Strong monogamy inequalities for four qubits

Abstract

We investigate possible generalizations of the Coffman-Kundu-Wootters monogamy inequality to four qubits, accounting for multipartite entanglement in addition to the bipartite terms. We show that the most natural extension of the inequality does not hold in general, and we describe the violations of this inequality in detail. We investigate alternative ways to extend the monogamy inequality to express a constraint on entanglement sharing valid for all four-qubit states, and perform an extensive numerical analysis of randomly generated four-qubit states to explore the properties of such extensions.

arXiv comment6 pages, 4 figures. Published version

References in corpus (32)

• Quantum entanglement
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Three qubits can be entangled in two inequivalent ways
• Entanglement of a Pair of Quantum Bits
• Distributed Entanglement
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Four qubits can be entangled in nine different ways
• Monogamy of entanglement and other correlations
• Normal forms and entanglement measures for multipartite quantum states
• Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity
• Quantifying entanglement resources
• Constructing N-qubit entanglement monotones from anti-linear operators
• Entangled three-qubit states without concurrence and three-tangle
• Are general quantum correlations monogamous?
• All Maximally Entangled Four Qubits States
• Strong monogamy conjecture for multiqubit entanglement: The four-qubit case
• Three-tangle for mixtures of generalized GHZ and generalized W states
• Strong Monogamy of Bipartite and Genuine Multipartite Entanglement: The Gaussian Case
• Negativity and strong monogamy of multi-party quantum entanglement beyond qubits
• Monogamy equalities for qubit entanglement from Lorentz invariance
• Three-Tangle for Rank-3 Mixed States: mixture of Greenberger-Horne-Zeilinger, W and flipped W states
• Multipartite-entanglement monotones and polynomial invariants
• Multipartite monogamy of the concurrence
• The maximally entangled set of 4-qubit states
• Entanglement sharing: from qubits to Gaussian states
• The invariant-comb approach and its relation to the balancedness of multipartite entangled states
• Possibility of generalized monogamy relations for multipartite entanglement beyond three qubits
• Entanglement quantification made easy: Polynomial measures invariant under convex decomposition
• A quantitative witness for Greenberger-Horne-Zeilinger entanglement
• Rescaling multipartite entanglement measures for mixed states
• Bounding Polynomial Entanglement Measures for Mixed States
• On Strong Monogamy Conjecture in Four-Qubit System

Cited by in corpus (21)

• Convex geometry of quantum resource quantification
• Monogamy of entanglement without inequalities
• Multipartite Entanglement Measure and Complete Monogamy Relation
• Versatile Multipartite Einstein-Podolsky-Rosen Steering via a Quantum Frequency Comb
• Exponentially many entanglement and correlation constraints for multipartite quantum states
• Monogamy of quantum entanglement
• When is a Genuine Multipartite Entanglement Measure Monogamous?
• Geometric approach to entanglement quantification with polynomial measures
• Generalized W-state of four qubits with exclusively threetangle
• Correlation constraints and the Bloch geometry of two qubits
• Realization of the tradeoff between internal and external entanglement
• The nine ways of four qubit entanglement and their threetangle
• Quantum memory for Rindler supertranslations
• Exact zeros of entanglement for arbitrary rank-two mixtures: how a geometric view of the zero-polytope makes life more easy
• On Monogamy of four qubit entanglement
• Entanglement Classification via Single Entanglement Measure
• Monogamy and polygamy for multi-qudit generalized $W$-class states based on concurrence of assistance and Tsallis-$q$ entanglement of assistance
• Distributed entanglement generation from asynchronously excited qubits
• Monogamy constraints on entanglement of four-qubit pure states
• Entanglement measures for multipartite quantum systems:limitations and new approaches
• Maximum residual strong monogamy inequality for multiqubit entanglement