Completely entangled subspaces of entanglement depth $k$

• URL: http://arxiv.org/abs/2312.08474v3
• Date: Tue, 2 Jul 2024 13:19:39 GMT
• Title: Completely entangled subspaces of entanglement depth $k$
• Authors: Maciej Demianowicz, Kajetan Vogtt, Remigiusz Augusiak,
• Abstract summary: We introduce a class of entangled subspaces: completely entangled subspaces of entanglement depth $k$ ($k$-CESs) We discuss the relation between these subspaces and unextendible product bases (UPBs)
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a class of entangled subspaces: completely entangled subspaces of entanglement depth $k$ ($k$-CESs). These are subspaces of multipartite Hilbert spaces containing only pure states with an entanglement depth of at least $k$. We present an efficient construction of $k$-CESs of any achievable dimensionality in any multipartite scenario. Further, we discuss the relation between these subspaces and unextendible product bases (UPBs). In particular, we establish that there is a non-trivial bound on the cardinality of a UPB whose orthocomplement is a $k$-CES. Further, we discuss the existence of such UPBs for qubit systems.

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