Uncertainty of quantum channels via modified generalized variance and modified generalized Wigner-Yanase-Dyson skew information

TL;DR

This paper introduces new measures for quantifying uncertainty in quantum channels using modified generalized variance and skew information, exploring their properties, relationships with entanglement and entropy, and proposing an experimental measurement scheme.

Contribution

It develops novel uncertainty measures for quantum channels, analyzes their properties and relationships with quantum information quantities, and suggests an experimental approach for measurement.

Findings

Total uncertainty properties are thoroughly analyzed.

Trade-off relations between uncertainty and entanglement fidelity are established.

An experimental measurement scheme using Mach-Zehnder interferometer is proposed.

Abstract

Uncertainty relation is a fundamental issue in quantum mechanics and quantum information theory. By using modified generalized variance (MGV), and modified generalized Wigner-Yanase-Dyson skew information (MGWYD), we identify the total and quantum uncertainty of quantum channels. The elegant properties of the total uncertainty of quantum channels are explored in detail. In addition, we present a trade-off relation between the total uncertainty of quantum channels and the entanglement fidelity and establish the relationships between the total uncertainty and entropy exchange/coherent information. Detailed examples are given to the explicit formulas of the total uncertainty and the quantum uncertainty of quantum channels. Moreover, utilizing a realizable experimental measurement scheme by using the Mach-Zehnder interferometer proposed in Nirala et al. (Phys Rev A 99:022111, 2019), we discuss how to measure the total/quantum uncertainty of quantum channels for pure states.