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

By Robert W. Spekkens. 2004

693 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/3b9af1ac06c92a2cf23a1951b8efc6f2a8a41568

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum picturalism (2009, background): “We called Spekkens’ toy theory casted as a dagger symmetric monoidal category Spek [64].”
Reformulating and Reconstructing Quantum Theory (2011, background): “The next class of theories, when r = 2, contains quantum theory (there are other toy theories having r = 2 that are not consistent with the postulates in this paper [49, 68]).”
The Language of Game Theory: Putting Epistemics into the Mathematics of Games (2014, background): “…†Address: Stern School of Business, New York University, 44 West Fourth Street, New York, NY 10012, adam.brandenburger@stern.nyu.edu, www.stern.nyu.edu/∼abranden To formulate the question in its essential form, von Neumann introduced the concept of a strategy — i.e., a complete plan of play…”
The Transactional Interpretation of Quantum Mechanics (2012, background): “Here is where I take note of the observation by Stapp (2011) that, even in orthodox QM, there is no “fact of the matter” about certain aspects of the past relative to the times of such delayed choices.”
Quantum-Bayesian Coherence (2009, background): “It is related to the basic idea underlying the toy model of R. W. Spekkens (Spekkens, 2007), with its “knowledge balance principle.””
Interacting quantum observables: categorical algebra and diagrammatics (2009, methodology): “[4], and it has provided a breath of fresh air for quantum foundations research [7, 43, 45, 72].”
QBism, the Perimeter of Quantum Bayesianism (2010, background): “There is no more beautiful demonstration of this than Robert Spekkens’s “toy model” for mimicking various features of quantum mechanics [12].”
Measurements on the reality of the wavefunction (2014, background): “There are compelling reasons to subscribe to the latter, epistemic view[5].”
Is the Quantum State Real? An Extended Review of -ontology Theorems (2014, background): “Many more can be found in [64], but I hope the present discussion has conveyed a flavor of the type of explanation that is possible in a realist ψ-epistemic theory.”