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.
|State||Published - Dec 2021|
Bibliographical noteFunding Information:
We thank Aharon Brodutch for insightful discussions. B.P. and A.T. also thank Ebrahim Karimi for their hospitality at the University of Ottawa and Elie Wolfe for their hospitality in Perimeter Institute. Both visits have been fruitful and advanced this work. This research was supported by grant number (FQXi-RFP-CPW-2006) from the Foundational Questions Institute and Fetzer Franklin Fund, a donor advised fund of Silicon Valley Community Foundation. E.C. acknowledges support from the Israel Innovation Authority under projects 70002 and 73795, from the Pazy Foundation and from the Quantum Science and Technology Program of the Israeli Council of Higher Education.
© 2021, The Author(s).