A note on uncertainty relations of arbitrary N quantum channels

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.

12 pages, 2 figures

References in corpus (4)

• Conjectured Strong Complementary Information Tradeoff
• Entropic uncertainty relation for mutually unbiased bases
• Rényi entropy uncertainty relation for successive projective measurements
• Discording power of quantum evolutions

Cited by in corpus (4)

• Product and sum uncertainty relations based on metric-adjusted skew information
• Sum uncertainty relations based on $(\alpha ,\beta ,\gamma )$ weighted Wigner-Yanase-Dyson skew information
• Enhanced quantum channel uncertainty relations by skew information
• Mixed-permutation channel with its application to estimate quantum coherence