Local models and hidden nonlocality in Quantum Theory

TL;DR

This thesis explores local hidden-variable models in quantum mechanics and demonstrates hidden nonlocality in Werner states, providing new models and insights into quantum correlations and their nonlocal properties.

Contribution

It details existing local models for Werner states and introduces a new local model for POVMs that reveals genuine hidden nonlocality after local filtering.

Findings

Werner's local model for entangled states

Hidden nonlocality in Werner states of dimension ≥5

Local model for POVMs showing genuine hidden nonlocality

Abstract

This Master's thesis has two central subjects: the simulation of correlations generated by local measurements on entangled quantum states by local hidden-variables models and the revelation of hidden nonlocality. We present and detail the Werner's local model and the hidden nonlocality of some Werner states of dimension $d\geq5$, the Gisin-Degorre's local model for a Werner state of dimension $d=2$ and the local model of Hirsch et al. for mixtures of the singlet state and noise, all of them for projective measurements. Finally, we introduce the local model for POVMs of Hirsch et al. for a state constructed upon the singlet with noise, that still violates the CHSH inequality after local filters are applied, hence presenting the so-called genuine hidden nonlocality.