Rapid measurement and purification using quantum feedback control

Abstract

I study the rate at which information can be extracted from a finite-dimensional open quantum system using the quantum trajectory description of a continuous measurement. I derive the rate at which information is extracted for a measurement without any control; this sets the benchmark to which the subsequent control protocols are compared. Next I consider control protocols that increase the rate of information extraction. The first such protocol applies feedback so the state and the measurement basis are unbiased at all times. The use of unbiased bases means that this protocol is essentially quantum mechanical in nature. For observables with equally spaced eigenvalues, the “speed-up” in the information extraction afforded by unbiased basis feedback, is proportional to the square of the observed system’s Hilbert space. The second protocol considered optimally permutes the eigenvalues of the quantum state in the logical basis. As the measured observable and state commute at all times this protocol is essentially classical in nature. The speed-up provided by this protocol is also quadratic. The final protocol I consider is a new type of control. It merges open-loop quantum control and quantum filtering. This method also affords an improvement in the rate of information extraction.