Qubit feedback and control with kicked quantum nondemolition measurements: A quantum Bayesian analysis

TL;DR

This paper develops a quantum Bayesian framework for kicked quantum nondemolition measurements on charge qubits, enabling feedback control to prepare and purify quantum states through measurement and conditional operations.

Contribution

It introduces a stochastic conformal map approach to quantum Bayesian equations for qubits and designs feedback protocols for state preparation and purification.

Findings

Feedback can produce arbitrary pure states after weak measurement

Initial mixed states can be purified with feedback

Measurement statistics for kicked QND measurements are derived

Abstract

The informational approach to continuous quantum measurement is derived from POVM formalism for a mesoscopic scattering detector measuring a charge qubit. Quantum Bayesian equations for the qubit density matrix are derived, and cast into the form of a stochastic conformal map. Measurement statistics are derived for kicked quantum nondemolition measurements, combined with conditional unitary operations. These results are applied to derive a feedback protocol to produce an arbitrary pure state after a weak measurement, as well as to investigate how an initially mixed state becomes purified with and without feedback.