How to Device-Independently Generate States for Which Unambiguous State Discrimination is Impossible

TL;DR

This paper presents a device-independent method to generate quantum states for which unambiguous state discrimination cannot be performed, based on a non-signaling black box framework.

Contribution

It introduces a formula for non-signaling black boxes and demonstrates how to generate states that defy unambiguous discrimination, independent of device imperfections.

Findings

Derived a formula for non-signaling black boxes.

Proved that certain generated states cannot be unambiguously discriminated.

Applicable to any device, perfect or imperfect.

Abstract

We describe how to device-independently generate a set of quantum states for which unambiguous state discrimination is not possible. First, we derive a formula that a certain non-signaling black box must satisfy. Then, we describe how to generate a set of quantum states. Devices for generating states and possible measurements on the states can be put into a black box. Because this black box is non-signaling, it satisfies the formula. Using the formula, we prove that unambiguous state discrimination is not possible for the generated states. Because we did not consider internal mechanisms but only outcomes, our argument is valid for any (imperfect) devices.