Lowering Helstrom Bound with non-standard coherent states

TL;DR

This paper explores how non-standard coherent states can reduce the Helstrom bound in quantum state discrimination, potentially achieving error probabilities lower than traditional limits in certain regimes.

Contribution

It introduces and compares generalized coherent states, demonstrating that some can significantly lower or eliminate the Helstrom bound in quantum measurement.

Findings

Helstrom bound can be significantly lowered with non-standard coherent states.

In some regimes, the Helstrom bound can be made to vanish.

Different classes of generalized coherent states exhibit varying quantum limits.

Abstract

In quantum information processing, {using a receiver device to differentiate between two nonorthogonal states leads to a quantum error probability. The minimum possible error is} known as the Helstrom bound. In this work we study and compare quantum limits for states which generalize the Glauber-Sudarshan coherent states, like non-linear, Perelomov, Barut-Girardello, and (modified) Susskind-Glogower coherent states. For some of these, we show that the Helstrom bound can be significantly lowered and even vanish in specific regimes.