Local unitary equivalence of absolutely maximally entangled states constructed from orthogonal arrays

• URL: http://arxiv.org/abs/2411.04096v1
• Date: Wed, 06 Nov 2024 18:22:23 GMT
• Title: Local unitary equivalence of absolutely maximally entangled states constructed from orthogonal arrays
• Authors: N Ramadas, Arul Lakshminarayan,
• Abstract summary: This study concerns a class of highly entangled multipartite states, the so-called absolutely maximally entangled (AME) states. We show that there are infinitely many local unitary inequivalent three-party AME states for local dimension $d > 2$ and five-party AME states for $d geq 2$.
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• Abstract: The classification of multipartite entanglement is essential as it serves as a resource for various quantum information processing tasks. This study concerns a particular class of highly entangled multipartite states, the so-called absolutely maximally entangled (AME) states. These are characterized by maximal entanglement across all possible bipartitions. In particular we analyze the local unitary equivalence among AME states using invariants. One of our main findings is that the existence of special irredundant orthogonal arrays implies the existence of an infinite number of equivalence classes of AME states constructed from these. In particular, we show that there are infinitely many local unitary inequivalent three-party AME states for local dimension $d > 2$ and five-party AME states for $d \geq 2$.

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