Irreducibility of coherent states

TL;DR

This paper proposes an optical test using a multiplexer and post-selection to identify a nonclassical feature called irreducibility in coherent states, distinguishing quantum from classical light behavior.

Contribution

It introduces a new optical method to detect irreducibility in coherent states, overcoming limitations of sub-binomiality as a nonclassical indicator.

Findings

Sub-binomiality can be negative for coherent states with post-selection.

Classical models can reproduce sub-binomiality, questioning its nonclassicality.

The proposed coincident probability test reveals nonclassicality by failing classical reproduction.

Abstract

We suggest an optical method which tests a nonclassical feature with a coherent state input. The test is designed with a multiplexer of on/off detectors and post-selection, adopting sub-binomiality as a nonclassical feature, replacing Mandel's $Q$-factor. The sub-binomiality is shown negative even for coherent states when the post-selection is made. However, we show that it can be reproduced also by a classical model assuming a stochastic on/off detectors. In the sense, the sub-binomiality is unlikely to identify the genuine nonclassicality. On the other hand, we propose a coincident probability of first two branches of the multiplexer and show that the classical model fails to reproduce the quantum coincident probability. The failure of the classical model results from the classical description of light, i.e. the divisibility of intensity into parts no matter how small it is. Then our optical test identifies a nonclassical feature of coherent states against the classical divisibility of light, which we call irreducibility.