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• W3103289615 abstract "A central question in quantum information theory is to determine how well lost information can be reconstructed. Crucially, the corresponding recovery operation should perform well without knowing the information to be reconstructed. In this work, we show that the quantum conditional mutual information measures the performance of such recovery operations. More precisely, we prove that the conditional mutual information I ( A : C | B ) of a tripartite quantum state ρ ABC can be bounded from below by its distance to the closest recovered state <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msub> <mml:mrow> <mml:mi mathvariant=script>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo stretchy=false>→</mml:mo> <mml:mi>B</mml:mi> <mml:mi>C</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mrow> <mml:mi>A</mml:mi> <mml:mi>B</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy=false>)</mml:mo> </mml:math> , where the C -part is reconstructed from the B -part only and the recovery map <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msub> <mml:mrow> <mml:mi mathvariant=script>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo stretchy=false>→</mml:mo> <mml:mi>B</mml:mi> <mml:mi>C</mml:mi> </mml:mrow> </mml:msub> </mml:math> merely depends on ρ BC . One particular application of this result implies the equivalence between two different approaches to define topological order in quantum systems." @default.
• W3103289615 created "2020-11-23" @default.
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• W3103289615 date "2016-02-01" @default.
• W3103289615 modified "2023-10-12" @default.
• W3103289615 title "Universal recovery map for approximate Markov chains" @default.
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• W3103289615 doi "https://doi.org/10.1098/rspa.2015.0623" @default.
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