Elementary test for non-classicality based on measurements of position and momentum

TL;DR

This paper extends a non-classicality test based on quadrature measurements to states lacking rotational symmetry and compares its effectiveness with classical tomography methods, demonstrating its simplicity and reliability.

Contribution

The authors generalize a non-classicality test to include asymmetric states and show it outperforms classical tomography in simplicity and statistical reliability.

Findings

The generalized test works for non-rotationally symmetric states.

It is simpler and more reliable than filtered back-projection methods.

The test's efficiency remains unaffected by the degree of squeezing.

Abstract

We generalise a non-classicality test described by Kot et al. [Phys. Rev. Lett. 108, 233601 (2010)], which can be used to rule out any classical description of a physical system. The test is based on measurements of quadrature operators and works by proving a contradiction with the classical description in terms of a probability distribution in phase space. As opposed to the previous work, we generalise the test to include states without rotational symmetry in phase space. Furthermore, we compare the performance of the non-classicality test with classical tomography methods based on the inverse Radon transform, which can also be used to establish the quantum nature of a physical system. In particular, we consider a non-classicality test based on the so-called filtered back-projection formula. We show that the general non-classicality test is conceptually simpler, requires less assumptions on the system and is statistically more reliable than the tests based on the filtered back-projection formula. As a specific example, we derive the optimal test for a quadrature squeezed single photon state and show that the efficiency of the test does not change with the degree of squeezing.