Epistemically restricted phase space representation, weak momentum value, and reconstruction of quantum wave function

Abstract

A phase space distribution associated with a quantum state was previously proposed, which incorporates a specific epistemic restriction parameterized by a global random variable on the order of Planck constant, transparently manifesting quantum uncertainty in phase space. Here we show that the epistemically restricted phase space (ERPS) distribution can be determined via weak measurement of momentum followed by post-selection on position. In the ERPS representation, the phase and amplitude of the wave function are neatly captured respectively by the position-dependent (conditional) average and variance of the epistemically restricted momentum fluctuation. They are in turn respectively determined by the real and imaginary parts of the weak momentum value, permitting a reconstruction of wave function using weak momentum value measurement, and an interpretation of momentum weak value in term of epistemically restricted momentum fluctuations. The ERPS representation thus provides a transparent and rich framework to study the deep conceptual links between quantum uncertainty embodied in epistemic restriction, quantum wave function, and weak momentum measurement with position post-selection, which may offer useful insight to better understand their meaning.

17 pages, comments welcome

References in corpus (13)

• Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification
• Experimental joint weak measurement on a photon pair as a probe of Hardy's Paradox
• Complex weak values in quantum measurement
• Negativity and contextuality are equivalent notions of nonclassicality
• Anomalous Weak Values Are Proofs of Contextuality
• Grounding Bohmian Mechanics in Weak Values and Bayesianism
• Frame representations of quantum mechanics and the necessity of negativity in quasi-probability representations
• Compressive Direct Measurement of the Quantum Wave Function
• Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation
• Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction
• Weak values in a classical theory with an epistemic restriction
• Quantum mechanics is a calculus for estimation under epistemic restriction
• Quantum Chaos and Quantum-Classical Correspondence

Cited by in corpus (3)

• Quantum mechanics is a calculus for estimation under epistemic restriction
• Nonlinear Schrödinger equations and generalized Heisenberg uncertainty principle violating the principle of estimation independence
• Estimation independence as an axiom for quantum uncertainty