Kochen-Specker for many qubits and the classical limit

TL;DR

This paper extends the Kochen-Specker argument to many qubits and demonstrates that quantum predictions converge to classical ones as the number of qubits increases, shedding light on the quantum-to-classical transition.

Contribution

It generalizes the Kochen-Specker argument to an arbitrary number of qubits and shows the classical limit emerges with increasing qubits, improving previous results for GHZ states.

Findings

Quantum and classical predictions converge as qubits increase.

The classical limit results from increasing the number of particles.

Extension of KS argument to all observables for many qubits.

Abstract

Several arguments demonstrate the incompatibility between Quantum Mechanics and classical Physics. Bell's inequalities and Greenberger-Horne-Zeilinger (GHZ) arguments apply to specific non-classical states. The Kochen-Specker (KS) one, instead, is especially appealing for it applies to any state. Nevertheless, in spite of the incompatibility, quantum predictions must converge to classical ones as the macroscopic scale is approached. This convergence is known as "classical limit", and is difficult to explain within quantum formalism. In this short paper, the simplified Mermin-Peres form (two qubits) of the KS argument is extended to an arbitrary number of qubits. It is shown that quantum and classical predictions converge as the number of qubits is increases to the macroscopic scale. This way to explain the classical limit concurs with, and improves, a result previously reported for GHZ states. The demonstration for the general case (i.e., for all possible observables) that the classical limit is the consequence of merely increasing the number of particles, is important and seems to be at hand.