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}
}
  • W. Wootters
  • Published 12 September 1997
  • Physics
  • Physical Review Letters
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
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.
TLDR
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
TLDR
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.
Quantum information theory of entanglement
2 20 J an 1 99 7 Quantum information theory of entanglement and measurement ?
TLDR
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.
TLDR
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
TLDR
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.
TLDR
Upper and lower bounds on the yield of pure singlets ($\ket{\Psi^-}$) distillable from mixed states $M$ are given, showing $D(M)>0$ if $\bra{Psi-}M\ket-}>\half$.
A Complete Classification of Quantum Ensembles Having a Given Density Matrix
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…
...
...