Distinguishing computable mixtures of quantum states

TL;DR

This paper presents a protocol to distinguish algorithmic mixtures of pure quantum states from the maximally mixed state with high success probability, and demonstrates a proof-of-concept experiment involving pseudorandomness in state preparation.

Contribution

It introduces a finite-time, high-success protocol for distinguishing certain quantum state mixtures and explores the role of pseudorandomness in quantum state preparation.

Findings

Protocol achieves high success probability in finite time

Distinguishes algorithmic mixtures from maximally mixed states

Pseudorandomness can make different quantum sequences distinguishable

Abstract

In this article we extend results from our previous work [Bendersky, de la Torre, Senno, Figueira and Ac\'in, Phys. Rev. Lett. 116, 230406 (2016)] by providing a protocol to distinguish in finite time and with arbitrarily high success probability any algorithmic mixture of pure states from the maximally mixed state. Moreover, we introduce a proof-of-concept experiment consisting in a situation where two different random sequences of pure states are prepared; these sequences are indistinguishable according to quantum mechanics, but they become distinguishable when randomness is replaced with pseudorandomness within the preparation process.