# Entanglement of Formation of an Arbitrary State of Two Qubits

@article{Wootters1998EntanglementOF, title={Entanglement of Formation of an Arbitrary State of Two Qubits}, author={William K. Wootters}, journal={Physical Review Letters}, year={1998}, volume={80}, pages={2245-2248} }

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 entanglement of an ensemble of pure states that represents the given mixed state. An earlier paper [Phys. Rev. Lett. 78, 5022 (1997)] conjectured an explicit formula for the entanglement of formation of a pair of binary quantum objects (qubits) as a function of their density matrix, and proved the…

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## References

SHOWING 1-10 OF 43 REFERENCES

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…

Concentrating partial entanglement by local operations.

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

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.

Entanglement measures and purification procedures

- Physics, Computer Science
- 1998

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.

2 20 J an 1 99 7 Quantum information theory of entanglement and measurement ?

- Physics, Computer Science
- 1997

A quantum information theory that allows for a consistent description of entanglement is presented and it is found that quantum conditional entropies can be negative for entangled systems, which leads to a violation of well-known bounds in Shannon information theory.

Mixed-state entanglement and quantum error correction.

- Computer SciencePhysical review. A, Atomic, molecular, and optical physics
- 1996

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.

On the measure of entanglement for pure states

- Physics, Computer Science
- 1996

It is shown that entropy of Entanglement is the unique measure of entanglement for pure states.

Purification of noisy entanglement and faithful teleportation via noisy channels.

- Computer SciencePhysical review letters
- 1996

Upper and lower bounds on the yield of pure singlets ($\ket{\Psi^-}$) distillable from mixed states $M$ are given, showing $D(M)>0$ if $\bra{Psi-}M\ket-}>\half$.

Quantifying Entanglement

- Physics
- 1997

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…