Leggett-Garg violations for continuous variable systems with gaussian states

• URL: http://arxiv.org/abs/2211.10292v3
• Date: Wed, 22 Mar 2023 13:31:11 GMT
• Title: Leggett-Garg violations for continuous variable systems with gaussian states
• Authors: Clement Mawby, Jonathan Halliwell
• Abstract summary: We seek LG violations for measurements of a dichotomic variable $Q = textrmsign(x)$. An exploration of parameter space reveals significant regimes in which the two-time LG inequalities are violated. We exploit the continuous nature of the underlying position variable and analyse the relevant quantum-mechanical currents.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Macrorealism (MR) is the world view that certain quantities may take definite values at all times irrespective of past or future measurements and may be experimentally falsified via the Leggett-Garg (LG) inequalities. We put this world view to the test for systems described by a continuous variable $x$ by seeking LG violations for measurements of a dichotomic variable $Q = \textrm{sign}(x)$, in the case of gaussian initial states in a quantum harmonic oscillator. Extending our earlier analysis [C. Mawby and J. J. Halliwell, Phys. Rev. A 105, 022221 (2022)] we find analytic expressions for the temporal correlators. An exploration of parameter space reveals significant regimes in which the two-time LG inequalities are violated, and likewise at three and four times. To obtain a physical picture of the LG violations, we exploit the continuous nature of the underlying position variable and analyse the relevant quantum-mechanical currents, Bohm trajectories, and Wigner function. Further, we extend the analysis LG tests using coherent state projectors, thermal coherent states, and squeezed states.

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