Optimum unambiguous identification of d unknown pure qudit states

TL;DR

This paper derives the optimal measurement strategy for unambiguously identifying an unknown pure qudit state among d reference states, maximizing success probability without prior knowledge of the states.

Contribution

It provides the explicit form of the optimal measurement operators and success probability for unambiguous identification of unknown pure qudit states.

Findings

Optimal measurement strategy is a generalized measurement.

Explicit measurement operators and success probability are derived.

Addresses unambiguous discrimination of d unknown mixed states.

Abstract

We address the problem of unambiguously identifying the state of a probe qudit with the state of one of d reference qudits. The reference states are assumed pure and linearly independent but we have no knowledge of them. The state of the probe qudit is assumed to coincide equally likely with either one of the d unknown reference states. We derive the optimum measurement strategy that maximizes the success probability of unambiguous identification and find that the optimum strategy is a generalized measurement. We give both the measurement operators and the optimum success probability explicitly. Technically, the problem we solve amounts to the optimum unambiguous discrimination of d known mixed quantum states.