Geometric measure of entanglement and applications to bipartite and multipartite quantum states

@article{Wei2003GeometricMO,
  title={Geometric measure of entanglement and applications to bipartite and multipartite quantum states},
  author={Tzu-Chieh Wei and Paul M. Goldbart},
  journal={Physical Review A},
  year={2003},
  volume={68},
  pages={042307}
}
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings [A. Shimony, Ann. NY. Acad. Sci. 755, 675 (1995); H. Barnum and N. Linden, J. Phys. A: Math. Gen. 34, 6787 (2001)], is explored for bipartite and multipartite pure and mixed states. The measure is determined analytically for arbitrary two-qubit mixed states and for generalized Werner… 

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References

SHOWING 1-10 OF 32 REFERENCES

Degree of Entanglement a

The present report exhibits some mathematical relations among three concepts associated with entanglement, restricted to the case of two particles, each associated with a two-dimensional Hilbert space, called “the two-by-two case”.

Characterizing the entanglement of symmetric many-particle spin-1/2 systems

Analyzing the properties of entanglement in many-particle spin-1/2 systems is generally difficult because the system's Hilbert space grows exponentially with the number of constituent particles, N.

Volume of the set of separable states

The question of how many entangled or, respectively, separable states there are in the set of all quantum states is considered. We propose a natural measure in the space of density matrices %

On the volume of the set of mixed entangled states II

A natural measure in the space of density matrices describing N-dimensional quantum systems is proposed. We study the probability P that a quantum state chosen randomly with respect to the natural

Maximal entanglement versus entropy for mixed quantum states

Maximally entangled mixed states are those states that, for a given mixedness, achieve the greatest possible entanglement. For two-qubit systems and for various combinations of entanglement and

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

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

On the characterization of entanglement

In the context of N-party composite systems some considerations about entanglement magnitudes defined on the set of their states are made. A minimal set of necessary and sufficient requirements any

Schmidt measure as a tool for quantifying multiparticle entanglement

We present a measure of quantum entanglement which is capable of quantifying the degree of entanglement of a multi-partite quantum system. This measure, which is based on a generalization of the

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.