General stabilizer approach for constructing highly entangled graph states

• URL: http://arxiv.org/abs/2111.08045v2
• Date: Tue, 22 Nov 2022 01:15:01 GMT
• Title: General stabilizer approach for constructing highly entangled graph states
• Authors: Zahra Raissi, Adam Burchardt, and Edwin Barnes
• Abstract summary: Highly entangled multipartite states such as k-uniform (kUNI) and absolutely maximally entangled (AME) states serve as critical resources in quantum networking and other quantum information applications. Here, we substantially broaden the class of known k-UNI and AME states by introducing a method for explicitly constructing such states that combines classical error correcting codes and qudit graph states.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Highly entangled multipartite states such as k-uniform (k-UNI) and absolutely maximally entangled (AME) states serve as critical resources in quantum networking and other quantum information applications. However, there does not yet exist a complete classification of such states, and much remains unknown about their entanglement structure. Here, we substantially broaden the class of known k-UNI and AME states by introducing a method for explicitly constructing such states that combines classical error correcting codes and qudit graph states. This method in fact constitutes a general recipe for obtaining multipartitite entangled states from classical codes. Furthermore, we show that at least for a large subset of this new class of k-UNI states, the states are inequivalent under stochastic local operations and classical communication. This subset is defined by an iterative procedure for constructing a hierarchy of k-UNI graph states.

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