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

TLDR

The authors introduce a toy theory based on the principle that, in a maximally known state, the number of answered questions about a system equals the number of unanswered questions. The toy theory is constructed by enforcing equal numbers of answered and unanswered questions about a system’s state, and the authors analyze its limitations—such as failure to reproduce Bell inequality violations and Kochen–Specker contextuality—to guide future research. The toy theory reproduces many quantum phenomena—including noncommutativity, interference, state decomposition, no‑cloning, teleportation, and others—providing evidence that quantum states represent incomplete knowledge rather than physical reality.

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.