Sequential scheme for locally discriminating bipartite unitary operations without inverses

TL;DR

This paper proves that any two bipartite unitary operations can be locally distinguished using a sequential scheme without requiring their inverses, broadening the method's applicability and experimental feasibility.

Contribution

It removes previous limitations by showing the sequential discrimination scheme works for any bipartite unitaries without needing their inverses.

Findings

Sequential scheme applicable to all bipartite unitaries

No need for inverse operations in discrimination

Enhances experimental feasibility of local discrimination

Abstract

Local distinguishability of bipartite unitary operations has recently received much attention. A nontrivial and interesting question concerning this subject is whether there is a sequential scheme for locally discriminating between two bipartite unitary operations, because a sequential scheme usually represents the most economic strategy for discrimination. An affirmative answer to this question was given in the literature, however with two limitations: (i) the unitary operations to be discriminated were limited to act on $d\otimes d$, i.e., a two-qudit system, and (ii) the inverses of the unitary operations were assumed to be accessible, although this assumption may be unrealizable in experiment. In this paper, we improve the result by removing the two limitations. Specifically, we show that any two bipartite unitary operations acting on $d_A\otimes d_B$ can be locally discriminated by a sequential scheme, without using the inverses of the unitary operations. Therefore, this paper enhances the applicability and feasibility of the sequential scheme for locally discriminating unitary operations.