Unambiguous comparison of unitary channels

TL;DR

This paper investigates how to unambiguously compare two unknown qudit unitary channels using process POVMs, highlighting entanglement as essential for optimality and proposing an experimentally feasible scheme.

Contribution

It characterizes all solutions for unambiguous comparison of unitary channels and identifies the role of entanglement as crucial for optimal performance.

Findings

Entanglement is necessary for optimal comparison.

The scheme achieves optimal unambiguous discrimination.

The proposed method is experimentally feasible.

Abstract

We address the problem of unambiguous comparison of a pair of unknown qudit unitary channels. Using the framework of process positive operator valued measures (PPOVM) we characterize all solutions and identify the optimal ones. We prove that the entanglement is the key ingredient in designing the optimal experiment for comparison of unitary channels. Without entanglement the optimality can not be achieved. The proposed scheme is also experimentally feasible.