Quantifying continuous-variable realism

Abstract

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, 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 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.

Information-based approach towards a unified resource theory

“…Irreality is known to be nonnegative and vanishing if and only if ρ = Φ A (ρ). This notion of "quantum irrealism" has recently been explored for different perspectives, such as for the statement of an information-reality complementarity relation [34], the discussion of continuousvariable realism [35], the identification of quantum irreality in quantum walks [36], and for the formulation of the realismbased nonlocality [12][13][14], which will be discussed in the next section. In terms of information, the irreality measure reads…”

Hardy’s Paradox as a Demonstration of Quantum Irrealism

“…In Ref. [44] the irreality formalism was extended to continuous variables and the "uncertainty relation"…”

Quantum resource covariance

“…e fact that these variables are continuous does not forbid the application of the formalism we introduced for the decomposition of information. In fact, an operational discretization method has been recently developed to treat position and momentum as discrete variables [43]. In Appendix A, the whole idea of our approach is applied and a particular solution is found to the problem of the breakdown, in the nonrelativistic quantum domain, of the universality of free fall.…”

“…A simple illustration of this fact can be given by use of the discrete approach (see Ref. [43] and Appendix A for further details), within which a position eigenstate is wri en as |x k = δq |k , where…”