Estimation independence as an axiom for quantum uncertainty

Abstract

Quantum uncertainty is the cornerstone of quantum mechanics which underlies many counterintuitive nonclassical phenomena. Recent studies remarkably showed that it also fundamentally limits nonclassical correlation, and crucially, a deviation from its exact form may lead to a violation of the second law of thermodynamics. Are there deep and natural principles which uniquely determines its form? Here we work within a general epistemic framework for a class of nonclassical theories, introducing an epistemic restriction to an otherwise classical theory, so that the distributions of positions are irreducibly parameterized by the underlying momentum fields. It was recently shown that the mathematics of quantum mechanics formally arises within an operational scheme, wherein an agent makes a specific estimation of the momentum given information on the positions and the experimental settings. Moreover, quantum uncertainty can be traced back to the `specific' choice of estimator and the associated estimation error. In the present work, we show that a plausible principle of estimation independence, which requires that the estimation of momentum of one system must be independent of the position of another system independently prepared of the first, singles out the specific forms of the estimator, and especially the estimation error up to its strength given by a global-nonseparable random variable on the order of Planck constant.

25 pages, comments welcome

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Cited by in corpus (5)

• Quantum uncertainty as classical uncertainty of real-deterministic variables constructed from complex weak values and a global random variable
• Nonlinear Schrödinger equations and generalized Heisenberg uncertainty principle violating the principle of estimation independence
• Efficient classical computation of expectation values in a class of quantum circuits with an epistemically restricted phase space representation
• Epistemic uncertainty from an averaged Hamilton-Jacobi formalism
• Conservation of correlation in measurement underlying the violation of Bell inequalities and a game of joint mapping