Citation Link: https://doi.org/10.3390/e25091260
Covariance-Matrix-Based Criteria for Network Entanglement
Publication Type
Article
Author(s)
Subjects
Quantum entanglement
Bipartite graph
Computer science
Simple (philosophy)
Mathematical proof
Theoretical computer science
Quantum network
Covariance matrix
Quantum
Topology (electrical circuits)
Mathematics
Algorithm
Quantum mechanics
Graph
Physics
Combinatorics
Date Issued
2023
Abstract
Quantum networks offer a realistic and practical scheme for generating multipArticle entanglement and implementing multipArticle quantum communication protocols. However, the correlations that can be generated in networks with quantum sources and local operations are not yet well understood. Covariance matrices, which are powerful tools in entanglement theory, have been also applied to the network scenario. We present simple proofs for the decomposition of such matrices into the sum of positive semi-definite block matrices and, based on that, develop analytical and computable necessary criteria for preparing states in quantum networks. These criteria can be applied to networks where nodes share at most one source, such as all bipartite networks.
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