Parallel distinguishability of quantum operations

TL;DR

This paper investigates when two quantum operations can be perfectly distinguished using parallel schemes, linking this to properties of associated operator subspaces and providing conditions for specific cases.

Contribution

It establishes a connection between quantum operation distinguishability and operator subspaces, offering a new framework for analyzing parallel distinguishability.

Findings

Parallel distinguishability depends on an operator subspace generated by Choi-Kraus operators.

A necessary and sufficient condition is provided for one-dimensional or Hermitian subspaces.

Non-existence of positive definite operators in the subspace is key for distinguishability.

Abstract

We find that the perfect distinguishability of two quantum operations by a parallel scheme depends only on an operator subspace generated from their Choi-Kraus operators. We further show that any operator subspace can be obtained from two quantum operations in such a way. This connection enables us to study the parallel distinguishability of operator subspaces directly without explicitly referring to the underlining quantum operations. We obtain a necessary and sufficient condition for the parallel distinguishability of an operator subspace that is either one-dimensional or Hermitian. In both cases the condition is equivalent to the non-existence of positive definite operator in the subspace, and an optimal discrimination protocol is obtained. Finally, we provide more examples to show that the non-existence of positive definite operator is sufficient for many other cases, but in general it is only a necessary condition.