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Counting the Identities of a Quantum State. (arXiv:1807.03995v1 [quant-ph] CROSS LISTED)
来源于:arXiv
A marquee feature of quantum behavior is that, upon probing, the microscopic
system emerges in one of multiple possible states. While quantum mechanics
postulates the respective probabilities, the effective abundance of these
simultaneous ``identities'', if a meaningful concept at all, has to be
inferred. To address such problems, we construct and analyze the theory of
functions assigning the quantity (effective number) of objects endowed with
probability weights. In a surprising outcome, the consistency of such
probability-dependent measure assignments entails the existence of a minimal
amount, realized by a unique effective number function. This result provides a
well-founded solution to identity-counting problems in quantum mechanics. Such
problems range from counting the basis states contained in an output of a
quantum computation, and relevant in the analysis of quantum algorithms, to a
novel way to characterize complex states such as QCD vacuum or eigenstates of
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