An uncertainty view on complementarity and a complementarity view on uncertainty
Marcos L. W. Basso, Jonas Maziero

TL;DR
This paper explores the deep relationship between quantum uncertainty, complementarity, and quantum correlations, providing new complete relations and measures that unify wave-particle duality and quantum correlations in mixed states.
Contribution
It introduces a comprehensive framework linking quantum and classical uncertainties with quantum correlations and coherence, extending complementarity relations to mixed states and new uncertainty measures.
Findings
Complete complementarity relation for quantum and classical uncertainties.
Quantum uncertainty equals Wigner-Yanase coherence.
Classical uncertainty quantifies quantum correlations.
Abstract
Since the uncertainty about an observable of a system prepared in a quantum state is usually described by its variance, when the state is mixed, the variance is a hybrid of quantum and classical uncertainties. Besides that, complementarity relations are saturated only for pure, single-quanton, quantum states. For mixed states, the wave-particle quantifiers never saturate the complementarity relation and can even reach zero for a maximally mixed state. So, to fully characterize a quanton it is not sufficient to consider its wave-particle aspect; one has also to regard its correlations with other systems. In this paper, we discuss the relation between quantum correlations and local classical uncertainty measures, as well as the relation between quantum coherence and quantum uncertainty quantifiers. We obtain a complete complementarity relation for quantum uncertainty, classical…
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