Experimental demonstration of optimal unambiguous two-out-of-four quantum state elimination

TL;DR

This paper demonstrates an experimental method to unambiguously exclude two out of four non-orthogonal quantum states using a six-outcome measurement on single photons, achieving high accuracy.

Contribution

It presents the first experimental realization of a quantum state elimination measurement for two-out-of-four states with minimal error and high success probability.

Findings

Incorrect ruling out rate of 3.3%

Implementation using four-dimensional photon states

Unambiguous exclusion of two states achieved

Abstract

A core principle of quantum theory is that non-orthogonal quantum states cannot be perfectly distinguished with single-shot measurements. However, it is possible to exclude a subset of non-orthogonal states without error in certain circumstances. Here we implement a quantum state elimination measurement which unambiguously rules out two of four pure, non-orthogonal quantum states -- ideally without error and with unit success probability. This is a generalised quantum measurement with six outcomes, where each outcome corresponds to excluding a pair of states. Our experimental realisation uses single photons, with information encoded in a four-dimensional state using optical path and polarisation degrees of freedom. The prepared state is incorrectly ruled out up to $3.3(2)\%$ of the time.