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.

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

References in corpus (3)

• 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

Cited by in corpus (11)

• Measure and detection of genuine multipartite entanglement for tripartite systems
• Analysing quantum systems with randomised measurements
• The norms of Bloch vectors and classification of four qudits quantum states
• Using squeezed field to preserve two-atom entanglement against spontaneous emissions
• Entanglement Measures for Intermediate Separability of Quantum States
• Bounds on Multipartite Concurrence and Tangle
• Necessary conditions for classifying m-separability of multipartite entanglements
• Valid and efficient entanglement verification with finite copies of a quantum state
• Spin correlation tensor for measurement of quantum entanglement in electron-electron scattering
• The Richness of Bell Nonlocality: Generalized Bell Polygamy and Hyper-Polygamy
• No-cost Bell nonlocality certification from quantum tomography and its applications in quantum-magic-resource witnessing