Construction of genuinely multipartite entangled subspaces and the associated bounds on entanglement measures for mixed states

Abstract

Genuine entanglement is the strongest form of multipartite entanglement. Genuinely entangled pure states contain entanglement in every bipartition and as such can be regarded as a valuable resource in the protocols of quantum information processing. A recent direction of research is the construction of genuinely entangled subspaces -- the class of subspaces consisting entirely of genuinely multipartite entangled pure states. In this paper we present several methods of construction of such subspaces including those of maximal possible dimension. The approach is based on the correspondence between bipartite entangled subspaces and quantum channels of a certain type. The examples include maximal subspaces for systems of three qubits, four qubits, three qutrits. We also provide lower bounds on two entanglement measures for mixed states, the concurrence and the convex-roof extended negativity, which are directly connected with the projection on genuinely entangled subspaces.

17 pages, 6 figures. REVTEX

References in corpus (5)

• Entanglement detection
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• Is Entanglement Monogamous?
• Lectures on Quantum Tensor Networks
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Cited by in corpus (5)

• Universal construction of genuinely entangled subspaces of any size
• Fully non-positive-partial-transpose genuinely entangled subspaces
• Construction of genuinely entangled multipartite subspaces from bipartite ones by reducing the total number of separated parties
• Negative result about the construction of genuinely entangled subspaces from unextendible product bases
• Frustration graph formalism for qudit observables