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arXiv:quant-ph/0602090 · Physical Review A

Generation of bipartite spin entanglement via spin-independent scattering

Lucas Lamata, Juan León

Published May 26, 2006• 33 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.73.052322

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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 \ensuremathθ\ensuremath{\theta}\ensuremathθ. 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 \ensuremathθ=\ensuremathπ∕2\ensuremath{\theta}=\ensuremath{\pi}∕2\ensuremathθ=\ensuremathπ∕2. We also analyze a simple \ensuremathθ\ensuremath{\theta}\ensuremathθ-dependent Bell's inequality, which is violated for \ensuremathπ∕4<\ensuremathθ\ensuremath⩽\ensuremathπ∕2\ensuremath{\pi}∕4<\ensuremath{\theta}\ensuremath{\leqslant}\ensuremath{\pi}∕2\ensuremathπ∕4<\ensuremathθ\ensuremath⩽\ensuremathπ∕2. This phenomenon is unrelated to the symmetrization postulate but does not appear for unequal particles.
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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 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.
Orbital rotations are used in quantum many-body physics and chemistry to reduce the complexity of quantum states by compressing their correlation into a small set of relevant orbitals. In striking contrast, quantum information processing strives for the opposite: orbitals that maximize entanglement as a resource. Motivated by this, we prove that Slater determinants of NNN fermions on a lattice of dA+dB=dd_A + d_B = ddA​+dB​=d sites, although free of particle correlation, can carry up to min⁡{dA,dB,N,d−N}\min\{d_A, d_B, N, d-N\}min{dA​,dB​,N,d−N} ebits of orbital entanglement. Given enough particles and holes, this equals the maximum over all fermionic states. For arbitrary free states, we derive the maximal orbital total correlation in closed form for all bipartitions, the finest partition, and all partitions of up to five sites, using new majorization relations for Hermitian matrices. Taken together, these results turn mean-field states, the starting point of most many-body methods in physics and chemistry, into a viable resource for quantum information processing.
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In this article, we have discussed about the scattering of charge and spin in spin-resolved mesoscopic systems. We have proposed a method to generate and detect the entanglement of electronic spin and electronic orbital degrees of freedom. It is observed that in a spin-resolved mesoscopic system, all form of entanglement existing between different electronic degrees of freedom can be generated. A method to detect Bell's inequality violation in terms of zero frequency current cross-correlators has been mentioned. Further, we have also studied the effect of quantum interference between spin flip and non-spin flip scattering matrices in determining the current and noise. We have obtained the expression for shot noise of spin and charge current when an arbitrarily polarised charge current is scattered at the spin resolved potential.