The Physics of crypto-nonlocality

TL;DR

This paper demonstrates that crypto-nonlocality does not naturally arise from the assumption of realistic photon polarization, showing that such theories cannot reproduce entangled photon experiment statistics and are refuted by entanglement detection.

Contribution

It proves that crypto-nonlocality is not a consequence of realistic polarization assumptions and characterizes the measurement statistics compatible with such theories.

Findings

Crypto-nonlocality does not follow from realistic photon polarization.

Experiments detecting entanglement refute these theories.

Measurement outcomes align with separable quantum states.

Abstract

In 2003, Leggett introduced his model of crypto-nonlocality based on considerations on the reality of the photon polarization. In this note, we prove that, contrary to hints in subsequent literature, crypto-nonlocality does not follow naturally from the postulate that polarization is a realistic variable. More explicitly, consider physical theories where: a) faster-than-light communication is impossible; b) all physical photon states have a definite polarization; and c) given two separate photons, if we measure one of them and post-select on the result, the measurement statistics of the remaining system correspond to a photon state. We show that the outcomes of any two-photon polarization experiment in these theories must follow the statistics generated by measuring a separable two-qubit quantum state. Consequently, in such experiments any instance of entanglement detection -and not necessarily a Leggett inequality violation- can be regarded as a refutation of this class of theories.