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Modern Physics Letters A

Quantifying coherence via the generalized Wigner–Yanase–Dyson skew information

Yajing Fan, X. Guo, Zhihua Guo, M. Zhang

Published Feb 28, 2024• 7 citations
Publisher

Abstract

Quantum coherence is an important feature that distinguishes quantum mechanics from classical physics. In this paper, we study the coherence of a quantum state with respect to a quantum channel, and introduce a coherence measure in terms of the generalized Wigner–Yanase–Dyson skew information. The basic properties and operational significance of the measure are expounded in detail, which shows that it is indeed a veritable quantity and satisfies many desirable conditions intuitively required for the coherence measures. We illustrate the significance of characterizing channels from the coherence perspective through some examples. Finally, we consider the average coherence of a state based on the generalized Wigner–Yanase–Dyson skew information with respect to any complete mutually unbiased bases in prime power dimensional systems, as well as with respect to all orthonormal bases, and show that these two averages are equivalent since they both can be seen as the coherence of the quantum state with respect to the depolarizing quantum channel.

DOI
10.1142/s0217732324500111

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Quantum coherence is an important feature that distinguishes quantum mechanics from classical physics. In this paper, we study the coherence of a quantum state with respect to a quantum channel, and introduce a coherence measure in terms of the generalized Wigner–Yanase–Dyson skew information. The basic properties and operational significance of the measure are expounded in detail, which shows that it is indeed a veritable quantity and satisfies many desirable conditions intuitively required for the coherence measures. We illustrate the significance of characterizing channels from the coherence perspective through some examples. Finally, we consider the average coherence of a state based on the generalized Wigner–Yanase–Dyson skew information with respect to any complete mutually unbiased bases in prime power dimensional systems, as well as with respect to all orthonormal bases, and show that these two averages are equivalent since they both can be seen as the coherence of the quantum state with respect to the depolarizing quantum channel.
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Nonclassical correlations are significant physical resources with extensive applications in quantum information processing. We introduce the modified Wigner-Yanase-Dyson skew information of a quantum state relative to a quantum channel, and a quantitative measure of quantum correlations. Their basic properties are explored in detail. Through a specific example, we also compare our correlations measure with the existing one. Moreover, the correlations relative to various channels including the von Neumann measurements, the unitary channels and the twirling channels are analyzed.
Abstract Uncertainty principle plays a vital role in quantum physics. The Wigner–Yanase skew information characterizes the uncertainty of an observable with respect to the measured state. We generalize the uncertainty relations for two quantum channels to arbitrary N quantum channels based on Wigner–Yanase skew information. We illustrate that these uncertainty inequalities are tighter than the existing ones by detailed examples. Especially, we also discuss the uncertainty relations for N unitary channels, which could be regarded as variance-based sum uncertainty relations with respect to any pure state.