Decision problems with quantum black boxes

TL;DR

This paper explores methods for distinguishing unknown unitary operators using quantum programs, optimizing strategies to minimize applications and improve discrimination accuracy, including entangled states and complex comparisons.

Contribution

It introduces new strategies for quantum operator discrimination that outperform simple pairwise comparisons, especially with limited applications of program transforms.

Findings

Unambiguous and minimum-error discrimination are achievable with suitable input states.

Complex strategies outperform pairwise comparisons in certain scenarios.

Entanglement enhances the discrimination process.

Abstract

We examine how to distinguish between unitary operators, when the exact form of the possible operators is not known. Instead we are supplied with "programs" in the form of unitary transforms, which can be used as references for identifying the unknown unitary transform. All unitary transforms should be used as few times as possible. This situation is analoguous to programmable state discrimination. One difference, however, is that the quantum state to which we apply the unitary transforms may be entangled, leading to a richer variety of possible strategies. By suitable selection of an input state and generalized measurement of the output state, both unambiguous and minimum-error discrimination can be achieved. Pairwise comparison of operators, comparing each transform to be identified with a program transform, is often a useful strategy. There are, however, situations in which more complicated strategies perform better. This is the case especially when the number of allowed applications of program operations is different from the number of the transforms to be identified.