Completing Quantum Mechanics with Quantized Hidden Variables

TL;DR

This paper proposes a model where quantum systems are described by both standard and hidden quantum states, reproducing quantum probabilities and explaining contextuality and nonlocality, with potential deviations in sequential measurements.

Contribution

It introduces a hidden-variable model combining standard and hidden quantum states that reproduces quantum probabilities and explains nonlocality and contextuality.

Findings

Reproduces standard quantum-mechanical probabilities

Explains contextuality and Bell nonlocality automatically

Potential deviations in sequential measurements if hidden state is not fully random

Abstract

I explore the possibility that a quantum system S may be described completely by the combination of its standard quantum state $|\psi\rangle$ and a (hidden) quantum state $|\phi\rangle$ (that lives in the same Hilbert space), such that the outcome of any standard projective measurement on the system S is determined once the two quantum states are specified. I construct an algorithm that retrieves the standard quantum-mechanical probabilities, which depend only on $|\psi\rangle$, by assuming that the (hidden) quantum state $|\phi\rangle$ is drawn at random from some fixed probability distribution Pr(.) and by averaging over Pr(.). Contextuality and Bell nonlocality turn out to emerge automatically from this algorithm as soon as the dimension of the Hilbert space of S is larger than 2. If $|\phi\rangle$ is not completely random, subtle testable deviations from standard quantum mechanics may arise in sequential measurements on single systems.