scholarly journals Maximum relative entropy of coherence for quantum channels

2021 ◽  
Vol 64 (8) ◽  
Author(s):  
Zhi-Xiang Jin ◽  
Long-Mei Yang ◽  
Shao-Ming Fei ◽  
Xianqing Li-Jost ◽  
Zhi-Xi Wang ◽  
...  
Keyword(s):  
Relative Entropy ◽  
Quantum Channels ◽  
Relative Entropy Of Coherence

scholarly journals A strengthened data processing inequality for the Belavkin–Staszewski relative entropy

2019 ◽  
Vol 32 (02) ◽  
pp. 2050005 ◽  
Author(s):  
Andreas Bluhm ◽  
Ángela Capel
Keyword(s):  
Data Processing ◽  
Relative Entropy ◽  
Quantum Channels ◽  
Equality Case ◽  
Standard Formula ◽  
Conditional Expectations ◽  
Data Processing Inequality ◽  
Equivalent Conditions ◽  
Arbitrary Quantum

In this work, we provide a strengthening of the data processing inequality for the relative entropy introduced by Belavkin and Staszewski (BS-entropy). This extends previous results by Carlen and Vershynina for the relative entropy and other standard [Formula: see text]-divergences. To this end, we provide two new equivalent conditions for the equality case of the data processing inequality for the BS-entropy. Subsequently, we extend our result to a larger class of maximal [Formula: see text]-divergences. Here, we first focus on quantum channels which are conditional expectations onto subalgebras and use the Stinespring dilation to lift our results to arbitrary quantum channels.

Evolution of Relative Entropy of Coherence for Two Qubits States

2020 ◽  
Vol 59 (3) ◽  
pp. 873-883
Author(s):  
Yuanfeng Song ◽  
Yaokun Wang ◽  
Hui Tang ◽  
Zhixin Zhao
Keyword(s):  
Relative Entropy ◽  
Relative Entropy Of Coherence

scholarly journals Relating Entropies of Quantum Channels

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1028
Author(s):  
Dariusz Kurzyk ◽  
Łukasz Pawela ◽  
Zbigniew Puchała
Keyword(s):  
Relative Entropy ◽  
Upper Bound ◽  
Quantum Channel ◽  
Von Neumann Entropy ◽  
Quantum Channels ◽  
Von Neumann ◽  
Channel One ◽  
Depolarizing Channel

In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi–Jamiołkowski state. The second one is based on the relative entropy of the output of the extended channel relative to the output of the extended completely depolarizing channel. This entropy then needs to be optimized over all possible input states. Our results first show that the former entropy provides an upper bound on the latter. Next, we show that for unital qubit channels, this bound is saturated. Finally, we conjecture and provide numerical intuitions that the bound can also be saturated for random channels as their dimension tends to infinity.

scholarly journals Thermodynamic Implementations of Quantum Processes

2021 ◽  
Author(s):  
Philippe Faist ◽  
Mario Berta ◽  
Fernando G. S. L. Brandao
Keyword(s):  
Relative Entropy ◽  
Thermal State ◽  
Single Letter ◽  
Small Scale ◽  
Input State ◽  
Quantum Channels ◽  
Quantum Processes ◽  
Cost Rate ◽  
Fixed Input

AbstractRecent understanding of the thermodynamics of small-scale systems have enabled the characterization of the thermodynamic requirements of implementing quantum processes for fixed input states. Here, we extend these results to construct optimal universal implementations of a given process, that is, implementations that are accurate for any possible input state even after many independent and identically distributed (i.i.d.) repetitions of the process. We find that the optimal work cost rate of such an implementation is given by the thermodynamic capacity of the process, which is a single-letter and additive quantity defined as the maximal difference in relative entropy to the thermal state between the input and the output of the channel. Beyond being a thermodynamic analogue of the reverse Shannon theorem for quantum channels, our results introduce a new notion of quantum typicality and present a thermodynamic application of convex-split methods.

scholarly journals Optimal bounds on functions of quantum states under quantum channels

2016 ◽  
Vol 16 (9&10) ◽  
pp. 845-861
Author(s):  
Chi-Kwong Li ◽  
Diane Christine Pelejo ◽  
Kuo-Zhong Wang
Keyword(s):  
Relative Entropy ◽  
Scalar Function ◽  
Quantum States ◽  
Quantum Channels ◽  
Trace Distance ◽  
Optimal Bounds ◽  
Class Of Functions

Let ρ1, ρ2 be quantum states and (ρ1, ρ2) 7→ D(ρ1, ρ2) be a scalar function such as the trace distance, the fidelity, and the relative entropy, etc. We determine optimal bounds for D(ρ1, Φ(ρ2)) for Φ blongs to S for different class of functions D(·, ·), where S is the set of unitary quantum channels, the set of mixed unitary channels, the set of unital quantum channels, and the set of all quantum channels.

Cohering power and decohering power of Gaussian unitary operations

2019 ◽  
Vol 19 (7&8) ◽  
pp. 575-586
Author(s):  
Yangyang Wang ◽  
Xiaofei Qi ◽  
Jinchuan Hou ◽  
Rufen Ma
Keyword(s):  
Relative Entropy ◽  
Continuous Variable ◽  
Quantum States ◽  
Entropy Measure ◽  
Quantum Channels ◽  
Gaussian States ◽  
Basic Properties ◽  
Suitable Measure

Having a suitable measure to quantify the coherence of quantum states, a natural task is to evaluate the power of quantum channels for creating or destroying the coherence of input quantum states. In the present paper, by introducing the maximal coherent Gaussian states based on the relative entropy measure of coherence, we propose the (generalized) cohering power and the (generalized) decohering power of Gaussian unitary operations for continuous-variable systems. Some basic properties are obtained and the cohering power and decohering power of two special kinds of Gaussian unitary operations are calculated.

DISCRIMINATING QUANTUM CHANNELS WITH RELATIVE ENTROPY

2008 ◽  
Vol 22 (05) ◽  
pp. 313-322 ◽  
Author(s):  
TAO QIN ◽  
MEISHENG ZHAO ◽  
YONGDE ZHANG
Keyword(s):  
Relative Entropy ◽  
Quantum Channels ◽  
Gaussian Channels

We address the possibilities of distinguishing the quantum channels in terms of relative entropy. Particularly, depolarizing channels and bosonic Gaussian channels are considered. To some extent, the relative entropy can be treated as a measure to discriminate the quantum channels.

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