General Quantum Hilbert Space Modeling Scheme for Entanglement

TL;DR

This paper develops a comprehensive Hilbert space framework for modeling all types of quantum entanglement, including complex measurement scenarios, extending to mixed states and challenging traditional quantum boundaries.

Contribution

It introduces a unified classification scheme for quantum entanglement in Hilbert space, encompassing entangled states and measurements, and extends the framework to mixed states.

Findings

Entanglement is a joint property of states and measurements.

Entangled measurements can model phenomena beyond traditional quantum limits.

The framework applies to pure and mixed quantum states.

Abstract

We work out a classification scheme for quantum modeling in Hilbert space of any kind of composite entity violating Bell's inequalities and exhibiting entanglement. Our theoretical framework includes situations with entangled states and product measurements ('customary quantum situation'), and also situations with both entangled states and entangled measurements ('nonlocal box situation', 'nonlocal non-marginal box situation'). We show that entanglement is structurally a joint property of states and measurements. Furthermore, entangled measurements enable quantum modeling of situations that are usually believed to be 'beyond quantum'. Our results are also extended from pure states to quantum mixtures.