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

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.