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Related Experiment Video

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Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Entanglement Quantification Made Easy: Polynomial Measures Invariant under Convex Decomposition.

Bartosz Regula¹, Gerardo Adesso¹

¹School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.

Physical Review Letters

|March 5, 2016

Summary

Quantifying quantum entanglement in composite systems is simplified. We show that specific entanglement measures become trivial under certain conditions, enabling analytical calculations for complex quantum states.

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Area of Science:

Quantum Information Science
Quantum Many-Body Systems
Entanglement Theory

Background:

Quantifying entanglement in composite quantum systems is a significant challenge.
Exact calculations are often hindered by complex optimization problems, like finding the convex roof of entanglement.
The convex roof represents the minimal average pure-state entanglement for a mixed state.

Purpose of the Study:

To identify conditions under which quantifying entanglement becomes analytically tractable.
To develop methods for evaluating entanglement measures in specific classes of quantum states.
To simplify the calculation of convex roof extended entanglement measures.

Main Methods:

Geometric argument to prove independence of entanglement measures from state decomposition.
Analysis of polynomial entanglement measures of degree 2.
Focus on mixed states with a unique pure unentangled state in their range.

Main Results:

Demonstrated that degree 2 polynomial entanglement measures are independent of pure-state decomposition under specific conditions.
Enabled analytical evaluation of convex roof extended entanglement measures for certain rank-2 states.
Provided explicit examples using the square root of the three-tangle for three-qubit states.
Identified classes of four-qubit pure states whose marginals satisfy the derived conditions.

Conclusions:

The study simplifies the quantification of entanglement in specific composite quantum systems.
The findings pave the way for analytical calculations of entanglement measures in previously intractable cases.
This work offers new tools for analyzing entanglement in multi-qubit systems.