A Contextual $\psi$-Epistemic Model of the $n$-Qubit Stabilizer Formalism

TL;DR

This paper constructs a contextual $ extit{ extbf{ extpsi}}$-epistemic model for the $n$-qubit stabilizer formalism, revealing a stronger form of contextuality than previously recognized, and explores its implications for quantum computation.

Contribution

It introduces a novel outcome deterministic $ extit{ extbf{ extpsi}}$-epistemic model for the $n$-qubit stabilizer formalism, highlighting a stronger form of contextuality.

Findings

The model is outcome deterministic with value assignments to all Pauli observables.

Value assignments must be updated after any stabilizer measurement, even for commuting observables.

The model exhibits a stronger form of contextuality than known no-go theorems.

Abstract

Contextuality, a generalization of non-locality, has been proposed as the resource that provides the computational speed-up for quantum computation. For universal quantum computation using qudits, of odd-prime dimension, contextuality has been shown to be a necessary and possibly sufficient resource. However, the role of contextuality in quantum computation with qubits remains open. The $n$-qubit stabilizer formalism, which by itself cannot provide a quantum computer super-polynomial computational advantage over a classical counterpart, is contextual. Therefore contextuality cannot be identified as a sufficient resource for quantum computation. However it can be identified as a necessary resource. In this paper we construct a contextual $\psi$-epistemic ontological model of the $n$-qubit stabilizer formalism, to investigate the contextuality present in the formalism. We demonstrate it is possible for such a model to be outcome deterministic, and therefore have a value assignment to all Pauli observables. In our model the value assignment must be updated after a measurement of any stabilizer observable. Remarkably, this includes the value assignments for observables that commute with the measurement. A stronger manifestation of contextuality than is required by known no-go theorems.