:
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