Superposition rule and entanglement in diagonal and probability representations of density states

TL;DR

This paper explores the relationships between diagonal and probability representations of quantum states, focusing on superposition, entanglement, and separability through operator-symbol frameworks.

Contribution

It introduces a unified approach to analyze quantum state representations and their properties using density-operator symbols, linking diagonal and probability frameworks.

Findings

Connection established between diagonal and probability representations.

Superposition rule expressed via density-operator symbols.

Entanglement properties characterized in terms of operator-symbols.

Abstract

The quasidistributions corresponding to the diagonal representation of quantum states are discussed within the framework of operator-symbol construction. The tomographic-probability distribution describing the quantum state in the probability representation of quantum mechanics is reviewed. The connection of the diagonal and probability representations is discussed. The superposition rule is considered in terms of the density-operator symbols. The separability and entanglement properties of multipartite quantum systems are formulated as the properties of the density-operator symbols of the system states.