Invariance of the bit error rate in the ancilla-assisted homodyne detection

TL;DR

This paper demonstrates that the minimum bit error rate in homodyne detection with ancilla assistance remains unchanged under certain operations, providing insights into the fundamental limits of quantum state discrimination.

Contribution

It proves the invariance of the minimum bit error rate in ancilla-assisted homodyne detection under real-time updates and classical feedforward operations.

Findings

Minimum bit error rate is invariant under specific ancilla-assisted operations.

The invariance holds for arbitrary pure ancillary states and fixed phase homodyne detection.

Discussion on extending homodyne detection schemes beyond the invariance condition.

Abstract

We investigated the minimum achievable bit error rate of discriminating binary coherent states by homodyne measurements with the help of arbitrary ancilla states coupled via beam splitters. We took into account arbitrary pure ancillary states those were updated in real-time by those partial measurements and classical feedforward operations where the partial measurements were made by homodyne detections with a common fixed phase. It was shown that the minimum bit error rate of the system was invariant under these operations. We also discussed how generalize the homodyne detection beyond the scheme which made the bit error rate invariant.