Quantifying coherence of quantum channels via trace distance

Fan, Yajing; Guo, Xulin; Yang, Xiangdong

doi:10.1007/s11128-022-03683-7

Cited by 4 publications

(8 citation statements)

References 34 publications

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“…Otherwise, they are only DIOs. These results further improve the conclusions of [33], and imply that our dephasing diamond measure can capture more dynamical coherence including coherence storage ability.…”

Section: Introductionsupporting

confidence: 78%

“…This means that the global coherence does not exceed the sum of the coherence of ρ 0 and E ′ . The form of this upper bound is similar with upper bounds for the coherence measure C l0 (E) defined by the Choi matrix [37] and the channel coherence measure C(E) introduced in [33].…”

Section: Proposition 5 (Amortization Inequality) For Any Channel E ∈ ...mentioning

confidence: 69%

“…Hence, C(E p ) = 0, then we only know that E p is a detection-creation-incoherent operation or DIO. This means our dynamical coherence measure C ∆ ⋄ can capture more dynamic coherence resources than the detection-creation-incoherent measure in [33]. Remark 6.…”

Section: Examplesmentioning

confidence: 94%

“…Particularly, the amplitude damping channel E AD with p = 1, the depolarizing channel E D with p = 1 and the phase damping channel E Z with p = 1 2 are classical channels. Otherwise, E AD , E D and E Z always are DIOs since it was proved that [33]. Moreover, both E Z with p = 1 and E D with p = 0 reduce to the identity channel id, then C ∆ ⋄ (id) = 1, but C(id) = 0.…”

Section: Examplesmentioning

confidence: 99%

“…In [32], the authors propose a measure of nonclassicality of a quantum operation utilizing the relative entropy to quantify its commutativity with the completely dephasing operation. Fan et al [33] use trace distance to replace relative entropy to quantify the nonclassicality of a quantum operation. Indeed, these two measures quantify the detection-creation coherence of quantum channels using the DIOs as free channels.…”

Section: Introductionmentioning

confidence: 99%

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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: Introductionsupporting

confidence: 78%

Section: Proposition 5 (Amortization Inequality) For Any Channel E ∈ ...mentioning

confidence: 69%

Section: Examplesmentioning

confidence: 94%

Section: Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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