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Separable states are more disordered globally than locally.

M A Nielsen¹, J Kempe

¹Centre for Quantum Computer Technology, University of Queensland, Queensland 4072, Australia. nielsen@physics.uq.edu.au

Physical Review Letters

|June 1, 2001

Summary

Quantum entanglement allows local states to be more disordered than global states (S(A)>S(A,B)). For separable states, global disorder is greater than local disorder, providing a new separability condition for bipartite systems.

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Area of Science:

Quantum Information Theory
Quantum Mechanics
Mathematical Physics

Background:

Quantum entanglement exhibits counterintuitive properties, where local subsystems can be more disordered than the entire system.
The inequality S(A)>S(A,B), using von Neumann entropy, is a known indicator of nonseparability in quantum states.

Purpose of the Study:

To investigate the relationship between local and global disorder in quantum states.
To establish a new necessary condition for the separability of bipartite quantum states in arbitrary dimensions.

Main Methods:

Analysis of the eigenvalue vectors of density matrices for bipartite systems (A and B).
Application of majorization theory to compare eigenvalue distributions.

Main Results:

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For separable states, the eigenvalue vector of the composite system AB is majorized by that of subsystem A.
This demonstrates that separable states are globally more disordered than locally.

Conclusions:

The majorization condition provides a novel and strong necessary condition for separability in bipartite quantum states.
This finding deepens the understanding of the distinction between separable and entangled states in quantum information theory.