Upper bounds on probabilities in channel measurements on qubit channels and their applications

TL;DR

This paper derives upper bounds on measurement outcome probabilities for specific quantum channels and demonstrates their importance through applications in channel convertibility and detection.

Contribution

It introduces new upper bounds for probabilities in quantum channel measurements and applies them to channel convertibility and detection problems.

Findings

Derived upper bounds for probabilities in quantum channel measurements.

Applied bounds to channel convertibility and detection.

Showed bounds' significance in quantum information tasks.

Abstract

One of the fundamental tasks in quantum information processing is to measure the quantum channels. Similar to measurements of quantum states, measurements of quantum channels are inherently stochastic, that is, quantum theory provides a formula to calculate the probability of obtaining an outcome. The upper bound on each probability associated with the measurement outcome of the quantum channels is a fundamental and important quantity. In this study, we derived the upper bounds of the probability in a channel measurement for specific classes of quantum channels. We also present two applications for the upper bounds. The first is the notion of convertibility considered by Alberti and Uhlmann and the second is the detection problem of a quantum channel. These applications demonstrate the significance of the obtained upper bounds.