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… 
Entanglement of Formation of an Arbitrary State of Two Rebits
We consider entanglement for quantum states defined in vector spaces over the real numbers. Such real entanglement is different from entanglement in standard quantum mechanics over the complex
Relative Entropy of Entanglement of One Class of Two-Qubit system
The relative entropy of entanglement of a mixed state ? for a bipartite quantum system can be defined as the minimum of the quantum relative entropy over the set of completely disentangled states.
Entanglement of General Two-Qubit States in a Realistic Framework
TLDR
New set of maximally entangled conditions are determined that provide the maximal amount of entanglement for certain values of the amplitudes of SCSs for the case of pure states.
ENTANGLEMENT OF FORMATION FOR A CLASS OF SPECIAL QUANTUM STATES
TLDR
The lower bound of entanglement of formation for a large class of density matrices whose decompositions lie in these D-computable quantum states is obtained and a kind of construction for this special state is presented.
Groverian measure of entanglement for mixed states
The Groverian entanglement measure, introduced earlier for pure quantum states of multiple qubits [O. Biham, M.A. Nielsen, and T. Osborne, Phys. Rev. A 65, 062312 (2002)], is generalized to the case
Relativity of Pure States Entanglement
Abstract Entanglement of any pure state of an N × N bi-partite quantum system may be characterized by the vector of coefficients arising by its Schmidt decomposition. We analyze various measures of
Note on Entanglement of an Arbitrary State of Two Qubits
It is shown that the norm of the polarization vector of the reduced density matrix can characterize the entanglement of two qubits and so it is defined as a simple measure of entanglement. It is then
Measuring entanglement of a rank-2 mixed state prepared on a quantum computer
We study the entanglement between a certain qubit and the remaining system in rank- 2 mixed states prepared on the quantum computer. The protocol, which we propose for this purpose, is based on the
Entanglement of formation of rotationally symmetric states
TLDR
An analytic expression is derived for the entanglement of formation of rotationally symmetric states of aspin-j particle and a spin-1/2 particle and expressions for the I-concurrence, I-tangle, and convex-roof-extended negativity are given.
Entanglement dynamics of two-qubit pure state
We show that the entanglement dynamics for the pure state of a closed two-qubit system is part of a 10-dimensional complex linear differential equation defined on a supersphere, and the coefficients
...
...

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.
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 $\bra{Psi-}M\ket-}>\half$.
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
...
...