Demonstration of quantum-limited discrimination of multi-copy pure versus mixed states

TL;DR

This paper demonstrates an optical receiver that reaches the quantum Chernoff bound for multi-copy discrimination of pure versus mixed states, revealing that single-copy Helstrom-bound strategies are suboptimal in this scenario.

Contribution

It introduces an optical receiver achieving the quantum Chernoff bound in multi-copy state discrimination and proves the suboptimality of single-copy Helstrom-bound strategies for such tasks.

Findings

Optical receiver reaches quantum Chernoff bound for pure vs. mixed states.

Single-copy Helstrom-bound strategies are at least twice worse in error exponent.

Classical analog: soft-decision outperforms hard-decision in noisy multi-copy detection.

Abstract

We demonstrate an optical receiver that achieves the quantum Chernoff bound for discriminating coherent states from thermal states in the multi-copy scenario. In contrast, we find that repeated use of the receiver approaching the Helstrom bound for single-copy measurement is sub-optimal in this multi-copy case. Furthermore, for a large class of multi-copy discrimination tasks between a pure and a mixed state, we prove that any Helstrom-bound achieving single-copy receiver is suboptimal by a factor of at least two in error-probability exponent compared to the multi-copy quantum Chernoff bound. This behavior has a classical analog in the performance gap between soft-decision and hard-decision receivers for detecting a multi-copy signal embedded in white Gaussian noise.