Experimentally accessible geometric measure for entanglement inN-qubit pure states

Abstract

We present a multipartite entanglement measure for $\mathit{N}$-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 $\mathit{N}$-qubit pure states such as Greenberger-Horne-Zeilinger and $\mathit{W}$ states and their superpositions. We compute this measure for interesting applications like the 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 $\mathit{N}$-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.