ResearchPod Summary
Bohr’s principle of complementarity, which posits that wave-like and particle-like behaviors are mutually exclusive, is a fundamental pillar of quantum mechanics. While traditionally formulated for double-slit experiments, this paper extends the duality to multi-path interferometry. The author introduces a basis-dependent predictability measure, derived from the Bures distance between a dephased state and the maximally mixed state, to quantify particle-like behavior. Simultaneously, it employs a coherence measure based on the nonclassicality of the Kirkwood-Dirac quasiprobability to quantify wave-like behavior.
The central result is a trade-off relation between these two measures. For pure states, the relation is an exact equality, demonstrating that the existence of coherence directly limits the predictability of measurement outcomes. For mixed states, the author utilizes the convex-roof construction to extend this relation into an inequality, where the normalized coherence and predictability sum to at most one. This mirrors the standard physical intuition that classical mixing and decoherence prevent the simultaneous maximization of wave and particle characteristics.
Beyond its theoretical elegance, this framework provides a concrete operational meaning for quantum coherence. By viewing a mixed state as an ensemble of pure states, the author interprets coherence as the portion of measurement uncertainty that cannot be removed even when the classical preparation label (the specific pure state in the ensemble) is known. This "classically irreducible randomness" is a critical resource for source-independent quantum random number generation (QRNG), where the duality relation allows for the derivation of tight, worst-case bounds on the guessing probability of measurement outcomes.
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