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.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.

arXiv:1206.0172Physical Review AJul 18, 201235 citations

Tightening monogamy and polygamy relations of unified entanglement in multipartite systems

Mei-Ming Zhang, Naihuan Jing, Hui Zhao

arXiv:2205.06394Quantum Information ProcessingMar 31, 202210 citations

Conditions for monogamy of quantum correlations: Greenberger-Horne-Zeilinger versus W states

R. Prabhu, Arun Kumar Pati, Aditi Sen +1 more

Quantum correlations are expected to respect all the conditions required for them to be good measures of quantumness in the bipartite scenario. In a multipartite setting, sharing entanglement between several parties is restricted by the monogamy of entanglement. We take over the concept of monogamy to an information-theoretic quantum correlation measure, and find that it violates monogamy in general. Using the notion of interaction information, we identify necessary and sufficient conditions for the measure to obey monogamy, for arbitrary pure and mixed quantum states. We show that while three-qubit generalized Greenberger-Horne-Zeilinger states follow monogamy, generalized $W$ states do not.Quantum correlations are expected to respect all the conditions required for them to be good measures of quantumness in the bipartite scenario. In a multipartite setting, sharing entanglement between several parties is restricted by the monogamy of entanglement. We take over the concept of monogamy to an information-theoretic quantum correlation measure, and find that it violates monogamy in general. Using the notion of interaction information, we identify necessary and sufficient conditions for the measure to obey monogamy, for arbitrary pure and mixed quantum states. We show that while three-qubit generalized Greenberger-Horne-Zeilinger states follow monogamy, generalized $W$ states do not.

arXiv:1108.5168Physical Review AApr 30, 2012107 citations

Algebraic Criteria for Entanglement in Multipartite Systems

J. D. M. Vianna, Marco A. S. Trindade, M.C.B. Fernandes

International Journal of Theoretical PhysicsSep 20, 20077 citations

Compatibility conditions from multipartite entanglement measures

Jianming Cai, Zheng-Wei Zhou, Shun Zhang +1 more

We consider an arbitrary ${d}_{1}\ensuremath{\bigotimes}{d}_{2}\ensuremath{\bigotimes}\ensuremath{\cdots}\ensuremath{\bigotimes}{d}_{N}$ composite quantum system and find necessary conditions for general $m$ -party subsystem states to be the reduced states of a common $N$ -party state. These conditions will lead to various monogamy inequalities for bipartite quantum entanglement and partial disorder in multipartite states. Our results are tightly connected with the measures of multipartite entanglement.We consider an arbitrary ${d}_{1}\ensuremath{\bigotimes}{d}_{2}\ensuremath{\bigotimes}\ensuremath{\cdots}\ensuremath{\bigotimes}{d}_{N}$ composite quantum system and find necessary conditions for general $m$-party subsystem states to be the reduced states of a common $N$-party state. These conditions will lead to various monogamy inequalities for bipartite quantum entanglement and partial disorder in multipartite states. Our results are tightly connected with the measures of multipartite entanglement.

arXiv:quant-ph/0611224Physical Review AMay 18, 200712 citations

W

states do not.

m

-party subsystem states to be the reduced states of a common

N

-party state. These conditions will lead to various monogamy inequalities for bipartite quantum entanglement and partial disorder in multipartite states. Our results are tightly connected with the measures of multipartite entanglement.