A note on uncertainty relations of arbitrary N quantum channels

TL;DR

This paper generalizes uncertainty relations for multiple quantum channels using Wigner-Yanase skew information, providing tighter bounds and special cases for unitary channels, advancing understanding of quantum measurement uncertainties.

Contribution

It introduces generalized uncertainty relations for N quantum channels based on Wigner-Yanase skew information, including unitary channels, improving upon existing bounds.

Findings

Uncertainty inequalities are tighter than previous ones.

Derived uncertainty relations for N unitary channels.

Applicable to arbitrary pure states.

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.