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arXiv · 1406.0361

Genuinely multipartite entangled states in higher dimensions: a generalization of balancedness

Andreas Osterloh
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Abstract

I generalize the concept of balancedness to qudits with arbitrary dimension $d$. It is an extension of the concept of balancedness in New J. Phys. {\bf 12}, 075025 (2010) [1]. At first, I define maximally entangled states as being the stochastic states (with local reduced density matrices $\id/d$ for a $d$-dimensional local Hilbert space) that are not product states and show that every so-defined maximal genuinely multi-qudit entangled state is balanced. Furthermore, all irreducibly balanced states are genuinely multi-qudit entangled and are locally equivalent with respect to $SL(d)$ transformations (i.e. the local filtering transformations (LFO)) to a maximally entangled state. In particular the concept given here gives the maximal genuinely multi-qudit entangled states for general local Hilbert space dimension $d$. All genuinely multi-qudit entangled states are an element of the partly balanced $SU(d)$-orbits.

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Andreas Osterloh. 2014-06-02. Genuinely multipartite entangled states in higher dimensions: a generalization of balancedness. https://doi.org/10.1088/1751-8113/47/49/495301

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