Rescaling multipartite entanglement measures for mixed states

Abstract

A relevant problem regarding entanglement measures is the following: Given an arbitrary mixed state, how does a measure for multipartite entanglement change if general local operations are applied to the state? This question is nontrivial as the normalization of the states has to be taken into account. Here we answer it for pure-state entanglement measures which are invariant under determinant 1 local operations and homogeneous in the state coefficients, and their convex-roof extension which quantifies mixed-state entanglement. Our analysis allows to enlarge the set of mixed states for which these important measures can be calculated exactly. In particular, our results hint at a distinguished role of entanglement measures which have homogeneous degree 2 in the state coefficients.

Published version plus one important reference (Ref. [39])

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• Entanglement quantification made easy: Polynomial measures invariant under convex decomposition
• A quantitative witness for Greenberger-Horne-Zeilinger entanglement
• Parametrization and optimization of Gaussian non-Markovian unravelings for open quantum dynamics
• Practical method to obtain a lower bound to the three-tangle
• Geometric approach to entanglement quantification with polynomial measures
• Generalized W-state of four qubits with exclusively threetangle
• The nine ways of four qubit entanglement and their threetangle
• Upper bound for SL-invariant entanglement measures of mixed states
• A heat bath can generate all classes of three-qubit entanglement
• SL-invariant entanglement measures in higher dimensions: the case of spin $1$ and $3/2$
• Linear response of tripartite entanglement to infinitesimal noise
• Threetangle in the XY-model class with a non-integrable field background