This paper addresses the question of the distillation of entanglement from a finite number of multipartite mixed states. It is shown that, if one can distill a pure entangled state from n copies of a mixed state ${\ensuremath{\sigma}}_{\mathrm{ABC}\ensuremath{\cdot}\ensuremath{\cdot}\ensuremath{\cdot}},$ there must be at least a subspace in the whole Hilbert space of all the copies such that the projection of ${\ensuremath{\sigma}}_{\mathrm{ABC}\ensuremath{\cdot}\ensuremath{\cdot}\ensuremath{\cdot}}^{\ensuremath{\bigotimes}n}$ onto the subspace is a pure entangled state. We also show that the purification of entanglement or distillation of entanglement can be carried out by local joint projective measurements with the help of classical communication and local general positive operator valued measurements on a single particle, in principle. Finally, we discuss experimental realizability of the entanglement purification.This paper addresses the question of the distillation of entanglement from a finite number of multipartite mixed states. It is shown that, if one can distill a pure entangled state from n copies of a mixed state ${\ensuremath{\sigma}}_{\mathrm{ABC}\ensuremath{\cdot}\ensuremath{\cdot}\ensuremath{\cdot}},$ there must be at least a subspace in the whole Hilbert space of all the copies such that the projection of ${\ensuremath{\sigma}}_{\mathrm{ABC}\ensuremath{\cdot}\ensuremath{\cdot}\ensuremath{\cdot}}^{\ensuremath{\bigotimes}n}$ onto the subspace is a pure entangled state. We also show that the purification of entanglement or distillation of entanglement can be carried out by local joint projective measurements with the help of classical communication and local general positive operator valued measurements on a single particle, in principle. Finally, we discuss experimental realizability of the entanglement purification.

arXiv:quant-ph/0311095Physical Review AJan 14, 20043 citations

Local cloning of multipartite entangled states

Guruprasad Kar, Ramij Rahaman

Quantum Information ProcessingAug 31, 20117 citations

Purification of multipartite entanglement by local operations

Ming Yang, Fei Yan, Zhuo‐Liang Cao

Multipartite entanglement purification is revisited by using the Local operations and classical communications(LOCCs). We demonstrate our idea by considering the tripartite case, i.e. the purification of tripartite entanglement. We express the general tripartite entangled states in a special representation of total spin operators $J_{123}^{2}$ and $% J_{12}^{2}$ of tripartite system with eigenvalues 15/4 and 2 respectively. This basis is a \textit{genuine basis} because it consists of of all the genuine entangled states of tripartite system. Our protocol is a recurrence one, and only two copies of the initial mixed tripartite entangled states are needed in each round. It is shown that if the initial fidelity is larger than a threshold 0.4, the purification process will succeed.The yield of the current protocol is higher than the previous multipartite entanglement purification protocols. As a by-product, we can get a bipartite pure Bell state when the purification protocol fails for W state. Our protocol also shows that there may be some special kind of tripartite entanglement which belongs to neither W-type entanglement nor GHZ-type entanglement.Multipartite entanglement purification is revisited by using the Local operations and classical communications(LOCCs). We demonstrate our idea by considering the tripartite case, i.e. the purification of tripartite entanglement. We express the general tripartite entangled states in a special representation of total spin operators $J_{123}^{2}$ and $% J_{12}^{2}$ of tripartite system with eigenvalues 15/4 and 2 respectively. This basis is a \textit{genuine basis} because it consists of of all the genuine entangled states of tripartite system. Our protocol is a recurrence one, and only two copies of the initial mixed tripartite entangled states are needed in each round. It is shown that if the initial fidelity is larger than a threshold 0.4, the purification process will succeed.The yield of the current protocol is higher than the previous multipartite entanglement purification protocols. As a by-product, we can get a bipartite pure Bell state when the purification protocol fails for W state. Our protocol also shows that there may be some special kind of tripartite entanglement which belongs to neither W-type entanglement nor GHZ-type entanglement.

arXiv:0904.2343Apr 15, 20091 citation

Purification of Multi-Particle Entanglement

Mio Murao, Martin Bodo Plenio, Sandu Popescu +2 more

Elsevier eBooksJan 1, 19992 citations

Catalysis of Entanglement Manipulation for Mixed States

Jens Eisert, Martin Wilkens

We consider entanglement-assisted remote quantum state manipulation of bipartite mixed states. Several aspects are addressed: we present a class of mixed states of rank two that can be transformed into another class of mixed states under entanglement-assisted local operations with classical communication, but for which such a transformation is impossible without assistance. Furthermore, we demonstrate enhancement of the efficiency of purification protocols with the help of entanglement-assisted operations. Finally, transformations from one mixed state to mixed target states which are sufficiently close to the source state are contrasted with similar transformations in the pure-state case.We consider entanglement-assisted remote quantum state manipulation of bipartite mixed states. Several aspects are addressed: we present a class of mixed states of rank two that can be transformed into another class of mixed states under entanglement-assisted local operations with classical communication, but for which such a transformation is impossible without assistance. Furthermore, we demonstrate enhancement of the efficiency of purification protocols with the help of entanglement-assisted operations. Finally, transformations from one mixed state to mixed target states which are sufficiently close to the source state are contrasted with similar transformations in the pure-state case.

arXiv:quant-ph/9912080Physical Review LettersJul 10, 200043 citations

J_{123}^{2}

and

% J_{12}^{2}

of tripartite system with eigenvalues 15/4 and 2 respectively. This basis is a \textit{genuine basis} because it consists of of all the genuine entangled states of tripartite system. Our protocol is a recurrence one, and only two copies of the initial mixed tripartite entangled states are needed in each round. It is shown that if the initial fidelity is larger than a threshold 0.4, the purification process will succeed.The yield of the current protocol is higher than the previous multipartite entanglement purification protocols. As a by-product, we can get a bipartite pure Bell state when the purification protocol fails for W state. Our protocol also shows that there may be some special kind of tripartite entanglement which belongs to neither W-type entanglement nor GHZ-type entanglement.