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Quantum Reactivity: An Indicator of Quantum Correlation.

Shahabeddin M Aslmarand¹, Warner A Miller¹, Verinder S Rana²

¹Department of Physics, Florida Atlantic University, Boca Raton, FL 33431, USA.

Entropy (Basel, Switzerland)

|December 8, 2020

Summary

We introduce quantum reactivity (QR), a geometric quantity to measure quantum correlations in high-dimensional quantum systems. Unlike quantum discord, QR is invariant under unitary operations and useful for quantum information processing.

Keywords:

entanglement monotones quantum correlations quantum entanglement quantum information quantum information geometry

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Area of Science:

Quantum Information Science
Quantum Physics
Geometric Methods in Physics

Background:

Geometry offers insights into complex physics problems.
Quantum correlations are crucial for quantum information processing.
Existing measures like quantum discord have limitations in higher dimensions.

Purpose of the Study:

Introduce a novel geometric quantity, quantum reactivity (QR).
Utilize QR to probe quantum correlations in higher-dimensional quantum systems.
Compare QR with existing measures like quantum discord.

Main Methods:

Generalize information distance to higher-dimensional volumes.
Define QR as the ratio of surface area to volume.
Apply QR to various multipartite quantum states (Werner, W, GHZ).

Main Results:

Quantum reactivity (QR) is a novel geometric quantity for quantum correlations.
QR is invariant under unitary operations, unlike quantum discord.
QR can effectively order quantum states based on their correlation levels.

Conclusions:

QR provides a new geometric perspective on quantum correlations.
The invariance property makes QR advantageous for certain quantum information tasks.
QR offers a valuable tool for analyzing complex quantum systems.