# Inseparability criterion for continuous variable systems

@article{Duan2000InseparabilityCF, title={Inseparability criterion for continuous variable systems}, author={Duan and Giedke and Cirac and Zoller}, journal={Physical review letters}, year={2000}, volume={84 12}, pages={ 2722-5 } }

An inseparability criterion based on the total variance of a pair of Einstein-Podolsky-Rosen type operators is proposed for continuous variable systems. The criterion provides a sufficient condition for entanglement of any two-party continuous variable states. Furthermore, for all Gaussian states, this criterion turns out to be a necessary and sufficient condition for inseparability.

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## References

SHOWING 1-10 OF 19 REFERENCES

Teleportation of continuous quantum variables

- PhysicsTechnical Digest. Summaries of Papers Presented at the International Quantum Electronics Conference. Conference Edition. 1998 Technical Digest Series, Vol.7 (IEEE Cat. No.98CH36236)
- 1998

Summary form only given. A particularly startling discovery by Bennett et al. is the possibility for teleportation of a quantum state, whereby an unknown state of a spin-1/2 particle is transported…

Teleportation of quantum states.

- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1994

The recent result of Bennett of teleportation of an unknown quantum state is obtained in the framework of nonlocal measurements proposed by Aharonov and Albert, and the latter method is generalized to the teleportation of a quantum state of a system with continuous variables.

Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?

- Philosophy
- 1935

Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that one is led to conclude that the description of reality as given by a wave function is not complete.

Unconditional quantum teleportation

- PhysicsScience
- 1998

The first realization of unconditional quantum teleportation where every state entering the device is actually teleported is realized, using squeezed-state entanglement.

Influence of noise on the fidelity and the entanglement fidelity of states

- Computer Science, Physics
- 1997

These two quantities, the fidelity and the entanglement fidelity, are calculated for different kinds of state which are transmitted in noisy channels and a general equation is obtained.

Reply to "Comment on 'Macroscopic Equation for the Roughness of Growing Interfaces in Quenched Disorder' "

- Physics
- 1999

. We argue that the fail in reproducing theearly time regime until the correlations are generated (t ≃ 1 at the depinning transition) isbecause the density of active sites of the interface is not a…

Quantum error correction for communication with linear optics

- PhysicsNature
- 1998

An efficient, compact scheme involving only linear optical elements and feedback, which performs error correction for both quantum and classical noise, which may find application in quantum cryptographic networks (where low noise is equivalent to high security), possibly extending their range far beyond limits imposed by system losses.

Separability Criterion for Density Matrices.

- PhysicsPhysical review letters
- 1996

It is proved that a necessary condition for separability is that a matrix, obtained by partial transposition of {rho}, has only non-negative eigenvalues.

Quantum Noise (2nd

- Ed.), Springer-Verlag
- 1999