Entanglement Polygon Inequality in Qubit Systems

Abstract

We prove a set of tight entanglement inequalities for arbitrary $N$-qubit pure states. By focusing on all bi-partite marginal entanglements between each single qubit and its remaining partners, we show that the inequalities provide an upper bound for each marginal entanglement, while the known monogamy relation establishes the lower bound. The restrictions and sharing properties associated with the inequalities are further analyzed with a geometric polytope approach, and examples of three-qubit GHZ-class and W-class entangled states are presented to illustrate the results.

arXiv comment8 pages, 4 figures

References in corpus (19)

• Quantum entanglement
• Entanglement of Formation of an Arbitrary State of Two Qubits
• A computable measure of entanglement
• Three qubits can be entangled in two inequivalent ways
• Distributed Entanglement
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Monogamy Inequality in terms of Negativity for Three-Qubit States
• Entangled three-qubit states without concurrence and three-tangle
• Are general quantum correlations monogamous?
• General monogamy relation for the entanglement of formation in multiqubit systems
• Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information
• Monogamy inequality for distributed Gaussian entanglement
• Monogamy properties of quantum and classical correlations
• Strong monogamy conjecture for multiqubit entanglement: The four-qubit case
• General Monogamy of Tsallis $q$-Entropy Entanglement in Multiqubit Systems
• Possibility of generalized monogamy relations for multipartite entanglement beyond three qubits
• Center-of-mass interpretation for bipartite purity analysis of $N$-party entanglement
• Robust Multiple-Range Coherent Quantum State Transfer
• A Geometric Approach to Quantum State Separation

Cited by in corpus (24)

• A Triangle Governs Genuine Tripartite Entanglement
• Genuine multipartite entanglement measure
• Thermodynamic Signatures of Genuinely Multipartite Entanglement
• Concurrence triangle induced genuine multipartite entanglement measure
• Entanglement in three-flavor collective neutrino oscillations
• Entanglement polygon inequality in qudit systems
• Monogamy relations for generalized W class states in terms of Tsallis entropy beyond qubits
• Quantification and observation of genuine three-party coherence: A solution based on classical optics
• Multipartite Entanglement: A Journey Through Geometry
• Sudden Freezing and Thawing of Entanglement Sharing in a Shrunken Volume
• Bridging Coherence Optics and Classical Mechanics -- A Universal Light Polarization-Entanglement Complementary Relation
• Complete monogamy of the multipartite quantum mutual information
• Faithful geometric measures for genuine tripartite entanglement
• Managing the Three-Party Entanglement Challenge
• A geometric formulation to measure global and genuine entanglement in three-qubit systems
• Geometric genuine multipartite entanglement for four-qubit systems
• Polygamy relation of quantum correlations with equality
• Tetrahedron genuine entanglement measure of four-qubit systems
• The polygon relation and subadditivity of entropic measures for discrete and continuous multipartite entanglement
• Entanglement of Assistance as a measure of multiparty entanglement
• Classification of three-qubit genuine entangled states using concurrence fill
• Geometry of two-body correlations in three-qubit states
• Monogamous nature of symmetric multiqubt states with distinct spinors
• Tripartite entanglement and tripartite steering in three-qubit pure states induced by vacuum--one-photon superpositions