Entanglement of a double dot with a quantum point contact

Abstract

Entanglement between particle and detector is known to be inherent in the measurement process. Gurvitz recently analyzed the coupling of an electron in a double dot (DD) to a quantum point contact (QPC) detector. In this paper we examine the dynamics of entanglement that result between the DD and QPC. The rate of entanglement is optimized as a function of coupling when the electron is initially in one of the dots. It decreases asymptotically towards zero with increased coupling. The opposite behavior is observed when the DD is initially in a superposition: the rate of entanglement increases unboundedly as the coupling is increased. The possibility that there are conditions for which measurement occurs versus entanglement is considered.

Entanglement in particle-detector interaction

“…In Ref. [3] we left open the question of whether or not there exist conditions for which projective measurement occurs. Note that if the QPC was a measuring device, then the measurement postulate should be applied, and there would be no entanglement between the two double-dots.…”

“…Entanglement between the DD and QPC and the rate of the entanglement, defined as R(τ )= △ dS dτ was determined for several cases and for various couplings. Several results in [3] are summarized below:…”

“…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.…”