# Generalized concurrence measure for faithful quantification of multiparticle pure state entanglement using Lagrange’s identity and wedge product

@article{Bhaskara2016GeneralizedCM,
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={Quantum Information Processing},
year={2016},
volume={16},
pages={1-15}
}
• Published 1 July 2016
• Physics
• Quantum Information Processing
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…
36 Citations
• Physics
Physical Review A
• 2022
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 strictly positive for entangled
• Physics
The European Physical Journal Plus
• 2021
The wedge product of vectors has been shown to yield the generalised entanglement measure I-concurrence, wherein the separability of the multiparty qubit system arises from the parallelism of vectors
• Physics
• 2022
Xie and Eberly introduced a genuine multipartite entanglement (GME) measure ‘concurrence ﬁll’( Phys. Rev. Lett., 127 , 040403 (2021) ) for three-party systems. It is deﬁned as the area of a triangle
• Physics
International Journal of Theoretical Physics
• 2022
Quantifying entanglement is a work in progress which is important for the active field of quantum information and computation. A measure of bipartite pure state entanglement is proposed here, named
• Physics
International Journal of Theoretical Physics
• 2022
Quantifying entanglement is a work in progress which is important for the active field of quantum information and computation. A measure of bipartite pure state entanglement is proposed here, named
• Physics
• 2020
In this article, we study the behavior of complete complementarity relations under the action of some common noisy quantum channels (amplitude damping, phase damping, bit flip, bit-phase flip, phase
• Computer Science
Journal of Physics A: Mathematical and Theoretical
• 2020
By exploring the purity of bi- and tri-partite pure quantum states, it is shown that it is possible to obtain complete complementarity relations and this procedure allows us to create a general framework for obtaining complete complement parity relations for a subsystem that belongs to an arbitrary multi- partite quantum system in a pure state.
• Physics
Brazilian Journal of Physics
• 2021
We investigate the system–environment information flow from the point of view of complete complementarity relations. We consider some commonly used noisy quantum channels: Amplitude damping, phase
• Physics
Proceedings of the Royal Society A
• 2021
It is well known that entanglement under Lorentz boosts is highly dependent on the boost scenario in question. For single-particle states, a spin-momentum product state can be transformed into an
• Physics
Journal of Physics A: Mathematical and Theoretical
• 2020
The three way distributive entanglement is shown to be related to the parallelism of vectors. Using a measurement based approach we form a set of 2-dimensional vectors, representing the post

## References

SHOWING 1-10 OF 27 REFERENCES

• Physics
• 2001
Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for the entanglement of formation of two qubits in terms of what he calls the concurrence of the joint density operator.
Suppose Alice and Bob jointly possess a pure state, |ψ〉. Using local operations on their respective systems and classical communication it may be possible for Alice and Bob to transform |ψ〉 into
• Physics, Mathematics
• 2010
We present a description of entanglement in composite quantum systems in terms of symplectic geometry. We provide a symplectic characterization of sets of equally entangled states as orbits of group
• Physics
• 2016
Recently Zhu (Int. J. Theor. Phys. 53, 4095, 2014) had shown that using GHZ-like states as quantum channel, it is possible to teleport an arbitrary unknown two-qubit state. We investigate this
• Physics
• 2005
We present a simple numerical optimization procedure to search for highly entangled states of 2, 3, 4 and 5 qubits. We develop a computationally tractable entanglement measure based on the negative
• Physics
• 2008
We investigate the usefulness of a recently introduced five qubit state by Brown $\it et al. \normalfont$ \cite{Brown} for quantum teleportation, quantum state sharing and superdense coding. It is
• Physics
• 2016
The problem of identifying maximally entangled quantum states of a composite quantum systems is analyzed. We review some states of multipartite systems distinguished with respect to certain measures
• Physics
• 1997
The entanglement of formation'' of a mixed state \ensuremath{\rho} of a bipartite quantum system can be defined as the minimum number of singlets needed to create an ensemble of pure states that
• Physics
• 2007
A comparison is made of various searching procedures, based upon different entanglement measures or entanglement indicators, for highly entangled multiqubits states. In particular, our present
• Physics
• 2006
Quantum teleportation1, a way to transfer the state of a quantum system from one location to another, is central to quantum communication2 and plays an important role in a number of quantum