Quantifying continuous-variable realism. (arXiv:1904.02490v2 [quant-ph] UPDATED)

The debate instigated by the seminal works of Einstein, Podolsky, Rosen, and
Bell, put the notions of realism and nonlocality at the core of almost all
philosophical and physical discussions underlying the foundations of quantum
mechanics. However, while experimental criteria and quantifiers are by now well
established for nonlocality, there is no clear quantitative measure for the
degree of reality associated with continuous variables such as position and
momentum. This work aims at filling this gap. Considering position and momentum
as effectively discrete observables, we implement an operational notion of
projective measurement and, from that, a criterion of reality for theses
quantities. Then, we introduce a quantifier for the degree of irreality of a
discretized continuous variable which, when applied to the conjugated pair
position-momentum, is shown to obey an uncertainty relation, this meaning that
quantum mechanics prevents classical realism for conjugated quantities. As an
application of our formalism, we study the emergence of elements of reality in
an instance where a Gaussian state is submitted to the dissipative dynamics
implied by the Caldirola-Kanai Hamiltonian. In particular, at the equilibrium,
we make some links with the measurement problem and identify aspects that can
be taken as the quantum counterpart for the notion of rest.

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