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 KochenSpecker theorem, provides clues for how to proceed with this research program.
 Authors:
 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 KochenSpecker 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}
}

We investigate the strengths and limitations of the Spekkens toy model, which is a local hidden variable model that replicates many important properties of quantum dynamics. First, we present a set of five axioms that fully encapsulate Spekkens' toy model. We then test whether these axioms can be extended to capture more quantum phenomena by allowing operations on epistemic as well as ontic states. We discover that the resulting group of operations is isomorphic to the projective extended Clifford group for two qubits. This larger group of operations results in a physically unreasonable model; consequently, we claim that a relaxedmore »

Quantum states for quantum processes: A toy model for ammonia inversion spectra
Chemical transformations are viewed here as quantum processes modulated by external fields, that is, as shifts in reactant to product amplitudes within a quantum state represented by a linear (coherent) superposition of electronuclear basis functions; their electronic quantum numbers identify the ''chemical species.'' This basis set can be mapped from attractors built from a unique electronic configurational space that is invariant with respect to the nuclear geometry. In turn, the quantum numbers that label these basis functions and the semiclassical potentials for the electronic attractors may be used to derive reaction coordinates to monitor progress as a function of themore » 
Quantum decay process of metastable vacuum states in SU(2) YangMills theory: A probability theoretical point of view
The problem of vacuumtunneling phenomena such as the quantum decay process of metastable vacuum states in SU(2) YangMills theory is investigated from a probability theoretical point of view. This is done by adopting the stochastic quantization procedure to quantize the YangMills field in the A/sub 0/ = 0 gauge. The mechanism of vacuum tunneling can be illustrated within the realm of the stochastic quantization. It is shown that the quantized vacuum field configuration, which manifests the decay process of metastable vacuum states, is a EuclideanMarkov field of Gaussian type. The validity of the Euclidean pathintegral description of vacuumtunneling phenomena ismore » 
Probing the origin of large inhomogeneities in inflation using a toy quantummechanical model
We study the quantum evolution of the homogeneous mode of a scalar field with simple potentials in RobertsonWalker spacetime. The simplicity of the model allows one to work out the eitalicxitalicaitaliccitalictitalic quantum evolution of a wave packet. The model mimics the inflationary scenario quite well and is used to study the nature and origin of various constraints. We conclude that any model in which (i) the potential has only a single energy scale (10/sup 14/10/sup 15/ GeV) and dimensionless parameters of order unity and (ii) the inflationary phase is endowed with a minimum temperature of (Hitalic/2..pi..) witaliciitaliclitaliclitalic produce density inhomogeneitymore » 
Quantum toy model for blackhole backreaction
We propose a simple quantum field theoretical toy model for blackhole evaporation and study the backreaction of Hawking radiation onto the classical background. It turns out that the horizon is also ''pushed back'' in this situation (i.e., the interior region shrinks) though this backreaction is not caused by energy conservation but by momentum balance. The effective heat capacity and induced entropy variation can have both signsdepending on the parameters of the model.