Leggett-Garg Inequalities for Squeezed States

TL;DR

This paper investigates the violation of Leggett-Garg inequalities in continuous-variable squeezed states, mapping conditions for violation, analyzing decoherence effects, and suggesting new experimental approaches.

Contribution

It systematically explores LGI violations in squeezed states across parameter space and assesses decoherence impacts, offering novel experimental insights.

Findings

LGI violations occur in certain squeezing configurations

No violation when all squeezing angles are zero

Decoherence reduces the detectability of LGI violations

Abstract

Temporal Bell inequalities, or Leggett-Garg Inequalities (LGI), are studied for continuous-variable systems placed in a squeezed state. The importance of those systems lies in their broad applicability which allows the description of many different physical settings in various branches of physics, ranging from cosmology to condensed matter physics and from optics to quantum information theory. LGI violations are explored and systematically mapped in squeezing parameter space. Configurations for which LGI violation occurs are found but it is shown that no violation can be obtained if all squeezing angles vanish, contrary to what happens for the spatial Bell inequalities. We also assess the effect of decoherence on the detectability of such violations. Our study opens up the possibility of new experimental designs for the observation of LGI violation.