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arXiv · 2312.08474

Completely entangled subspaces of entanglement depth $k$

Maciej Demianowicz·Kajetan Vogtt·Remigiusz Augusiak
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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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Maciej Demianowicz, Kajetan Vogtt, Remigiusz Augusiak. 2023-12-13. Completely entangled subspaces of entanglement depth $k$. https://arxiv.org/abs/2312.08474

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