Superadditivity of Quantum Relative Entropy for General States

Angela Capel; Angelo Lucia; David Perez-Garcia

doi:10.1109/TIT.2017.2772800

Superadditivity of Quantum Relative Entropy for General States

Angela Capel, Angelo Lucia, David Perez-Garcia

Department of Mathematical Sciences

1 Citation (Scopus)

Abstract

The property of superadditivity of the quantum relative entropy states that, in a bipartite system H_AB=H_A⊗HB , for every density operator Ρ_AB , one has D(Ρ_AB||σ_A⊗σB)=D(Ρ_A||σ_A)+D(ΡB||σB) . In this paper, we provide an extension of this inequality for arbitrary density operators σ_AB . More specifically, we prove that a(σ_AB)D(Ρ_AB||σ_AB)=D(Ρ_A||σ_A)+D(ΡB||σB) holds for all bipartite states Ρ_AB and σ_AB , where a(σ_AB)=1+2?σ^-1/2A⊗σ^-1/2Bσ_ABσ^-1/2A⊗σ^-1/2B-1_AB?∞.

Original language	English
Journal	IEEE Transactions on Information Theory
Volume	64
Issue number	7
Pages (from-to)	4758-4765
ISSN	0018-9448
DOIs	https://doi.org/10.1109/TIT.2017.2772800
Publication status	Published - Jul 2018

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10.1109/TIT.2017.2772800

http://arxiv.org/abs/1705.03521

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title = "Superadditivity of Quantum Relative Entropy for General States",

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?∞.",

author = "Angela Capel and Angelo Lucia and David Perez-Garcia",

year = "2018",

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doi = "10.1109/TIT.2017.2772800",

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T1 - Superadditivity of Quantum Relative Entropy for General States

AU - Capel, Angela

AU - Lucia, Angelo

AU - Perez-Garcia, David

PY - 2018/7

Y1 - 2018/7

N2 - 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?∞.

AB - 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?∞.

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DO - 10.1109/TIT.2017.2772800

M3 - Journal article

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VL - 64

SP - 4758

EP - 4765

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 7

ER -

Superadditivity of Quantum Relative Entropy for General States

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