Distinguishing quantum operations having few Kraus operators

TL;DR

This paper offers an alternative proof for bounds on the auxiliary system size needed to distinguish quantum operations, emphasizing cases with few Kraus operators and leveraging familiar quantum information concepts.

Contribution

It provides a new proof for bounds on auxiliary system dimensions required for optimal quantum operation discrimination, focusing on operations with few Kraus operators.

Findings

Optimal distinguishability bounds depend on Kraus operator count.

An alternative proof for the auxiliary dimension bound is presented.

The proof uses standard quantum information theory tools.

Abstract

Entanglement is sometimes helpful in distinguishing between quantum operations, as differences between quantum operations can become magnified when their inputs are entangled with auxiliary systems. Bounds on the dimension of the auxiliary system needed to optimally distinguish quantum operations are known in several situations. For instance, the dimension of the auxiliary space never needs to exceed the dimension of the input space of the operations for optimal distinguishability, while no auxiliary system whatsoever is needed to optimally distinguish unitary operations. Another bound, which follows from work of R. Timoney, is that optimal distinguishability is always possible when the dimension of the auxiliary system is twice the number of operators needed to express the difference between the quantum operations in Kraus form. This paper provides an alternate proof of this fact that is based on concepts and tools that are familiar to quantum information theorists.