Universal Recovery Maps and Approximate Sufficiency of Quantum Relative Entropy

Marius Junge; Renato Renner; David Sutter; Mark M. Wilde; Andreas Winter

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Universal Recovery Maps and Approximate Sufficiency of Quantum Relative Entropy

机译：普遍恢复地图和量子相对熵的近似充足

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The data processing inequality states that the quantum relative entropy between two states $$ho $$ ρ and $$sigma $$ σ can never increase by applying the same quantum channel $$mathcal {N}$$ N to both states. This inequality can be strengthened with a remainder term in the form of a distance between $$ho $$ ρ and the closest recovered state $$(mathcal {R} circ mathcal {N})(ho )$$ ( R ° N ) ( ρ ) , where $$mathcal {R}$$ R is a recovery map with the property that $$sigma = (mathcal {R} circ mathcal {N})(sigma )$$ σ = ( R ° N ) ( σ ) . We show the existence of an explicit recovery map that is universal in the sense that it depends only on $$sigma $$ σ and the quantum channel $$mathcal {N}$$ N to be reversed. This result gives an alternate, information-theoretic characterization of the conditions for approximate quantum error correction.

机译：数据处理不等式状态表示两种状态之间的量子相对熵$$ rho $$ρ和$$ sigma $$Σ可以通过应用相同的量子通道$$ mathcal {n} $ n至两个状态来增加。这种不平等可以通过剩余的术语以$$ rho $$ρ和最接近的恢复状态$$（ mathcal {r} circ mathcal {n}）（ rho）$$之间的剩余术语来加强（R°N）（ρ），其中$$ Mathcal {R} $$ R是带有$$ sigma =（ MATHCAL {R} CIRC MATHCAL {N}）的属性的恢复映射（ SIGMA ）$$σ=（r°n）（σ）。我们展示了一个明确的恢复映射，这是一个普遍的意义，即它仅取决于$$ sigma $$σ和量子通道$$ mathcal {n} $$ n。该结果给出了近似量子误差校正的条件的替代，信息理论表征。

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《Annales Henri Poincare》 |2018年第10期|共24页
作者
Marius Junge; Renato Renner; David Sutter; Mark M. Wilde; Andreas Winter;
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作者单位

Department of Mathematics University of Illinois at Urbana-Champaign;

Institute for Theoretical Physics ETH Zurich;

Institute for Theoretical Physics ETH Zurich;

Department of Physics and Astronomy Center for Computation and Technology Hearne Institute for Theoretical Physics Louisiana State University;

ICREA &

Física Teòrica: Informació i Fenòmens Quàntics Universitat Autònoma de Barcelona;

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正文语种 eng
中图分类理论物理学;
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专利

1. Universal Recovery Maps and Approximate Sufficiency of Quantum Relative Entropy [J] . Marius Junge, Renato Renner, David Sutter, Annales Henri Poincare . 2018,第10期

机译：普遍恢复地图和量子相对熵的近似充足
2. Universal recovery map for approximate Markov chains [J] . Sutter David, Fawzi Omar, Renner Renato Proceedings of the Royal Society. Mathematical, physical and engineering sciences . 2016,第2186期

机译：近似马尔可夫链的通用恢复图
3. Strengthened Monotonicity of Relative Entropy via Pinched Petz Recovery Map [J] . David Sutter, Marco Tomamichel, Aram W. Harrow IEEE Transactions on Information Theory . 2016,第5期

机译：通过捏Petz恢复图增强相对熵的单调性
4. Universal Non-destructive Estimation of Quantum Relative Entropy [C] . Alexei Kaltchenko IEEE International Symposium on Information Theory . 2004

机译：万能非破坏性估计量子相对熵
5. On the necessity and sufficiency of universals. [D] . Borghini, Andrea. 2007

机译：论普遍性的必要性和充分性。
6. Universal recovery map for approximate Markov chains [O] . David Sutter, Omar Fawzi, Renato Renner -1

机译：近似马尔可夫链的通用恢复图
7. Universal recovery from a decrease of quantum relative entropy [O] . Junge, Marius, Renner, Renato, Sutter, David, 2016

机译：从量子相对熵的减少中普遍恢复

Universal Recovery Maps and Approximate Sufficiency of Quantum Relative Entropy

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