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arXiv:2311.11102 · Physical Review A

Multipartite entanglement from consecutive scatterings

Gonçalo M. Quinta, Rui André

Published Feb 23, 2024• 5 citations
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Abstract

We study how the successive scattering of spin-1/2 particles with a central spin-1/2 target particle can generate entanglement between the helicity degrees of freedom of all scattered particles, effectively producing a multipartite entangled state. We show that the bipartite entanglement between each pair of scattered particles, as quantified by the concurrence, is largest for reflected particles and decreases with the number of scatterings. We study the entanglement generation as a function of the scattered particles momenta, angular distribution, and mass ratios, and show that there is always a combination of optimal helicities and momentum, which generate the largest amount of bipartite entanglement.

DOI
10.1103/physreva.109.022433

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We study how the successive scattering of spin-1/2 particles with a central spin-1/2 target particle can generate entanglement between the helicity degrees of freedom of all scattered particles, effectively producing a multipartite entangled state. We show that the bipartite entanglement between each pair of scattered particles, as quantified by the concurrence, is largest for reflected particles and decreases with the number of scatterings. We study the entanglement generation as a function of the scattered particles momenta, angular distribution, and mass ratios, and show that there is always a combination of optimal helicities and momentum, which generate the largest amount of bipartite entanglement.
We consider the bipartite spin entanglement between two identical fermions generated in spin-independent scattering. We show how the spatial degrees of freedom act as ancillas for the creation of entanglement to a degree that depends on the scattering angle $\ensuremath{\theta}$. The number of Slater determinants generated in the process is greater than 1, corresponding to genuine quantum correlations between the identical fermions. The maximal entanglement attainable of 1 ebit is reached at $\ensuremath{\theta}=\ensuremath{\pi}∕2$. We also analyze a simple $\ensuremath{\theta}$-dependent Bell's inequality, which is violated for $\ensuremath{\pi}∕4<\ensuremath{\theta}\ensuremath{\leqslant}\ensuremath{\pi}∕2$. This phenomenon is unrelated to the symmetrization postulate but does not appear for unequal particles.
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.
We study the behavior of entanglement between different degrees of freedom of scattering fermions, based on an exemplary QED scattering process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. The variation of entanglement entropy between two fermions from an initial state to the final state was computed, with respect to different entanglement between the ingoing particles. This variation of entanglement entropy is found to be proportional to an area quantity, the total cross section. We also study the spin-momentum and helicity-momentum entanglements within one particle in the aforementioned scattering process. The calculations of the relevant variations of mutual information in the same inertial frame reveals that, for a maximally entangled initial state, the scattering between the particles does not affect the degree of both of these entanglements of one particle in the final state. It is also found that the increasing degree of entanglement between two ingoing particles would restrict the generation of entanglement between spin (helicity) and momentum of one outgoing particle. And the entanglement between spin and momentum within one particle in the final state is shown to always be stronger than that for helicity-momentum for a general initial entanglement state, implying significantly distinct properties of entanglement for the helicity and spin perceived by an inertial observer.
We analyze the entanglement generation in a one-dimensional scattering process. The two colliding particles have a Gaussian wave function and interact by hard-core repulsion. In our analysis, results on the entanglement of two-mode Gaussian states are used. The produced entanglement depends in a nonobvious way on the ratio of masses and initial widths for the two particles. The asymptotic wave function of the two particles and its associated ellipse yield additional geometric insight into these conditions. We discuss the difference from the quantitative analysis of the amount of entanglement generated by beam splitters with squeezed light.
Quantum entanglement cannot be unlimitedly shared among an arbitrary number of qubits. The degree of bipartite entanglement decreases as the number of entangled pairs in an N-qubit system increases. We analyze a system of N qubits in which an arbitrary pair of particles is entangled. We show that the maximum degree of entanglement (measured in the concurrence) between any pair of qubits is 2/N.2/N.2/N. This tight bound can be achieved when the qubits are prepared in a pure symmetric (with respect to permutations) state with just one qubit in the basis state ∣0〉|0〉∣0〉 and the others in the basis state ∣1〉.|1〉.∣1〉.