Probability and the Classical/Quantum Divide

TL;DR

This paper proposes probabilistic tests to distinguish classical from quantum phenomena in macroscopic systems, using outcome ratio conditions that differ between classical and quantum cases, including entangled states.

Contribution

It introduces specific probability ratio criteria for differentiating classical and quantum states, including non-maximally and maximally entangled particles, under noisy measurement conditions.

Findings

Classical case: Ps/Pn = 1/2 with no 3-way coincidences.

Quantum case: Ps/Pn = 1/3 for quantum states.

For non-maximally entangled objects, separation is possible if r < 5.83.

Abstract

This paper considers the problem of distinguishing between classical and quantum domains in macroscopic phenomena using tests based on probability and it presents a condition on the ratios of the outcomes being the same (Ps) to being different (Pn). Given three events, Ps/Pn for the classical case, where there are no 3-way coincidences, is one-half whereas for the quantum state it is one-third. For non-maximally entangled objects we find that so long as r < 5.83, we can separate them from classical objects using a probability test. For maximally entangled particles (r = 1), we propose that the value of 5/12 be used for Ps/Pn to separate classical and quantum states when no other information is available and measurements are noisy.