Generation Of Entanglement In Systems Research Articles

Entanglement generation through particle detection in systems of identical fermions

We investigate the generation of entanglement in systems of identical fermions through a process involving particle detection, focusing on the implications that these kindsof processes have for the concept of entanglement between fermionic particles. As a paradigmatic example we discuss in detail a scheme based on a splitting-plus-detection operation. The aim of this scheme is to generate states with a definite number of particles at two separated locations, that can effectively be described as entangled states of two distinguishable qubits, starting from an initial pure state of two indistinguishable fermions exhibiting correlations purely due to antisymmetrization. It is argued that the proposed extraction of a useful entanglement-based resource, given by two distinguishable qubits entangled in the standard sense, does not contravene the notion of entanglement in identical-fermion systems as describing correlations beyond those purely due to their indistinguishability. In point of fact, it is shown that this concept of entanglement, here referred to as fermionic entanglement, actually helps to clarify some essential aspects of the entanglement generation process. In particular, we prove that the amount of entanglement exhibited by the above mentioned pair of distinguishable qubits, obtained after post-selection of a state having a definite number of particles in two separated locations, equals the amount of fermionic entanglement created by this detection process. The aforementioned scheme is generalized for the case of N-identical fermion systems of arbitrary dimension. It transpires from our present discussion that a proper analysis of entanglement generation during the splitting-plus-detection operation is not only consistent with the concept of fermionic entanglement, but actually reinforces it.

Generation of entanglement in systems of intercoupled qubits

We consider systems of two and three qubits, mutually coupled by Heisenberg-type exchange interaction and interacting with external laser fields. We show that these systems allow one to create maximally entangled Bell states, as well as three qubit Greenberger-Horne-Zeilinger and W states. In particular, we point out that some of the target states are the eigenstates of the initial bare system. Due to this, one can create entangled states by means of pulse area and adiabatic techniques, when starting from a separable (non-entangled) ground state. On the other hand, for target states, not present initially in the eigensystem of the model, we apply the robust stimulated Raman adiabatic passage and $\pi$ pulse techniques, that create desired coherent superpositions of non-entangled eigenstates.

Entanglement dynamics via semiclassical propagators in systems of two spins

We analyze the dynamical generation of entanglement in systems of two interacting spins initially prepared in a product of spin coherent states. For arbitrary time-independent Hamiltonians, we derive a semiclassical expression for the purity of the reduced density matrix as a function of time. The final formula, subsidiary to the linear entropy, shows that the short-time dynamics of entanglement depends exclusively on the stability of trajectories governed by the underlying classical Hamiltonian. In addition, this semiclassical measure is shown to reproduce the general properties of its quantum counterpart and give the expected result in the large spin limit. The accuracy of the semiclassical formula is further illustrated in a problem of phase exchange for two particles of spin $j$.