nt - p h / 02 08 19 3 v 1 3 0 A ug 2 00 2 Entanglement in particle - detector interactions

It is predicted by Schrödinger's equation that entanglement will occur in the interaction between detector and particle. We provide an analysis of the entanglement using the Gurvitz model of double-dot and detector. New results on entangled doubled-dots are provided as well as implications on Quantum Information processing. The prediction of entanglement under Schrödinger evolution is apparent when one considers the interaction of a particle with a detector. One can see this by the well-known and simple argument that a particle will become correlated with the eigenstates of a measuring device. Hence if the particle were in an initial superposition of these eigenstates, then by invoking linearity, the result follows. A more general theoretical proof of the resulting entanglement was provided recently by Bassi and Ghirardi [1]. In this paper, we proceed further on investigating the dynamics of the predicted entanglement. In order to answer this question a more realistic model of a detector is needed. Gurvitz [2] recently has made an important contribution in the study of the measurement problem in his analysis of an electron in a double-dot (DD) interacting with a quantum point contact (QPC). His analysis considers the two components of the system: the current through the QPC and the density matrix of the electron. In this paper, we first provide a summary of results found in [3] in which we extended Gurvitz's analysis by quantifying the dynamical entanglement that results between a single DD and QPC. We also provide new results in the consideration of two entangled DDs whereby one of the DDs interacts with the QPC. 1 Background In order to examine the role of entanglement for this paper we utilize as a measure the entropy of entanglement of a pure composite bipartite state. The entropy of entanglement (S) of a bipartite pure state ρ ∈ K(H A ⊗H B) is given by Von Neumann's entropy of either ρ A or ρ B , S(ρ) = −Tr(ρ A log ρ A) Gurvitz [2] considered the measurement of a single electron oscillating in a double-dot by using a quantum point contact detector. We briefly review the setup in Fig. 1, but refer the reader to [2]. The barrier shown in the figure is connected with two reservoirs at the potentials µ L and µ R