From Full Counting Statistics to Quantum Metrology

Andrey V. Lebedev^a

co-authors: G.B. Lesovik^b, and G. Blatter^a

^a ITP ETH Zurich, Switzerland
^b Landau Institute, Moscow, Russia

Full Counting Statistics describes the complete statistical properties of charge transport through a mesoscopic device. A proper theoretical description of Full Counting Statistics (FCS) requires the inclusion of a spin or qubit as a measurement device. An experimental realization can be implemented with an array of qubits (a qubit-register); while a simple statistical readout of the register state provides statistical information on the number of transmitted particle, a more sophisticated sequential readout corresponding to a semi-classical Fourier transform allows to measure the precise particle number traversing the system. The relation of this quantum counting algorithm to the phase estimation algorithm allows to exploit the latter's stability and extend the counting scheme to the measurement of continuous quantities, opening the way to quantum metrology and attain the Heisenberg limit.

Alternatively to the digital counting scheme, we discuss an analogue measurement procedure where the qubit register is replaced by several ensembles of non-interacting qubits. The latter scheme does not require separate access to each qubit, goes beyond the shot-noise limit, but does not reach the Heisenberg limit.

A simple implementation of this analogue procedure can be done with the help of a two-componenst Bose gas. The basic quantum resource exploited in all this analysis is the coherent quantum evolution of a spin.