Generalized concurrence measure for faithful quantification of multiparticle pure state entanglement using Lagrange's identity and wedge product
arXiv:1607.00164 · doi:10.1007/s11128-017-1568-0
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.
10 pages, added general derivation for arbitrary dimensions, accepted version of manuscript