Quantum correlations; quantum probability approach

TL;DR

This survey explores quantum correlations through quantum probability, detailing their mathematical structures, physical concepts, and implications for understanding entanglement and quantumness.

Contribution

It provides a comprehensive overview of quantum correlations, integrating physical concepts with mathematical frameworks, and discusses new insights into entanglement and quantum states.

Findings

Analysis of classical and quantum correlation functionals

Definitions and properties of entangled states and separability

Description of quantum entanglement measures and PPT states

Abstract

This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical and quantum), mathematical structures, and their consequences. These include the canonical form of classical correlation functionals, general definitions of separable (entangled) states, definition and analysis of quantumness of correlations, description of entanglement of formation, and PPT states. This work is intended both for physicists interested not only in collection of results but also in the mathematical methods justifying them, and mathematicians looking for an application of quantum probability to concrete new problems of quantum theory.