Light Cone-Like Behavior of Quantum Monogamy Score and Multisite Entanglement

TL;DR

This paper uncovers a cone-like structure in the space of quantum correlation measures for pure three-qubit states, revealing fundamental constraints akin to light cones in relativity, linking monogamy and multisite entanglement.

Contribution

It analytically relates different quantum correlation measures and demonstrates a universal cone-like region accessible to pure three-qubit states, highlighting fundamental geometric constraints.

Findings

Quantum correlation measures form a cone-like region for pure three-qubit states.

Analytical relations connect information-theoretic and entanglement-separability measures.

Pure three-qubit states cannot exist outside the identified cone-like structure.

Abstract

There are two important paradigms for defining quantum correlations in quantum information theory, viz. the information-theoretic and the entanglement-separability ones. We find an analytical relation between two measures of quantum correlations, one in each paradigm, and show that only a certain cone-like region on the two-dimensional space spanned by these measures is accessible to pure three-qubit states. The information-theoretic multiparty quantum correlation measure is related to the monogamy considerations of a bipartite information-theoretic quantum correlation measure, while the entanglement-separability multiparty measure is the generalized geometric measure, a genuine multiparty entanglement measure. We also find an analytical relation between two multiparty entanglement measures, and again obtain a cone-like accessible region in this case. One of the multisite measures in this case is related to the monogamy of a bipartite entanglement measure, while the other is again the generalized geometric measure. Just like in relativity, events cannot occur outside the space-time light cone, we analogously find here that state points corresponding to pure three-qubit states cannot fall outside the two-dimensional cone-like structure between quantum monogamy scores and a genuine multisite entanglement measure.