Spin-spin correlations of entangled qubit pairs in the Bohm interpretation of quantum mechanics

TL;DR

This paper explores the spin-spin correlations of entangled qubit pairs within the de Broglie-Bohm interpretation, providing new insights into entangled dynamics and correlations through numerical analysis and geometric visualization.

Contribution

It introduces a detailed Bohmian analysis of entangled qubits, including probability distributions and geometric interpretations, comparing results with standard quantum mechanics.

Findings

Bohmian spin-spin correlators match quantum predictions for Bell inequality violations.

Entangled qubits exhibit a unison precession with a constant angle between their angular momenta.

Probability distributions in the Bohmian framework offer a novel understanding of entangled qubit behavior.

Abstract

A general entangled qubit pair is analyzed in the de Broglie-Bohm formalism corresponding to two spin-1/2 quantum rotors. Several spin-spin correlators of Bohm's hidden variables are analyzed numerically and a detailed comparison with results obtained by standard quantum mechanics is outlined. In addition to various expectation values the Bohm interpretation allows also a study of the corresponding probability distributions, which enables a novel understanding of entangled qubit dynamics. In particular, it is shown how the angular momenta of two qubits in this formalism can be viewed geometrically and characterized by their relative angles. For perfectly entangled pairs, for example, a compelling picture is given, where the qubits exhibit a unison precession making a constant angle between their angular momenta. It is also demonstrated that the properties of standard quantum mechanical spin-spin correlators responsible for the violation of Bell's inequalities are identical to their counterparts emerging from the probability distributions obtained by the Bohmian approach.