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

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.