Generalized concurrence measure for faithful quantification of multiparticle pure state entanglement using Lagrange's identity and wedge product
Abstract
Concurrence, introduced by Hill and Wootters [Phys. Rev. Lett. 78, 5022 (1997)], provides an important measure of entanglement for a general pair of qubits that is faithful: strictly positive for entangled states and vanishing for all separable states. Such a measure captures the entire content of entanglement, providing necessary and sufficient conditions for separability. We present an extension of concurrence to multiparticle pure states in arbitrary dimensions by a new framework using the Lagrange's identity and wedge product representation of separability conditions, which coincides with the "I-concurrence" of Rungta et al. [Phys. Rev. A 64, 042315 (2001)] who proposed by extending Wootters's spin-flip operator to a so-called universal inverter superoperator. Our framework exposes an inherent geometry of entanglement, and may be useful for the further extensions to mixed and continuous variable states.
Keywords
Cite
@article{arxiv.1607.00164,
title = {Generalized concurrence measure for faithful quantification of multiparticle pure state entanglement using Lagrange's identity and wedge product},
author = {Vineeth S. Bhaskara and Prasanta K. Panigrahi},
journal= {arXiv preprint arXiv:1607.00164},
year = {2017}
}
Comments
10 pages, added general derivation for arbitrary dimensions, accepted version of manuscript