Discriminating mixed qubit states with collective measurements

TL;DR

This paper demonstrates an experimental protocol using collective measurements on a quantum processor to distinguish two copies of qubit states with lower error probability than separable measurements, highlighting the advantage of collective strategies.

Contribution

It introduces and experimentally verifies a collective measurement protocol for two-qubit states with unequal priors, outperforming non-entangling measurements, on a superconducting quantum processor.

Findings

Collective measurements on two qubits outperform separable measurements in state discrimination.

Three and four copy collective measurements performed poorly compared to two-copy measurements.

Experimental implementation on IBM Q System One confirms theoretical advantages.

Abstract

It is a central fact in quantum mechanics that non-orthogonal states cannot be distinguished perfectly. This property ensures the security of quantum key distribution. It is therefore an important task in quantum communication to design and implement strategies to optimally distinguish quantum states. In general, when we have access to multiple copies of quantum states the optimal measurement will be a collective measurement. However, to date, collective measurements have not been used to enhance quantum state discrimination. One of the main reasons for this is the fact that, in the usual state discrimination setting with equal prior probabilities, at least three copies of a quantum state are required to be measured collectively to outperform separable measurements. This is very challenging experimentally. In this work, by considering unequal prior probabilities, we propose and experimentally demonstrate a protocol for distinguishing two copies of single qubit states using collective measurements which achieves a lower probability of error than can be achieved by any non-entangling measurement. We implement our measurements on an IBM Q System One device, a superconducting quantum processor. Additionally, we implemented collective measurements on three and four copies of the unknown state and found they performed poorly.