-qudit pure states, using the norm of the correlation tensor which occurs in the Bloch representation of the state. We compute this measure for important class of

N

-qutrit pure states, namely general GHZ states. 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

-qudit mixed states via convex roof construction and establish its various properties, including its monotonicity.

DOI: 10.48550/arxiv.0901.2398

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An Experimentally accessible geometric measure for entanglement in

N

-qudit pure states

We present a multipartite entanglement measure for

N

-qudit pure states, using the norm of the correlation tensor which occurs in the Bloch representation of the state. We compute this measure for important class of

N

N

-qudit mixed states via convex roof construction and establish its various properties, including its monotonicity.

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.

We present a multipartite entanglement measure for

N

-qudit pure states, using the norm of the correlation tensor which occurs in the Bloch representation of the state. We compute this measure for an important class of

N

-qutrit pure states, namely, general GHZ states. We prove that this measure possesses all the essential and many desirable properties expected of a good entanglement measure, including monotonicity. We also discuss the feasibility of the experimental evaluation of this measure for an

N

-qutrit system.

m\mathrm{GHZ}

states,

W

states, inverted

W

states, qudits, and nonsymmetric states, are used to demonstrate the power of the proposed methods. Given a pure state, one can always find a change of basis (a unitary transformation) so that all the probability amplitudes of the pure state are non-negative under the new basis. Therefore, the methods proposed here can be applied to a very wide class of multipartite pure states.

l_{1}

-norm of coherence, the geometric measure of coherence, and the coherence of formation. Furthermore, all the lower bounds are based on the fidelity between the chosen pure state and the target state, and we obtain the lower bounds of several real experimental states as examples of our results.