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Joint IFSA World Congress and NAFIPS International Conference

Characterizing quantum channels via Wigner-Yanase skew information

Zhihua Zhang, Lan Shu, Zhiwen Mo, Jun Ping Zheng

Published Jun 1, 2013• 0 citations
Publisher

Abstract

Based on the Wigner-Yanase skew information, we introduce a new measure to characterize the difference of the global information content with respect to the local operations. The effectiveness of the measure is shown by several examples. By comparing with the decoherent information of a quantum channel, we conclude that the measure can be used as an alternative quantity in the description of capability of quantum channels, which is in term of skew information, instead of von Neumann entropy.

DOI
10.1109/ifsa-nafips.2013.6608618

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Based on the Wigner-Yanase skew information, we introduce a new measure to characterize the difference of the global information content with respect to the local operations. The effectiveness of the measure is shown by several examples. By comparing with the decoherent information of a quantum channel, we conclude that the measure can be used as an alternative quantity in the description of capability of quantum channels, which is in term of skew information, instead of von Neumann entropy.
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In order to quantify the information content of quantum states in the presence of conserved quantities, Wigner and Yanase introduced the notion of skew information [Proc. Natl. Acad. Sci. USA 49, 910, (1963)], which was later identified as a paradigmatic version of quantum Fisher information. The skew information is quite different from, yet deeply connected with, the ubiquitous quantum entropies and has important applications in quantum theory. In this paper, pursuing further the original idea of Wigner and Yanase, we propose a measure for correlations in terms of the skew information, investigate its fundamental properties, and elucidate its characteristics. An appealing feature of this measure for correlations is that its evaluation does not involve any optimization, in sharp contrast to the entanglement and discord measures, and can be straightforwardly calculated. In particular, the algorithm and explicit formulas for general bipartite states are prescribed, and simple analytical expressions for some special states, including arbitrary bipartite pure states, the Bell-diagonal states, and some highly symmetric states such as the Werner states and the isotropic states, are obtained.
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.
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Skew information was introduced by Wigner and Yanase in the context of quantum measurements. It was later recognized that skew information in addition to its original significance as a measure of the information content of states admits several interpretations of a more physical and information theory nature. This quantity has now found many applications in quantum information. An intriguing and subtle feature of skew information is the involvement of the square root of quantum states (density operators). Comparing skew information with some of its natural modifications reveals mathematical and also physical reasons for using the square root. We further use skew information to quantify the asymmetry of quantum states with respect to group representations.