Quantum mechanics is compatible with counterfactual definiteness

TL;DR

This paper demonstrates that quantum mechanics can be compatible with counterfactual definiteness by clarifying the role of factual and counterfactual contexts, challenging the common belief that quantum theory inherently violates CFD.

Contribution

It shows that considering only one factual context at a time allows quantum systems to satisfy counterfactual definiteness, clarifying misconceptions about noncontextuality in quantum mechanics.

Findings

Quantum systems can satisfy CFD when only one context is factual.

CFD is distinct from noncontextuality and can hold in quantum mechanics.

The common claim that quantum mechanics violates CFD is not fully substantiated.

Abstract

Counterfactual definiteness (CFD) means that if some property is measured in some context, then the outcome of the measurement would have been the same had this property been measured in a different context. A context includes all other measurements made together with the one in question, and the spatiotemporal relations among them. The proviso for CFD is non-disturbance: any physical influence of the contexts on the property being measured is excluded by the laws of nature, so that no one measuring this property has a way of ascertaining its context. It is usually claimed that in quantum mechanics CFD does not hold, because if one assigns the same value to a property in all contexts it is measured in, one runs into a logical contradiction, or at least contravenes quantum theory and experimental evidence. We show that this claim is not substantiated if one takes into account that only one of the possible contexts can be a factual context, all other contexts being counterfactual. With this in mind, any system of random variables can be viewed as satisfying CFD. The concept of CFD is closely related to but distinct from that of noncontextuality, and it is the latter property that may or may not hold for a system, in particular being contravened by some quantum systems