Mixed State Entanglement Via the Cauchy-Schwarz Inequality

TL;DR

This paper introduces the Cauchy-Schwarz Violation (CSV) Condition as a new, physically intuitive criterion for detecting entanglement in mixed quantum states, applicable to various models including the Jaynes-Cummings and Rabi models.

Contribution

It proposes the CSV condition as a simple, physically motivated entanglement criterion that relates directly to system properties like populations and coherences.

Findings

CSV condition effectively detects entanglement in key quantum models

Provides insights into entanglement related to system symmetries

Offers a more accessible alternative to negativity measures

Abstract

The entanglement properties of mixed states are of great importance in the study of open quantum systems and quantum information science, but commonly used entanglement measures, such as negativity, can be difficult to apply or connect to physical properties of the system. We introduce the Cauchy-Schwarz Violation (CSV) Condition, which has a simple dependence on the populations and coherences of the density operator. A sufficient condition for entanglement, it provides a more direct connection to the physical characteristics of the system such as its symmetries. We illustrate the often surprising insights gained from the CSV condition by applying it to the Jaynes-Cummings Model, the Quantum Rabi Model, and an open-system Quantum Rabi Model.