Quantum uncertainty as classical uncertainty of real-deterministic variables constructed from complex weak values and a global random variable

نویسندگان

چکیده

What does it take for real-deterministic $c$-valued (i.e., classical, commuting) variables to comply with the Heisenberg uncertainty principle? Here, we construct a class of out weak values obtained via nonperturbing measurement quantum operators postselection over complete set state vectors basis, which always satisfies Kennard-Robertson-Schr\"odinger relation. First, introduce an auxiliary global random variable and couple imaginary part value convert incompatibility between operator basis into fluctuation ``error term,'' then superimpose onto real value. We show that this ``$c$-valued physical quantities'' provides contextual hidden-variable model expectation certain operators. Schr\"odinger Kennard-Robertson lower bounds can be separately by imposing classical relation quantities associated pair Hermitian Within representation, complementarity two incompatible observables manifests absence wherein error terms simultaneously vanish. Furthermore, principle is captured specific irreducible epistemic restriction quantities, foreign in mechanics, constraining allowed form their joint distribution. suggest interpretation decomposing quantity as optimal estimate under estimation error, discuss limit.

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ژورنال

عنوان ژورنال: Physical review

سال: 2021

ISSN: ['0556-2813', '1538-4497', '1089-490X']

DOI: https://doi.org/10.1103/physreva.103.022215