Multicopy observables for the detection of optically nonclassical states

TL;DR

This paper introduces multicopy observables that serve as practical witnesses for optical nonclassicality, enabling detection without full state tomography through linear optics and photon detectors.

Contribution

It proposes a novel class of multicopy observables that directly measure nonclassicality, simplifying experimental detection compared to previous matrix-of-moments methods.

Findings

Successfully designed observables acting on multiple copies of a state

Provided schemes using linear optics and photon detectors for implementation

Demonstrated the effectiveness of these observables in detecting nonclassicality

Abstract

Distinguishing quantum states that admit a classical counterpart from those that exhibit nonclassicality has long been a central issue in quantum optics. Finding an implementable criterion certifying optical nonclassicality (i.e, the incompatibility with a statistical mixture of coherent states) is of major importance as it often is a prerequisite to quantum information processes. A hierarchy of conditions for detecting whether a quantum state exhibits optical nonclassicality can be written based on some matrices of moments of the optical field [Phys. Rev. A 72, 043808 (2005)]. Here, we design optical nonclassicality observables that act on several replicas of a quantum state and whose expectation value coincides with the determinant of these matrices, hence providing witnesses of optical nonclassicality that overcome the need for state tomography. These multicopy observables are used to construct a family of physically implementable schemes involving linear optical operations and photon number detectors.