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

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.

8 pages, revtex4. arXiv admin note: text overlap with arXiv:1309.6235

References in corpus (8)

• Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
• Constructing N-qubit entanglement monotones from anti-linear operators
• Maximally multipartite entangled states
• Genuinely multipartite entangled states and orthogonal arrays
• Entanglement monotones and maximally entangled states in multipartite qubit systems
• Exploring pure quantum states with maximally mixed reductions
• On polynomial invariants of several qubits
• Classification scheme of pure multipartite states based on topological phases

Cited by in corpus (1)

• Entanglement of genuinely entangled subspaces and states: exact, approximate, and numerical results