Probabilistic entanglement transformation by local overlap modification (original) (raw)

Deterministic Entanglement of Two Trapped Ions

Physical Review Letters, 1998

We have prepared the internal states of two trapped ions in both the Bell-like singlet and triplet entangled states. In contrast to all other experiments with entangled states of either massive particles or photons, we do this in a deterministic fashion, producing entangled states on demand without selection. The deterministic production of entangled states is a crucial prerequisite for large-scale quantum computation.

Protocols for entanglement transformations of bipartite pure states

Physical Review A, 2003

We present a general theoretical framework for both deterministic and probabilistic entanglement transformations of bipartite pure states achieved via local operations and classical communication. This framework unifies and greatly simplifies previous works. A necessary condition for "pure contraction" transformations is given. Finally, constructive protocols to achieve both probabilistic and deterministic entanglement transformations are presented.

Approximate transformations of bipartite pure-state entanglement from the majorization lattice

Physica A: Statistical Mechanics and its Applications, 2017

We study the problem of deterministic transformations of an initial pure entangled quantum state, |ψ , into a target pure entangled quantum state, |φ , by using local operations and classical communication (LOCC). A celebrated result of Nielsen [Phys. Rev. Lett. 83, 436 (1999)] gives the necessary and sufficient condition that makes this entanglement transformation process possible. Indeed, this process can be achieved if and only if the majorization relation ψ ≺ φ holds, where ψ and φ are probability vectors obtained by taking the squares of the Schmidt coefficients of the initial and target states, respectively. In general, this condition is not fulfilled. However, one can look for an approximate entanglement transformation. Vidal et. al [Phys. Rev. A 62, 012304 (2000)] have proposed a deterministic transformation using LOCC in order to obtain a target state |χ opt most approximate to |φ in terms of maximal fidelity between them. Here, we show a strategy to deal with approximate entanglement transformations based on the properties of the majorization lattice. More precisely, we propose as approximate target state one whose Schmidt coefficients are given by the supremum between ψ and φ. Our proposal is inspired on the observation that fidelity does not respect the majorization relation in general. Remarkably enough, we find that for some particular interesting cases, like two-qubit pure states or the entanglement concentration protocol, both proposals are coincident.

Enhancing entanglement of two qubits undergoing independent decoherences by local pre- and postmeasurements

Physical Review A, 2012

We consider two entangled qubits, each of which is coupled to its own reservoir, so that their entanglement degrades with time. To enhance the qubits' entanglement at a time during the evolution we propose a proper combination of pre-and postmeasurements to be performed locally on individual qubits. The premeasurements are weak measurements, but the postmeasurements may be either quantum measurement reversals or weak measurements again, depending on the situation at the time they are applied. Given the parameters of the initial qubits' state, the premeasurements' strength, and the evolution time, we establish the optimal conditions for the postmeasurements so that the qubits' entanglement becomes the largest possible. Actually, by our scheme, less entangled qubits can evolve into more entangled ones with a finite probability, or even into a near-maximally entangled state but with a vanishingly low probability. We also examine the entanglement distribution among different pairs of subsystems involved and find out that the pairwise concurrence dynamics in our scheme differs strikingly from that in the situation without any control actions.

Entanglement transformation between sets of bipartite pure quantum states using local operations

Journal of Mathematical Physics, 2012

Alice and Bob are given an unknown initial state chosen from a set of pure quantum states. Their task is to transform the initial state to a corresponding final pure state using local operations only. We prove necessary and sufficient conditions on the existence of such a transformation. We also provide efficient algorithms that can quickly rule out the possibility of transforming a set of initial states to a set of final states.

General entanglement-assisted transformation for bipartite pure quantum states

Journal of Physics A: Mathematical and Theoretical, 2007

We introduce the general catalysts for pure entanglement transformations under local operations and classical communications in such a way that we disregard the profit and loss of entanglement of the catalysts per se. As such, the possibilities of pure entanglement transformations are greatly expanded. We also design an efficient algorithm to detect whether a k × k general catalyst exists for a given entanglement transformation. This algorithm can as well be exploited to witness the existence of standard catalysts.

Uniform decoherence effect on localizable entanglement in random multiqubit pure states

Physical Review A, 2020

We investigate the patterns in distributions of localizable entanglement over a pair of qubits for random multi-qubit pure states. We observe that the mean of localizable entanglement increases gradually with increasing the number of qubits of random pure states while the standard deviation of the distribution decreases. The effects on the distributions, when the random pure multi-qubit states are subjected to local as well as global noisy channels, are also investigated. Unlike the noiseless scenario, the average value of the localizable entanglement remains almost constant with the increase in the number of parties for a fixed value of noise parameter. We also find out that the maximum strength of noise under which entanglement survives can be independent of the localizable entanglement content of the initial random pure states.

Useful entanglement from the Pauli principle

Physical Review B, 2007

We address the question whether identical-particle entanglement is a useful resource for quantum information processing. We answer this question positively by reporting a scheme to create entanglement using semiconductor quantum wells. The Pauli exclusion principle forces quantum correlations between the spins of two independent fermions in the conduction band. Selective electron-hole recombination then transfers this entanglement to the polarization of emitted photons, which can subsequently be used for quantum information tasks.

Recovering entanglement by local operations

Annals of Physics, 2014

We show that any quantification of the bipartite entanglement of mixed states uniquely based on the density operator may lead to a paradoxical increase of entanglement under purely local operations. This apparent paradox is solved in the physical ensemble description of the system state by introducing the concept of "hidden" entanglement, which measures the amount of entanglement that may be recovered without the help of any non-local operation. For two noninteracting qubits under a low-frequency stochastic noise, we show that entanglement can be recovered by local pulses only. We also discuss how hidden entanglement may provide new insights about entanglement revivals in non-Markovian dynamics. We finally propose a simple quantum information scheme, implementable by all-optical setups, which gives evidence of the concept of hidden entanglement. PACS numbers: 03.67.-a,03.65.Ud, 03.65.Yz