An approach to constructing genuinely entangled subspaces of maximal dimension

Abstract

Genuinely entangled subspaces (GESs) are the class of completely entangled subspaces that contain only genuinely multiparty entangled states. They constitute a particularly useful notion in the theory of entanglement but also have found an application, for instance, in quantum error correction and cryptography. In a recent study (Demianowicz and Augusiak in Phys Rev A 98:012313, 2018), we have shown how GESs can be efficiently constructed in any multiparty scenario from the so-called unextendible product bases. The provided subspaces, however, are not of maximal allowable dimensions, and our aim here is to put forward an approach to building such. The method is illustrated with few examples in small systems. Connections with other mathematical problems, such as spaces of matrices of equal rank and the numerical range, are discussed.

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Cited by in corpus (11)

• Quantum Codes of Maximal Distance and Highly Entangled Subspaces
• Universal construction of genuinely entangled subspaces of any size
• Simple sufficient condition for subspace to be completely or genuinely entangled
• Construction of genuinely multipartite entangled subspaces and the associated bounds on entanglement measures for mixed states
• 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
• Performance Analysis of Quantum CSS Error-Correcting Codes via MacWilliams Identities
• Entangled Subspaces through Algebraic Geometry
• Detection of genuine tripartite entanglement by two bipartite entangled states
• Progress in the study of the (non)existence of genuinely unextendible product bases