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arXiv:2302.00650 · Quantum Information Processing

Multipartite entanglement detection via correlation minor norm

Rain Lenny, Amit Te’eni, Bar Y. Peled, Avishy Y. Carmi, Eliahu Cohen

Published Jul 19, 2023• 3 citations
arXivHTMLPDF
DOI
10.1007/s11128-023-04046-6

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In this paper we develop an approach for detecting entanglement, which is based on measuring quantum correlations and constructing a correlation matrix. The correlation matrix is then used for defining a family of parameters, named Correlation Minor Norms, which allow one to detect entanglement. This approach generalizes the computable cross-norm or realignment (CCNR) criterion, and moreover requires measuring a state-independent set of operators. Furthermore, we illustrate a scheme which yields for each Correlation Minor Norm a separable state that maximizes it. The proposed entanglement detection scheme is believed to be advantageous in comparison to other methods because correlations have a simple, intuitive meaning and in addition they can be directly measured in experiment. Moreover, it is demonstrated to be stronger than the CCNR criterion. We also illustrate the relation between the Correlation Minor Norm and entanglement entropy for pure states. Finally, we discuss the relation between the Correlation Minor Norm and quantum discord. We demonstrate that the CMN may be used to define a new measure for quantum discord.
Multipartite entanglement constitutes one of the key resources in quantum information processing. We exploit correlation tensor norms to develop a framework for its experimental detection without the need for shared frames of reference. By bounding these norms for partially separable states and states of limited dimension, we achieve an extensive characterization of entanglement in multipartite systems in an experimentally feasible way. Furthermore, we show that both bi- and multipartite dimensionality of entanglement can be revealed by our methods.