Non-classical features of Polarization Quasi-Probability Distribution

TL;DR

This paper explores the non-classical features of polarization quasi-probability distribution (PQPD), revealing its singularities and negativity, and proposes a method to visualize bright nonclassical states by 'highlighting' the quantum state with a strong coherent beam.

Contribution

It introduces a technique to overcome PQPD positivity issues in bright states by adding a coherent beam, linking polarization tomography with Wigner-function tomography.

Findings

PQPD exhibits singularities and negativity at integer Stokes values.

Adding a strong coherent beam 'highlights' the quantum state, making PQPD positive and regular.

The method enables verification of bright nonclassical states like squeezed Fock states.

Abstract

Polarization quasi-probability distribution (PQPD) is defined in the Stokes space, and it enables the calculation of mean values and higher-order moments for polarization observables using simple algebraic averaging. It can be reconstructed with the help of polarization quantum tomography and provides a full description of the polarization properties of quantum states of light. We show here that, due to its definition in terms of the discrete-valued Stokes operators, polarization quasi-probability distribution has singularities and takes negative values at integer values of the Stokes observables. However, in experiments with `bright' many-photon states, the photon-number resolution is typically smeared due to the technical limitations of contemporary photodetectors. This results in a PQPD that is positive and regular even for such strongly nonclassical states as single-photon seeded squeezed vacuum. This problem can be solved by `highlighting' the quantum state, that is, by adding a strong coherent beam into the orthogonal polarization mode. This procedure bridges polarization quantum tomography with the Wigner-function tomography, while preserving the main advantage of the first one, namely, immunity to the common phase fluctuations in the light path. Thus, it provides a convenient method for the verification of bright nonclassical states of light, such as squeezed Fock states.