Estimation independence as an axiom for quantum uncertainty
arXiv:2005.07044 · doi:10.1103/PhysRevA.101.022102
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
References in corpus (13)
- The uncertainty principle determines the non-locality of quantum mechanics
- Complex weak values in quantum measurement
- A derivation of quantum theory from physical requirements
- Grounding Bohmian Mechanics in Weak Values and Bayesianism
- Non-locality distillation and post-quantum theories with trivial communication complexity
- Bell inequalities for continuous-variable correlations
- Entropic Dynamics, Time and Quantum Theory
- Implications of Superstrong Nonlocality for Cryptography
- Local commutativity versus Bell inequality violation for entangled states and versus non-violation for separable states
- Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction
- Quantum mechanics is a calculus for estimation under epistemic restriction
- Epistemically restricted phase space representation, weak momentum value, and reconstruction of quantum wave function
- The chain rule implies Tsirelson's bound: an approach from generalized mutual information