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

TL;DR

This paper introduces methods for constructing genuinely multipartite entangled subspaces, explores their maximal dimensions, and establishes bounds on entanglement measures for mixed states, advancing quantum information processing resources.

Contribution

It presents novel construction techniques for genuinely entangled subspaces, including maximal dimension cases, and links these to bounds on entanglement measures for mixed states.

Findings

Constructed maximal genuinely entangled subspaces for various quantum systems.

Established lower bounds on concurrence and negativity for mixed states.

Demonstrated the connection between subspace projections and entanglement measures.

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.