Antidistinguishability of Pure Quantum States

TL;DR

This paper investigates the algebraic conditions for antidistinguishability of pure quantum states, providing new criteria and analyzing how many states need to be added to achieve antidistinguishability, with implications for quantum foundations.

Contribution

It introduces a novel sufficient condition for antidistinguishability of pure quantum states and explores how many states must be added to make a set antidistinguishable.

Findings

A new sufficient algebraic condition for antidistinguishability is proposed.

In qubit systems, adding one state suffices to make a set antidistinguishable.

In finite-dimensional systems, at most n states need to be added, where n is the set size.

Abstract

The Pusey-Barrett-Rudolph theorem has recently provoked a lot of discussion regarding the reality of the quantum state. In this article we focus on a property called antidistinguishability, which is a main component in constructing the proof for the PBR theorem. In particular we study algebraic conditions for a set of pure quantum states to be antidistinguishable, and a novel sufficient condition is presented. We also discuss a more general criterion which can be used to show that the sufficient condition is not necessary. Lastly, we consider how many quantum states needs to be added into a set of pure quantum states in order to make the set antidistinguishable. It is shown that in the case of qubit states the answer is one, while in the general but finite dimensional case the answer is at most $n$, where $n$ is the size of the original set.