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Title: Evidence for the epistemic view of quantum states: A toy theory

Abstract

We present a toy theory that is based on a simple principle: the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge. Many quantum phenomena are found to have analogues within this toy theory. These include the noncommutativity of measurements, interference, the multiplicity of convex decompositions of a mixed state, the impossibility of discriminating nonorthogonal states, the impossibility of a universal state inverter, the distinction between bipartite and tripartite entanglement, the monogamy of pure entanglement, no cloning, no broadcasting, remote steering, teleportation, entanglement swapping, dense coding, mutually unbiased bases, and many others. The diversity and quality of these analogies is taken as evidence for the view that quantum states are states of incomplete knowledge rather than states of reality. A consideration of the phenomena that the toy theory fails to reproduce, notably, violations of Bell inequalities and the existence of a Kochen-Specker theorem, provides clues for how to proceed with this research program.

Authors:
 [1]
  1. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada N2L 2Y5 (Canada)
Publication Date:
OSTI Identifier:
20982241
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.032110; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BELL THEOREM; ENERGY LEVELS; GAME THEORY; INTERFERENCE; MIXED STATE; MULTIPLICITY; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; QUANTUM TELEPORTATION

Citation Formats

Spekkens, Robert W. Evidence for the epistemic view of quantum states: A toy theory. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.032110.
Spekkens, Robert W. Evidence for the epistemic view of quantum states: A toy theory. United States. doi:10.1103/PHYSREVA.75.032110.
Spekkens, Robert W. Thu . "Evidence for the epistemic view of quantum states: A toy theory". United States. doi:10.1103/PHYSREVA.75.032110.
@article{osti_20982241,
title = {Evidence for the epistemic view of quantum states: A toy theory},
author = {Spekkens, Robert W.},
abstractNote = {We present a toy theory that is based on a simple principle: the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge. Many quantum phenomena are found to have analogues within this toy theory. These include the noncommutativity of measurements, interference, the multiplicity of convex decompositions of a mixed state, the impossibility of discriminating nonorthogonal states, the impossibility of a universal state inverter, the distinction between bipartite and tripartite entanglement, the monogamy of pure entanglement, no cloning, no broadcasting, remote steering, teleportation, entanglement swapping, dense coding, mutually unbiased bases, and many others. The diversity and quality of these analogies is taken as evidence for the view that quantum states are states of incomplete knowledge rather than states of reality. A consideration of the phenomena that the toy theory fails to reproduce, notably, violations of Bell inequalities and the existence of a Kochen-Specker theorem, provides clues for how to proceed with this research program.},
doi = {10.1103/PHYSREVA.75.032110},
journal = {Physical Review. A},
number = 3,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}