# Quantum Information with Continuous Variables

@article{Braunstein2003QuantumIW, title={Quantum Information with Continuous Variables}, author={Samuel L. Braunstein and Peter van Loock}, journal={Reviews of Modern Physics}, year={2003}, volume={77}, pages={513-577} }

Preface. About the Editors. Part I: Quantum Computing. 1. Quantum computing with qubits S.L. Braunstein, A.K. Pati. 2. Quantum computation over continuous variables S. Lloyd, S.L. Braunstein. 3. Error correction for continuous quantum variables S.L. Braunstein. 4. Deutsch-Jozsa algorithm for continuous variables A.K. Pati, S.L. Braunstein. 5. Hybrid quantum computing S. Lloyd. 6. Efficient classical simulation of continuous variable quantum information processes S.D. Bartlett, B.C. Sanders, S.L…

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## References

SHOWING 1-10 OF 284 REFERENCES

### Quantum versus classical domains for teleportation with continuous variables

- Physics
- 2001

By considering the utilization of a classical channel without quantum entanglement, fidelity Fclassical=1/2 has been established as setting the boundary between classical and quantum domains in the…

### Quantum Communication with Continuous Variables

- Physics
- 2002

The bottom line of this work is that a particular kind of entanglement, namely that based on continuous quantum variables, can be created relatively easily, and only squeezers and beam splitters are required to entangle arbitrarily many electromagnetic modes.

### Quantum computation and quantum information

- Physics, Computer Science
- 2000

This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.

### Quantum state of a propagating laser field

- PhysicsQuantum Inf. Comput.
- 2002

A quantum information-theoretic description of a propagating continuous-wave laser field is given and it is shown that optical coherent states do play a privileged role in the description of propagating laser fields even though they cannot be ascribed such a role for the intracavity field.

### Theory of quantum error-correcting codes

- Computer Science
- 1997

A general theory of quantum error correction based on encoding states into larger Hilbert spaces subject to known interactions is developed and necessary and sufficient conditions for the perfect recovery of an encoded state after its degradation by an interaction are obtained.

### Quantum teleportation and dense coding by means of bright amplitude-squeezed light and direct measurement of a Bell state

- Physics
- 2000

Recent theoretical and experimental studies on quantum communication through the use of nonlocal quantum correlations of entangled states show great promise for establishing new kinds of information…

### Encoding a qubit in an oscillator

- Physics
- 2001

Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes…

### Quantum repeaters based on entanglement purification

- Physics, Computer Science
- 1999

A scheme is presented that allows entanglement purification over arbitrary long channels and tolerates errors on the percent level and requires a polynomial overhead in time, and an overhead in local resources that grows only logarithmically with the length of the channel.

### Quantum-information distributors: Quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit

- Physics
- 2001

We show that for any Hilbert-space dimension, the optimal 1!2 universal quantum cloner can be constructed from essentially the same quantum circuit, i.e., we find a universal design for universal…

### Quantum copying: Beyond the no-cloning theorem.

- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1996

It is shown that there exists a ‘‘universal quantum-copying machine’’ ~i.e., transformation! which approximately copies quantum-mechanical states such that the quality of its output does not depend on the input.