# 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} }

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

### Generalized entanglement measure for continuous-variable systems

- PhysicsPhysical 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…

### Geometric quantification of multiparty entanglement through orthogonality of vectors

- PhysicsThe 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…

### Geometric genuine multipartite entanglement for four-qubit systems

- 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…

### Quantifying Entanglement with Coherence

- PhysicsInternational 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…

### Quantifying Entanglement with Coherence

- PhysicsInternational 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…

### Dynamics of complete complementarity relations under quantum channels

- 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…

### Complete complementarity relations for multipartite pure states

- Computer ScienceJournal 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.

### Complete Complementarity Relations in System–environment Decoherent Dynamics

- PhysicsBrazilian 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…

### Complete complementarity relations and their Lorentz invariance

- PhysicsProceedings 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…

### Quantifying parallelism of vectors is the quantification of distributed n-party entanglement

- PhysicsJournal 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

### Universal state inversion and concurrence in arbitrary dimensions

- 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.…

### Conditions for a Class of Entanglement Transformations

- Physics
- 1999

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…

### Symplectic Geometry of Entanglement

- 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…

### Quantum Teleportation of an Arbitrary N-qubit State via GHZ-like States

- 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…

### Searching for highly entangled multi-qubit states

- 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…

### Perfect teleportation, quantum-state sharing, and superdense coding through a genuinely entangled five-qubit state

- 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…

### Maximally Entangled Multipartite States: A Brief Survey

- 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…

### Entanglement of a Pair of Quantum Bits

- 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…

### Multiqubit systems: highly entangled states and entanglement distribution

- 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…

### Experimental quantum teleportation of a two-qubit composite system

- 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…