Tight bounds on the distinguishability of quantum states under separable measurements

TL;DR

This paper investigates the limits of distinguishing multipartite quantum states using separable measurements, providing bounds and examples where these bounds are tight, and exploring the relationship between success probability and fidelity.

Contribution

It characterizes the distinguishability of quantum states under separable measurements, deriving bounds and demonstrating cases where these bounds are optimal, including the relation between success probability and fidelity.

Findings

Bounds on separable fidelity are established and shown to be tight in certain cases.

Optimal strategies for orthogonal states maximize both success probability and fidelity.

Examples demonstrate that fidelity and success probability can differ depending on state orthogonality.

Abstract

One of the many interesting features of quantum nonlocality is that the states of a multipartite quantum system cannot always be distinguished as well by local measurements as they can when all quantum measurements are allowed. In this work, we characterize the distinguishability of sets of multipartite quantum states when restricted to separable measurements -- those which contain the class of local measurements but nevertheless are free of entanglement between the component systems. We consider two quantities: The separable fidelity -- a truly quantum quantity -- which measures how well we can "clone" the input state, and the classical probability of success, which simply gives the optimal probability of identifying the state correctly. We obtain lower and upper bounds on the separable fidelity and give several examples in the bipartite and multipartite settings where these bounds are optimal. Moreover the optimal values in these cases can be attained by local measurements. We further show that for distinguishing orthogonal states under separable measurements, a strategy that maximizes the probability of success is also optimal for separable fidelity. We point out that the equality of fidelity and success probability does not depend on an using optimal strategy, only on the orthogonality of the states. To illustrate this, we present an example where two sets (one consisting of orthogonal states, and the other non-orthogonal states) are shown to have the same separable fidelity even though the success probabilities are different.