An Experimentally accessible geometric measure for entanglement in $N$-qubit pure states

Abstract

We present a multipartite entanglement measure for $N$-qubit pure states, using the norm of the correlation tensor which occurs in the Bloch representation of the state. We compute this measure for several important classes of $N$-qubit pure states such as GHZ states, W states and their superpositions. We compute this measure for interesting applications like one dimensional Heisenberg antiferromagnet. We use this measure to follow the entanglement dynamics of Grover's algorithm. We prove that this measure possesses almost all the properties expected of a good entanglement measure, including monotonicity. Finally, we extend this measure to $N$-qubit mixed states via convex roof construction and establish its various properties, including its monotonicity. We also introduce a related measure which has all properties of the above measure and is also additive.

arXiv comment23 pages, 6 figures, presented in part at ISCQI (Bhubaneswar, India), comments are welcome

References in corpus (25)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• A computable measure of entanglement
• Scaling of Entanglement close to a Quantum Phase Transitions
• Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat The Diffraction Limit
• Entanglement in a simple quantum phase transition
• Entanglement Measures and Purification Procedures
• On the volume of the set of mixed entangled states
• Quantum privacy amplification and the security of quantum cryptography over noisy channels
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Entanglement monotones
• Entanglement-Assisted Classical Capacity of Noisy Quantum Channels
• Generalized Schmidt decomposition and classification of three-quantum-bit states
• Global entanglement in multiparticle systems
• Entanglement Measures under Symmetry
• Teleportation and Dense Coding with Genuine Multipartite Entanglement
• The Bloch Vector for N-Level Systems
• Fidelity and Concurrence of conjugated states
• Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation
• The Entanglement of Formation for Isotropic States
• The Schmidt Measure as a Tool for Quantifying Multi-Particle Entanglement
• Spin chains and channels with memory
• Characterizing multiparticle entanglement in symmetric N-qubit states via negativity of covariance matrices
• Multipartite quantum correlation and entanglement in four-qubit pure states
• Quasi multipartite entanglement measure based on quadratic functions

Cited by in corpus (27)

• Tight lower bound to the geometric measure of quantum discord
• Quantum entanglement from random measurements
• Multipartite Entanglement Analysis From Random Correlations
• Correlations between outcomes of random measurements
• Measure and detection of genuine multipartite entanglement for tripartite systems
• Thermal quantum and classical correlations in two qubit XX model in a nonuniform external magnetic field
• Genuine multipartite entanglement detection and lower bound of multipartite concurrence
• Spatial entanglement using a quantum walk on a many-body system
• Analysing quantum systems with randomised measurements
• The decoherence dynamics of the multipartite entanglement in non-Markovian environment
• The norms of Bloch vectors and classification of four qudits quantum states
• Genuine $N$-partite entanglement without $N$-partite correlation functions
• Viable entanglement detection of unknown mixed states in low dimensions
• Higher dimensional entanglement without correlations
• Using squeezed field to preserve two-atom entanglement against spontaneous emissions
• Geometric measure of quantum discord and total quantum correlations in a N-partite quantum state
• Geometrical entanglement of highly symmetric multipartite states and the Schmidt decomposition
• Entanglement Measures for Intermediate Separability of Quantum States
• Bounds on Multipartite Concurrence and Tangle
• Valid and efficient entanglement verification with finite copies of a quantum state
• Necessary conditions for classifying m-separability of multipartite entanglements
• Entanglement Capacity of Nonlocal Hamiltonians : A Geometric Approach
• Multipartite entanglement in fermionic systems via a geometric measure
• Mutual Uncertainty, Conditional Uncertainty and Strong Sub-Additivity
• Spin correlation tensor for measurement of quantum entanglement in electron-electron scattering
• No-cost Bell nonlocality certification from quantum tomography and its applications in quantum-magic-resource witnessing
• The Richness of Bell Nonlocality: Generalized Bell Polygamy and Hyper-Polygamy