Defeating entanglement sudden death by a single local filtering

Abstract

Genuine multipartite entanglement of a quantum system can be partially destroyed by local decoherence. Is it possible to retrieve the entanglement to some extent by a single local operation? The answer to this question depends very much on the type of initial genuine entanglement. For initially pure W and cluster states and if the decoherence is given by generalized amplitude damping, the answer is shown to be positive. In this case, the entanglement retrieving is achieved just by redistributing the remained entanglement of the system.Comment: 4 pages, 5 figure

Rank-dependant factorization of entanglement evolution

“…At the same time the approximations exploiting Eqs. (9) and (11) where the channels are the BPF, become separable only for p = 0.5. Thus, the factorization approximations provide even better description of the long-time entanglement dynamics then the original lower bound (3) in applications to high-rank mixed state density matrices.…”

“…(9) and (11) is to choose which of these equations should be used for the approximation, since they provide different description of the entanglement dynamics. In principle, it should be possible to construct an entanglement measure E that approximates a complex multi-sided entanglement dynamics E ([A ⊗ ... ⊗ Z] |ψ ψ|) by a function of terms E(A), ..., E(Z) describing the single-sided entanglement dynamics, where A, ..., Z are defined by analogy with Eq.…”

“…In spite of the above limitations, concurrence (1) has been shown to be quite powerful measure of entanglement [9,12,14]. Using the bipartite concurrence Li et al [26] formulated an analytical lower bound for multiqubit concurrence, which is given by a squared sum of the bipartite concurrences computed for all possible bi-partitioning of the multiqubit system.…”

“…In this special case the state inversion is unique, and there is only single term in the right hand side of Eq. (9). If, in contrast, the GHZ state (7) is affected by three channels A, B and C, so that the final state density matrix has rank four, the two-qubit subsystem subjected to the action of the channels A and B belongs to a four-dimensional subspace, while the singlequbit subsystem affected by channel C is the subject of a two-dimensional subspaces.…”

“…However, apart from entanglement generation [2][3][4] and detection [5], successful practical utilization of entanglement-based quantum technologies demands efficient protocols for entanglement protection from detrimental environmental influence [6] and its recovery after a possible partial loss [7][8][9]. The construction of the protocols, in turn, requires exact methods for entanglement quantitative description as well as clear understanding of the fundamental laws of the entanglement evolution.…”