Monogamy Relations for Multiqubit Systems

Abstract

Recently a new class of monogamy relations (actually, exponentially many) was provided by Christopher Eltschka et al. in terms of squared concurrence. Their approach restricted to the distribution of bipartite entanglement shared between different subsystems of a global state. We have critically analyzed those monogamy relations in three as well as in four qubit pure states using squared negativity. We have been able to prove that in case of pure three qubit states those relations are always true in terms of squared negativity. However, if we consider the pure four qubit states, the results are not always true. Rather, we find opposite behaviour in some particular classes of four qubit pure states where some of the monogamy relations are violated. We have provided analytical and numerical evidences in support of our claim.

arXiv comment9 pages, 9 figures, latex2e, comments welcome

References in corpus (19)

• Separability Criterion for Density Matrices
• A computable measure of entanglement
• Distributed Entanglement
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Four qubits can be entangled in nine different ways
• Quantum error-correcting codes associated with graphs
• Monogamy Inequality in terms of Negativity for Three-Qubit States
• Bell Inequalities for Graph States
• All Maximally Entangled Four Qubits States
• Strong monogamy conjecture for multiqubit entanglement: The four-qubit case
• Should Entanglement Measures be Monogamous or Faithful?
• Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity
• Monogamy of Correlations vs. Monogamy of Entanglement
• Disentangling Theorem and Monogamy for Entanglement Negativity
• Monogamy of entanglement without inequalities
• Monogamy of $\alpha$th Power Entanglement Measurement in Qubit Systems
• Multipartite entanglement in four-qubit cluster-class states
• Exponentially many entanglement and correlation constraints for multipartite quantum states
• On Strong Monogamy Conjecture in Four-Qubit System

Cited by in corpus (1)

• Multipartite Monogamy of Entanglement for Three Qubit States