The quantum uncertainty relations of quantum channels

TL;DR

This paper explores the fundamental limits of quantum channels' uncertainties in qubit systems, deriving new relations based on coherence measures under different measurement bases.

Contribution

It introduces novel quantum uncertainty relations for quantum channels in qubit systems, focusing on relative entropy and $l_1$ norm of coherence, expanding understanding of quantum measurement limits.

Findings

Derived uncertainty relations for quantum channels using relative entropy of coherence.

Established uncertainty bounds for unitary channels with respect to the $l_1$ norm of coherence.

Provided detailed examples illustrating the theoretical results.

Abstract

The uncertainty relation reveals the intrinsic difference between the classical world and the quantum world. We investigate the quantum uncertainty relation of quantum channel in qubit systems. Under two general measurement bases, we first derive the quantum uncertainty relation for quantum channels with respect to the relative entropy of coherence. Then we obtain the quantum uncertainty relation for unitary channels with respect to the $l_1$ norm of coherence. Some examples are given in detail.