Compressing the hidden variable space of a qubit

Abstract

In previously exhibited hidden variable models of quantum state preparation and measurement, the number of continuous hidden variables describing the actual state of a single realization is never smaller than the quantum state manifold dimension. We introduce a simple model for a qubit whose hidden variable space is one-dimensional, i.e., smaller than the two-dimensional Bloch sphere. The hidden variable probability distributions associated with the quantum states satisfy reasonable criteria of regularity. Possible generalizations of this shrinking to a N-dimensional Hilbert space are discussed.

References updated and added some more discussions of results

References in corpus (5)

• In defense of the epistemic view of quantum states: a toy theory
• Matchgates and classical simulation of quantum circuits
• Exponential complexity and ontological theories of quantum mechanics
• A condition for any realistic theory of quantum systems
• Efficient Hidden-Variable Simulation of Measurements in Quantum Experiments

Cited by in corpus (9)

• Distinct Quantum States Can Be Compatible with a Single State of Reality
• Epistemic view of quantum states and communication complexity of quantum channels
• State space dimensionality in short memory hidden variable theories
• Communication complexity and the reality of the wave-function
• Onthological models predictively inequivalent to quantum theory
• Measurement contextuality is implied by macroscopic realism
• How Real are Quantum States in $\psi$-ontic Models?
• Exponential communication gap between weak and strong classical simulations of quantum communication
• Approximate simulation of entanglement with a linear cost of communication