Uncertainty-Reality Complementarity and Entropic Uncertainty Relations

TL;DR

This paper explores the relationship between the reality of quantum observables and quantum uncertainty, introducing entropic measures and state-independent inequalities to quantify their complementarity and trade-offs.

Contribution

It introduces state-independent complementarity inequalities linking entropic measures of reality and uncertainty for two observables, advancing understanding of quantum foundations.

Findings

Entropic uncertainty relations with quantum memory are complemented by reality measures.

State-independent inequalities connect reality and uncertainty in quantum systems.

Trade-offs between reality and uncertainty are quantitatively characterized.

Abstract

Reality of quantum observables, a feature of long-standing interest within foundations of quantum mechanics, has recently been quantified and deeply studied by means of entropic measures [Phys. Rev. A 97, 022107 (2018)]. However, there is no state-independent "reality trade-off" between noncommuting observables, as in certain systems all observables are real [Europhys. Lett. 112, 40005 (2015)]. We show that the entropic uncertainty relation in the presence of quantum memory [Nature Phys. 6, 659 (2010)] perfectly supplements the discussed notion of reality, rendering trade-offs between reality and quantum uncertainty. State-independent complementarity inequalities involving entropic measures of both, uncertainty and reality, for two observables are presented.