Entanglement generation by qubit scattering in three dimensions

Abstract

A qubit (a spin-1/2 particle) prepared in the up state is scattered by local spin-flipping potentials produced by the two target qubits (two fixed spins), both prepared in the down state, to generate an entangled state in the latter when the former is found in the down state after scattering. The scattering process is analyzed in three dimensions, both to lowest order and in full order in perturbation, with an appropriate renormalization for the latter. The entanglement is evaluated in terms of the concurrence as a function of the incident and scattering angles, the size of the incident wave packet, and the detector resolution, to clarify the key elements for obtaining an entanglement with high quality. The characteristics of the results are also discussed in the context of (in)distinguishability of alternative paths for a quantum particle.

Efficient generation of a maximally entangled state by repeated on- and off-resonant scattering of ancilla qubits

“…are those on the spin-3 2 and spin-1 2 sectors of XAB, respectively [15] (note that they are all commuting with each other and satisfy Q 3 2 P − = P − Q 3 2 = 0). ‡ The other operators…”

“…. , N are characterized by a common probability distribution function f (k i , q i ), the state (5.14) averaged over the probability distribution reads 15) where in this caseM It is worth stressing that, differently from the case treated in the previous subsection, one can show that the average mapM is mixing, provided that the distribution f (k, q) overlaps with a resonant wave vector in k and has only measure zero in q at resonances. Indeed, splitM into two parts as…”

Extraction of an entanglement by repetition of the resonant transmission of an ancilla qubit

“…and the Lippmann-Schwinger equation (A.5) yields [6] −iΩ(σ Note that T A/B and R A/B describe the changes induced in the spin state of XAB when X is transmitted and reflected, respectively, by the single scatterer A/B. It is clear from the power series expansions of (A.11) and (A.12),…”

Entanglement of magnetic impurities through electron scattering in an electric field

“…Although this asymmetry does not eliminate all the resonant effects, it restricts the constructive quantum interference [34]. It also affects the indistinguishability of the Feynmann paths of the scattered electron, decreasing the level of entanglement created [26,25]. Because our main aim is to analyse the effect of electric field and the sake of clarity, we consider the impurities initial spin state as always parallel.…”