Tight bounds on the distinguishability of quantum states under separable measurements

SMC Author

Michael Nathanson

SMC Affiliated Work

1

Status

Faculty

School

School of Science

Department

Math/Computer Science

Document Type

Article

Publication Date

11-2013

Publication / Conference / Sponsorship

Physical Review A

Description/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 the 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 nonorthogonal states) are shown to have the same separable fidelity even though the success probabilities are different.

Scholarly

yes

DOI

10.1103/PhysRevA.88.052313

Volume

88

Issue

5

First Page

052313

Disciplines

Physics

Rights

Open Access. Author manuscript (arXiv)

Original Citation

Michael Nathanson (Mathematics and Computer Science): “Tight bounds on the distinguishability of quantum states under separable measurements,” with Somchubhro Bandyopadhyay, in Physical Review A 88 issue 5 (2013). https://doi.org/10.1103/PhysRevA.88.052313

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