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Title: Weak measurement and Bohmian conditional wave functions

It was recently pointed out and demonstrated experimentally by Lundeen et al. that the wave function of a particle (more precisely, the wave function possessed by each member of an ensemble of identically-prepared particles) can be “directly measured” using weak measurement. Here it is shown that if this same technique is applied, with appropriate post-selection, to one particle from a perhaps entangled multi-particle system, the result is precisely the so-called “conditional wave function” of Bohmian mechanics. Thus, a plausibly operationalist method for defining the wave function of a quantum mechanical sub-system corresponds to the natural definition of a sub-system wave function which Bohmian mechanics uniquely makes possible. Similarly, a weak-measurement-based procedure for directly measuring a sub-system’s density matrix should yield, under appropriate circumstances, the Bohmian “conditional density matrix” as opposed to the standard reduced density matrix. Experimental arrangements to demonstrate this behavior–and also thereby reveal the non-local dependence of sub-system state functions on distant interventions–are suggested and discussed. - Highlights: • We study a “direct measurement” protocol for wave functions and density matrices. • Weakly measured states of entangled particles correspond to Bohmian conditional states. • Novel method of observing quantum non-locality is proposed.
Authors:
 [1] ;  [2]
  1. Physics Department, Smith College, Northampton, MA 01060 (United States)
  2. Departments of Mathematics and Philosophy, Rutgers University, Hill Center, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019 (United States)
Publication Date:
OSTI Identifier:
22403436
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 350; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOHM CRITERION; DENSITY MATRIX; EXPERIMENTAL DATA; LOCALITY; PARTICLES; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; WAVE FUNCTIONS