The theory of quantum information constitutes the functional value of the quantum entanglement, i.e., quantum entanglement is essential for high fidelity of quantum protocols, while fundamental physical processes behind the formation of quantum entanglement are less relevant for practical purposes. In the present work, we explore physical mechanisms leading to the emergence of quantum entanglement in the initially disentangled system. In particular, we analyze spin entanglement of outgoing electrons in a nonrelativistic quantum $(e,2e)$ collision on a target with one active electron. Our description exploits the time-dependent scattering formalism for typical conditions of scattering experiments, and contrary to the customary stationary formalism operates with realistic scattering states. We quantify the spin entanglement in the final scattering channel through the pair concurrence and express it in terms of the experimentally measurable spin-resolved $(e,2e)$ triple differential cross sections. Besides, we consider Bell's inequality and inspect the regimes of its violation in the final channel. We address both the pure and the mixed initial spin state cases and uncover kinematical conditions of the maximal entanglement of the outgoing electron pair. The numerical results for the pair concurrence, entanglement of formation, and violation of Bell's inequality obtained for the $(e,2e)$ ionization process of atomic hydrogen show that the entangled electron pairs indeed can be formed in the $(e,2e)$ collisions even with spin-unpolarized projectile and target electrons in the initial channel. The positive entanglement balance---the difference between entanglements of the initial and final electron pairs---can be measured in the experiment.
We study the significance of Photon/Phonons bunching and antibunching on the dynamics of the quantum entanglement in the presence of coupled PT-symmetry systems with balanced/unbalanced gain and loss. We suggest a hybrid electromechanical system to realize a strong and tunable coupling between a Coplanar-Waveguide (CPW) microwave cavity and a nanomechanical resonator (NAMR) via a superconducting Transmon qubit. The hybrid electromechanical system consists of a non-hermitian Hamiltonian with balanced/unbalanced gain and loss. The interplay between the quantum entanglement and the -symmetry syst…
We study a connection between quantum detailed balance, which is a concept of importance in statistical mechanics, and entanglement. We also explore how this connection fits into thermofield dynamics.
We adopt the view according to which information is the primary physical entity that posseses objective meaning. Basing on two postulates that (i) entanglement is a form of quantum information corresponding to internal energy (ii) sending qubits corresponds to work, we show that in the closed bipartite quantum communication systems the information is conserved. We also discuss entanglement-energy analogy in context of the Gibbs-Hemholtz-like equation connecting the entanglement of formation, distillable entanglement and bound entanglement. Then we show that in the deterministic protocols of di…
A definition of detailed balance tailored to a system of indistinguishable fermions is suggested and studied using an entangled fermionic state. This is done in analogy to a known characterization of standard quantum detailed balance with respect to a reversing operation.
We study entanglement in the scattering processes by fixed impurity and Kondo impurity. The fixed impurity plays a role as spin state filter that is employed to concentrate entanglement between the scattering particle and the unscattering particle. One Kondo impurity can entangle two noninteracting scattering particles while one scattering particle can entangle two separate noninteracting Kondo impurities.
This article considers dynamical entanglement in non-relativistic particle scattering. Three questions are explored: what kinds of entanglement occur in this system, how do global symmetries constrain entanglement, and how do the boundary conditions of scattering affect dynamical entanglement? First, a simple model of scattering spin systems is considered, then the full system is discussed.
The coherent control of scattering processes is considered, with electron impact dissociation of H$_2^+$ used as an example. The physical mechanism underlying coherently controlled stationary state scattering is exposed by analyzing a control scenario that relies on previously established entanglement requirements between the scattering partners. Specifically, initial state entanglement assures that all collisions in the scattering volume yield the desirable scattering configuration. Scattering is controlled by preparing the particular internal state wave function that leads to the favored col…
We study the emergence of localization and entanglement in many-body systems as a result of scattering measurements. We show that consecutive scattering measurements on a many-body system can produce superposition states in position space. The resulting states are signaled in the scattering distribution and these states are robust under continued scattering. We also show that the average scattering distribution for an ensemble of experiments gives the initial state scattering distribution even when the initial state is completely destroyed by the scattering process.
Generation of entanglement between two qubits by scattering an entanglement mediator is discussed. The mediator bounces between the two qubits and exhibits a resonant scattering. It is clarified how the degree of the entanglement is enhanced by the constructive interference of such bouncing processes. Maximally entangled states are available via adjusting the incident momentum of the mediator or the distance between the two qubits, but their fine tunings are not necessarily required to gain highly entangled states and a robust generation of entanglement is possible.
With the mechanism of pairwise scattering of photons between two atoms, we propose a novel scheme to highly entangle the motional state between two ultracold neutral atoms by a single photon scattering and detection. Under certain conditions, it is shown that an arbitrary amount of entanglement can be obtained with this scheme.
Single--photon which is initially uncorrelated with atom, will evolve to be entangled with the atom on their continuous kinetic variables in the process of resonant scattering. We find the relations between the entanglement and their physical control parameters, which indicates that high entanglement can be reached by broadening the scale of the atomic wave or squeezing the linewidth of the incident single--photon pulse.
The process of stimulated Brillouin scattering is described by the model of two-dimensional oscillator. The phenomenon of entanglement which appears in the photon-phonon modes after the interaction with matter is discussed.
We calculate the effect of polarization-dependent scattering by disorder on the degree of polarization-entanglement of two beams of radiation. Multi-mode detection converts an initially pure state into a mixed state with respect to the polarization degrees of freedom. The degree of entanglement decays exponentially with the number of detected modes if the scattering mixes the polarization directions and algebraically if it does not.
The ability to detect the interaction of light and matter at the single-particle level is becoming increasingly important for many areas of science and technology. The absorption or emission of a photon on a narrow transition of a trapped ion can be detected with near unit probability, thereby enabling the realization of ultra-precise ion clocks and quantum information processing applications. Extending this sensitivity to broad transitions is challenging due to the difficulty of detecting the rapid photon scattering events in this case. Here, we demonstrate a technique to detect the scatterin…
We report on a two-particle matter wave interferometer realized with pairs of trapped 87Rb atoms. Each pair of atoms is confined at a single site of an optical lattice potential. The interferometer is realized by first creating a coherent spin-mixture of the two atoms and then tuning the inter-state scattering length via a Feshbach resonance. The selective change of the inter-state scattering length leads to an entanglement dynamics of the two-particle state that can be detected in a Ramsey interference experiment. This entanglement dynamics is employed for a precision measurement of atomic in…
We analyse 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 non-obvious way on the parameters ratio of masses and initial widths. The asymptotic wavefunction of the two particles and its associated ellipse yield additional geometric insight into these conditions. The difference to the quantitative analysis of the amount of entanglement generated by beam splitter…
We consider the problem of correct measurement of a quantum entanglement in the two-body electron-electron scattering. An expression is derived for a spin correlation tensor of a pure two-electron state. A geometrical measure of a quantum entanglement as the distance between two forms of this tensor in entangled and separable cases is presented. We prove that this measure satisfies properties of a valid entanglement measure: nonnegativity, discriminance, normalization, non-growth under local operations and classical communication. This measure is calculated for a problem of electron-electron s…
Treating Coulomb scattering of two free electrons in a stationary approach, we explore the momentum and spin entanglement created by the interaction. We show that a particular discretisation provides an estimate of the von Neumann entropy of the one-electron reduced density matrix from the experimentally accessible Shannon entropy. For spinless distinguishable electrons the entropy is sizeable at low energies, indicating strong momentum entanglement, and drops to almost zero at energies of the order of 10 keV when the azimutal degree of freedom is integrated out, i.e. practically no entangleme…
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, $θ$. 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 $θ=π/2$. We also analyze a simple $θ$ dependent Bell's inequality, which is violated for $π/4<θ\leqπ/2$. This phenomenon…
We study the properties of entanglement entropy among scattering particles as observed from different inertial moving frames, based on an exemplary QED process $e^+e^-\rightarrowμ^+μ^-$. By the explicit calculation of the Wigner rotation, the entanglement entropy of scattering particles is found to be Lorentz invariant. We also study the behavior of the entanglement between spin degrees of freedom for scattering particles in moving frames. This quantity, being found to change with different inertial reference frames, does not exhibit as a Lorentz invariant.
We show how to measure the structural witnesses proposed in [P. Krammer et al., Phys. Rev. Lett. 103, 100502 (2009)] for detecting entanglement in a spin chain using photon scattering. The procedure, moreover, allows one to measure the two-point correlation function of the spin array. This proposal could be performed in existing experimental platforms realizing ion chains in Paul traps or atomic arrays in optical lattices.
Particle systems admit a variety of tensor product structures (TPSs) depending on the complete system of commuting observables chosen for the analysis. Different notions of entanglement are associated with these different TPSs. Global symmetry transformations and dynamical transformations factor into products of local unitary operators with respect to certain TPSs and not with respect to others. Symmetry-invariant and dynamical-invariant TPSs and corresponding measures of entanglement are defined for particle scattering systems.
Particle systems admit a variety of tensor product structures (TPSs) depending on the algebra of observables chosen for analysis. Global symmetry transformations and dynamical transformations may be resolved into local unitary operators with respect to certain TPSs and not with respect to others. Symmetry-invariant and dynamical-invariant TPSs are defined and various notions of entanglement are considered for scattering states.
We study by means of time-dependent numerical simulations the behavior of the entanglement stemming from the Coulomb scattering between two charged particles subject to a pulse of sinusoidal potential. We show that the splitting of the spatial wavefunction brought about by the interaction with the potential pulse plays a key role in the appearance of quantum correlation, thus leading under specific conditions to a peculiar behavior. The dependence of the final entanglement upon the physical parameters describing the pulse is discussed. Our results can be applied to a number of physical systems…
We perform the quantitative evaluation of the entanglement dynamics in scattering events between two insistinguishable electrons interacting via Coulomb potential in 1D and 2D semiconductor nanostructures. We apply a criterion based on the von Neumann entropy and the Schmidt decomposition of the global state vector suitable for systems of identical particles. From the timedependent numerical solution of the two-particle wavefunction of the scattering carriers we compute their entanglement evolution for different spin configurations: two electrons with the same spin, with different spin, single…
We show how entanglement between two conduction electrons is generated in the presence of a localized magnetic impurity embedded in an otherwise ballistic conductor of special geometry. This process is a generalization of beam-splitter mediated entanglement generation schemes with a localized spin placed at the site of the beam splitter. Our entangling scheme is unconditional and robust to randomness of the initial state of the impurity. The entangled state generated manifests itself in noise reduction of spin-dependent currents.
We propose a scheme of generating and verifying mesoscopic-level entanglement between two atomic ensembles using non-resonant stimulated Raman scattering. Entanglement can be generated by direct detection or balanced homodyne detection of the Stokes fields from the two cells, after they interfere on a beam splitter. The entanglement of the collective atomic fields can be transferred to the anti-Stokes fields in a readout process. By measuring the operator moments of the anti-Stokes fields, we can verify the presence of entanglement. We model the effects of practical factors such as Stokes fiel…
We derive a formula for the entanglement entropy of two regions in momentum space that is generated by the scattering of weakly interacting scalar particles. We discuss an example where weak interactions entangle momentum scales above and below an infrared cutoff.
In this paper we discuss the scattering effect on entanglement propagation in RCFTs. In our setup, we consider the time evolution of excited states created by the insertion of many local operators. Our results show that because of the finiteness of quantum dimension, entanglement is not changed after the scattering in RCFTs. In this mean, entanglement is conserved after the scattering event in RCFTs, which reflects the integrability of the system. Our results are also consistent with the free quasiparticle picture after the global quenches.
This article provides a convenient framework for quantitative evaluation of the entanglement generated when two structureless, distinguishable particles scatter non-relativistically in one dimension. It explores how three factors determine the amount of entanglement generated: the momentum distributions of the incoming particles, their masses, and the interaction potential. Two important scales emerge, one set by the kinematics and one set by the dynamics. This method also provides two approximate analytic formulas useful for numerical evaluation of entanglement and reveals an interesting conn…
We demonstrate the control of entanglement of a single photon between several spatial modes propagating through a strongly scattering medium. Measurement of the scattering matrix allows the wavefront of the photon to be shaped to compensate the distortions induced by multiple scattering events. The photon can thus be directed coherently to a single or multi-mode output. Using this approach we show how entanglement across different modes can be manipulated despite the enormous wavefront disturbance caused by the scattering medium.
Quantum Beam Splitter as a Deterministic Entanglement Source: Exact Photon-Number Statistics, Hong-Ou-Mandel Interference, and von Neumann Entropy Scaling from Balanced Inputs
This paper investigates the dynamical generation of entanglement in scattering systems, in particular two spin systems that interact via rotationally-invariant scattering. The spin degrees of freedom of the in-states are assumed to be in unentangled, pure states, as defined by the entropy of entanglement. Because of the restriction of rotationally-symmetric interactions, perfectly-entangling S-matrices, i.e. those that lead to a maximally entangled out-state, only exist for a certain class of separable in-states. Using Clebsch-Gordan coefficients for the rotation group, the scattering phases t…
Protocols for probabilistic entanglement-assisted quantum teleportation and for entanglement swapping of material qubits are presented. They are based on a protocol for postselective Bell-state projection which is capable of projecting two material qubits onto a Bell state with the help of ancillary coherent multiphoton states and postselection by balanced homodyne photodetection. Provided this photonic postselection is successful we explore the theoretical possibilities of realizing unit fidelity quantum teleportation and entanglement swapping with $25\%$ success probability. This photon-assi…
We show that the entanglement between two distant magnetic impurities, generated via electron scattering, can be easily modulated by controlling the magnitude of an applied external electric field. We assume that the two magnetic impurities are fixed and located on an one-dimensional quantum wire. A ballistic electron moving through the wire is scattered off by both impurities, so the electron spin can be seen as a mediator between the spins of the impurities. Heisenberg operators are used to describe the interactions between electron and impurities spins. We use a wave guide formalism to mode…
The generation of entanglement produced by a local potential interaction in a bipartite system is investigated. The degree of entanglement is contrasted with the underlying classical dynamics for a Rydberg molecule (a charged particle colliding on a kicked top). Entanglement is seen to depend on the structure of classical phase-space rather than on the global dynamical regime. As a consequence regular classical dynamics can in certain circumstances be associated with higher entanglement generation than chaotic dynamics. In addition quantum effects also come into play: for example partial reviv…
We study how two magnetic impurities embedded in a solid can be entangled by an injected electron scattering between them and by subsequent measurement of the electron's state. We start by investigating an ideal case where only the electronic spin interacts successively through the same unitary operation with the spins of the two impurities. In this case, high (but not maximal) entanglement can be generated with a significant success probability. We then consider a more realistic description which includes both the forward and back scattering amplitudes. In this scenario, we obtain the entangl…
Intriguing quantum effects that result from entangled molecular rovibrational states are shown to provide a novel means for controlling both differential and total collision cross sections in identical particle diatom-diatom scattering. Computational results on elastic and inelastic scattering of para--H$_2$ and para--H$_2$ are presented, with the collision energy ranging from 400 cm$^{-1}$ to the ultracold regime. The experimental realization and possible extension to other systems are discussed.
We present an information geometric analysis of entanglement generated by an s-wave scattering between two Gaussian wave packets. We conjecture that the pre and post-collisional quantum dynamical scenarios related to an elastic head-on collision are macroscopic manifestations emerging from microscopic statistical structures. We then describe them by uncorrelated and correlated Gaussian statistical models, respectively. This allows us to express the entanglement strength in terms of scattering potential and incident particle energies. Furthermore, we show how the entanglement duration can be re…
This paper explores the connections between particle scattering and quantum information theory in the context of the non-relativistic, elastic scattering of two spin-1/2 particles. An untangled, pure, two-particle in-state is evolved by an S-matrix that respects certain symmetries and the entanglement of the pure out-state is measured. The analysis is phrased in terms of unitary, irreducible representations (UIRs) of the symmetry group in question, either the rotation group for the spin degrees of freedom or the Galilean group for non-relativistic particles. Entanglement may occurs when multip…
It has now been possible to prepare chain of ions in an entangled state and thus question arises --- how the optical properties of a chain of entangled ions differ from say a chain of independent particles. We investigate nonlinear optical processes in such chains. We explicitly demonstrate the possibility of entanglement produced super Raman scattering. Our results in contrast to Dicke's work on superradiance are applicable to stimulated processes and are thus free from the standard complications of multimode quantum electrodynamics. Our results suggest the possibility of similar enhancement …
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 p…
High-dimensional entangled quantum states improve the performance of quantum technologies compared to qubit-based approaches. In particular, they enable quantum communications with higher information capacities or enhanced imaging protocols. However, the presence of optical disorder such as atmospheric turbulence or biological tissue perturb quantum state propagation and hinder their practical use. Here, we demonstrate a wavefront shaping approach to transmit high-dimensional spatially entangled photon pairs through scattering media. Using a transmission matrix approach, we perform wavefront c…
We investigate the effects of spontaneous scattering on the evolution of entanglement of two atomic samples, probed by phase shift measurements on optical beams interacting with both samples. We develop a formalism of conditional quantum evolutions and present a wave function analysis implemented in numerical simulations of the state vector dynamics. This method allows to track the evolution of entanglement and to compare it with the predictions obtained when spontaneous scattering is neglected. We provide numerical evidence that the interferometric scheme to entangle atomic samples is only ma…
The prospect of controlling entanglement in interacting quantum systems offers a myriad of technological and scientific promises, given the progress in experimental studies in systems such as ultracold trapped gases. This control is often challenging because of decoherence, the process by which environmental interactions create spurious entanglements that can destroy the desired entanglement. Considering the collisional decoherence that is relevant for quantum measurements utilizing scattering in one-dimensional trapped gases, here we derive a relationship between particle masses and wave pack…
We investigate the time evolution of entanglement in a process where a mobile particle is scattered by static spins. We show that entanglement increases monotonically during a transient and then saturates to a steady-state value. For a quasi-monochromatic mobile particle, the transient time depends only on the group-velocity and width of the incoming wavepacket and is insensitive to the interaction strength and spin-number of the scattering particles. These features do not depend on the interaction model and can be seen in various physical settings.
Recent work arXiv:1812.03138 [nucl-th] conjectured that entanglement is minimized in low-energy hadronic scattering processes. It was shown that the minimization of the entanglement power (EP) of the low-energy baryon-baryon $S$-matrix implies novel spin-flavor symmetries that are distinct from large-$N_c$ QCD predictions and are confirmed by high-precision lattice QCD simulations. Here the conjecture of minimal entanglement is investigated for scattering processes involving pions and nucleons. The EP of the $S$-matrix is constructed for the $ππ$ and $πN$ systems, and the consequences of minim…
When two non-relativistic particles scatter in one dimension, they can become entangled. This entanglement process is constrained by the symmetries of the scattering system and the boundary conditions on the incoming state. Applying these constraints, three different mechanisms of entanglement can be identified: the superposition of reflected and transmitted modes, momentum correlations of the reflected mode due to inversion of the relative momentum, and momentum correlations in the transmitted and reflected modes due to dependence of the scattering amplitude on the relative momentum. We consi…
We consider the scattering of entangled two-photon states from collections of small particles. We also study the related Mie problem of scattering from a sphere. In both cases, we calculate the entropy of entanglement and investigate the influence of the entanglement of the incident field on the entanglement of the scattered field.
Relations between photon scattering, entanglement and multi-mode detection are investigated. We first establish a general framework in which one- and two-photon elastic scattering processes can be discussed, then we focus on the study of the intrinsic entanglement degradation caused by a multi-mode detection. We show that any multi-mode scattered state cannot maximally violate the Bell-CHSH inequality because of the momentum spread. The results presented here have general validity and can be applied to both deterministic and random scattering processes.
It is found that the differential cross section of photon-photon scattering is a function of the degree of polarization entanglement of the two-photon state. A reduced, general expression for the differential cross section of photon-photon scattering is derived by applying simple symmetry arguments. An explicit expression is obtained for the example of photon-photon scattering due to virtual electron-positron pairs in Quantum Electrodynamics. It is shown how the effect in this explicit example can be explained as an effect of quantum interference and that it fits with the idea of distance-depe…
A scheme for generating an entangled state in a two spin-1/2 system by means of a spin-dependent potential scattering of another qubit is presented and analyzed in three dimensions. The entanglement is evaluated in terms of the concurrence both at the lowest and in full order in perturbation with an appropriate renormalization for the latter, and its characteristics are discussed in the context of (in)distinguishability of alternative paths for a quantum particle.
Ultracold collisions of Bose-Einstein condensates can be used to generate a large number of counterpropagating pairs of entangled atoms, which collectively form a thin spherical shell in momentum space, called a scattering halo. Here we generate a scattering halo composed almost entirely of pairs in a symmetric entangled state and observe a scattering angle-dependent mixing to the anti-symmetric state due to the presence of an inhomogeneous magnetic field. We report on a proof-of-principle application of the observed parity dynamics to demonstrate magnetic gradiometry, insensitive to common-mo…
We show that it is possible to entangle three different many-particle states by Bragg spectroscopy with nonclassical light in a Bose condensate of weakly interacting atomic gases. Among these three states, two are of atoms corresponding to two opposite momentum side-modes of the condensate; and the other is of single-mode photons of the output probe beam. We demonstrate strong dependence of the multiparticle entanglement on the quantum statistics of the probe light. We present detailed results on entanglement keeping in view of the possible experimental situation.
