A comparison of entanglement measures

@article{Eisert1999ACO,
  title={A comparison of entanglement measures},
  author={Jens Eisert and Martin Bodo Plenio},
  journal={Journal of Modern Optics},
  year={1999},
  volume={46},
  pages={145-154}
}
Abstract We compare the entanglement of formation with a measure defined as the modulus of the negative eigenvalue of the partial transpose. In particular we investigate whether both measures give the same ordering of density operators with respect to the amount of entanglement 

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References

SHOWING 1-10 OF 20 REFERENCES

Statistical Inference, Distinguishability of Quantum States, And Quantum Entanglement

We argue from the point of view of statistical inference that the quantum relative entropy is a good measure for distinguishing between two quantum states (or two classes of quantum states) described

Entanglement measures and purification procedures

It is argued that the statistical basis of the measure of entanglement determines an upper bound to the number of singlets that can be obtained by any purification procedure.

Entanglement of Formation of an Arbitrary State of Two Qubits

The entanglement of a pure state of a pair of quantum systems is defined as the entropy of either member of the pair. The entanglement of formation of a mixed state is defined as the minimum average

Composed ensembles of random unitary matrices

Composed ensembles of random unitary matrices are defined via products of matrices, each pertaining to a given canonical circular ensemble of Dyson. We investigate statistical properties of spectra

Multi-Particle Entanglement Purification Protocols

Purification schemes for multiparticle entangled states cannot be treated as straightforward extensions of those two-particle ones because of the lack of symmetry they possess. We propose

Concentrating partial entanglement by local operations.

Any pure or mixed entangled state of two systems can be produced by two classically communicating separated observers, drawing on a supply of singlets as their sole source of entanglement.

Experimental quantum teleportation

It is shown that during teleportation, one of a pair of entangled photons are subjected to a measurement such that the second photon of the entangled pair acquires the polarization of the initial photon.

Quantifying Entanglement

We have witnessed great advances in quantum information theory in recent years. There are two distinct directions in which progress is currently being made: quantum computation and error correction

Mixed-state entanglement and quantum error correction.

It is proved that an EPP involving one-way classical communication and acting on mixed state M (obtained by sharing halves of Einstein-Podolsky-Rosen pairs through a channel) yields a QECC on \ensuremath{\chi} with rate Q=D, and vice versa, and it is proved Q is not increased by adding one- way classical communication.

Inseparable Two Spin- 1 2 Density Matrices Can Be Distilled to a Singlet Form

A quantum system is called inseparable if its density matrix cannot be written as a mixture of product states. In this Letter we apply the separability criterion, local filtering, and Bennett et al.