Universal construction of genuinely entangled subspaces of any size
Maciej Demianowicz
Abstract
We put forward a simple construction of genuinely entangled subspaces – subspaces supporting only genuinely multipartite entangled states – of any permissible dimensionality for any number of parties and local dimensions. The method uses nonorthogonal product bases, which are built from totally nonsingular matrices with a certain structure. We give an explicit basis for the constructed subspaces. An immediate consequence of our result is the possibility of constructing in the general multiparty scenario genuinely multiparty entangled mixed states with ranks up to the maximal dimension of a genuinely entangled subspace.
Topics & Concepts
Linear subspaceMultipartiteDimension (graph theory)Subspace topologySimple (philosophy)Invertible matrixProduct (mathematics)Curse of dimensionalityMathematicsBasis (linear algebra)Pure mathematicsDiscrete mathematicsComputer scienceQuantum entanglementQuantumPhysicsQuantum mechanicsEpistemologyGeometryPhilosophyMathematical analysisStatisticsQuantum Information and CryptographyQuantum Mechanics and ApplicationsQuantum Computing Algorithms and Architecture