Success probabilities for universal unambiguous discriminators between unknown pure states

TL;DR

This paper derives the success probabilities of optimal universal unambiguous discriminators for unknown pure states, showing they are independent of dimension and approach classical limits with increasing copies.

Contribution

It provides analytic expressions for success probabilities and reveals their independence from the dimension, advancing understanding of universal state discrimination.

Findings

Success probabilities are independent of the dimension d.

Success probabilities approach those of classical unambiguous discrimination as copies increase.

Analytic expressions for optimal measurement operators are derived.

Abstract

A universal programmable discriminator can perform the discrimination between two unknown states, and the optimal solution can be approached via the discrimination between the two averages over the uniformly distributed unknown input pure states, which has been widely discussed in previous works. In this paper, we consider the success probabilities of the optimal universal programmable unambiguous discriminators when applied to the pure input states. More precisely, the analytic results of the success probabilities are derived with the expressions of the optimal measurement operators for the universal discriminators and we find that the success probabilities have nothing to do with the dimension d while the amounts of the copies in the two program registers are equal. The success probability of programmable unambiguous discriminator can asymptoticly approach to that of usual unambiguous discrimination (state comparison) as the number of copies in program registers (data register) goes to infinity.