An Alternative Framework For Quantifying Coherence Of Quantum Channels

Kong, Shi-Yun; Wu, Ya-Juan; Lv, Qiao-Qiao; Wang, Zhi‐Xi; Fei, Shao-Ming

doi:10.1007/s10773-022-05100-2

Cited by 4 publications

(2 citation statements)

References 32 publications

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“…Then, the maximum relative entropy of coherence for quantum channels [38], and skew information and Hellinger distance of coherence for quantum channels [39] are given using Choi states. Recently, an equivalent framework of [37] is introduced in [40]. Note that the difference between [35] and [37] is that the former uses the generalized channel divergence as a channel measure to quantify the channel coherence, while the latter argues that quantifying the coherence of the channel is equivalent to quantifying the coherence of the corresponding Choi state.…”

Section: Introductionmentioning

confidence: 99%

Quantifying channel coherence via the norm distance

Ye,

Luo,

2023

J. Phys. A: Math. Theor.

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Quantifying the number of resources contained in a physical object has been one of the core topics in the resource theory of coherence. In this paper, we introduce the dynamical coherence measures based on a class of norms in the classical channel setting. It is proved that it satisfies faithfulness, decreases monotonically under the maximally incoherent superchannels, and is convex. Moreover, we show that it satisfies subadditivity under both the composition and tensor product of channels. Especially, the diamond measure as a special case is discussed in detail, it can reduce to trace norm of coherence, satisfies amortization inequality, and can be calculated efficiently using a semidefinite program. In addition, we introduce the creation-coherent diamond measure and find that neither the detection coherence nor the creation coherence of a channel exceeds the coherence of the channel, which does not exceed the purity of the channel. Second, we introduce the corresponding dephasing measure, which is a dynamical coherence measure under the dephasing-covariant incoherent superchannels. Meanwhile, we also introduce the dephasing diamond measure as a special case. Third, we use the dephasing diamond measure to accurately calculate the coherence values of some important noisy channels such as amplitude damping channel, phase damping channel, and depolarizing channel, respectively, and give the sufficient and necessary conditions for an unital qubit channel with a parameter probability vector to be a coherent channel. Finally, the operational interpretation of our diamond measure in the binary channel discrimination task is investigated.

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Section: Introductionmentioning

confidence: 99%

Quantifying channel coherence via the norm distance

Ye,

Luo,

2023

J. Phys. A: Math. Theor.

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“…Luo et al [37] introduced the coherence weight of quantum channels to investigate the quantum resource theory of dynamical coherence. Kong et al [38] presented an alternative framework to quantify the coherence of quantum channels.…”

Section: Introductionmentioning

confidence: 99%

Coherence monotones of quantum channels based on two generalized quantum relative entropies

Fan,

Wu,

Fei

2023

Laser Phys. Lett.

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By using the Choi–Jamiołkowski isomorphism, we propose two classes of coherence monotones of quantum channels based on the unified (r, s)-relative entropy and the sandwiched Rényi relative entropy. Elegant properties of the coherence monotones for quantum channels are explored. Moreover, we present the upper bounds of the coherence monotones and derive the explicit formulas of the coherence monotones for qubit unitary channels.

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