On Strong Monogamy Conjecture in Four-Qubit System

Monogamy is a defining feature of entanglement, having far reaching applications. Recently, Regula \textit{et.al.} in Phys. Rev. Lett. \textbf{113}, 110501(2014) have proposed a stronger version of monogamy relation for concurrence. We have extended the strong monogamy inequality for another entanglement measure, viz., negativity. In particular, we have concentrated on four-qubit system and provided a detail study on the status of strong monogamy on pure states. Further, we have analytically provided some classes of states for which negativity and squared negativity satisfy strong monogamy. Numerical evidences have also been shown in proper places. Our analysis also provides cases where strong monogamy is violated.Comment: 8 pages, 8 figures, revtex, comments welcom

Characterization of Tripartite Quantum States with Vanishing Monogamy Score

Quantum discord, an information-theoretic quantum correlation measure, can satisfy as well as violate monogamy, for three-party quantum states. We quantify the feature using the concept of discord monogamy score. We find a necessary condition of a vanishing discord monogamy score for arbitrary three-party states. A necessary and sufficient condition is obtained for pure states. We prove that the class of states having a vanishing discord monogamy score cannot have arbitrarily high genuine multipartite entanglement, as quantified by generalized geometric measure. In the special case of three-qubit pure states, their classification with respect to the discord monogamy score, reveals a rich structure that is different from that which had been obtained by using the monogamy score corresponding to the entanglement measure called concurrence. We investigate properties like genuine multipartite entanglement and violation of the multipartite Bell inequality for these states.Comment: v1: 8 pages, 7 figures, RevTeX 4.1; v2: published versio

Monogamy of Einstein-Podolsky-Rosen steering in the background of an asymptotically flat black hole

We study the behavior of monogamy deficit and monogamy asymmetry for Einstein-Podolsky-Rosen steering of Gaussian states under the influence of the Hawking effect. We demonstrate that the monogamy of quantum steering shows an extreme scenario in the curved spacetime: the first part of a tripartite system cannot individually steer two other parties, but it can steer the collectivity of the remaining two parties. We also find that the monogamy deficit of Gaussian steering, a quantifier of genuine tripartite steering, are generated due to the influence of the Hawking thermal bath. Our results elucidate the structure of quantum steering in tripartite quantum systems in curved spacetime.Comment: 16 pages, 4 figure