3 research outputs found
The information about the state of a qubit gained by a weakly coupled detector
We analyze the information that one can learn about the state of a quantum
two-level system, i.e. a qubit, when probed weakly by a nearby detector. In
particular, we focus on the case when the qubit Hamiltonian and the qubit's
operator being probed by the detector do not commute. Because the qubit's state
keeps evolving while being probed and because the measurement data is mixed
with a detector-related background noise, one might expect the detector to fail
in this case. We show, however, that under suitable conditions and by proper
analysis of the measurement data useful information about the state of the
qubit can be extracted. It turns out that the measurement basis is
stochastically determined every time the experiment is repeated. We analyze in
detail the probability distributions that govern the choice of measurement
bases. We also analyze the information acquisition rate and show that it is
largely unaffected by the apparent conflict between the measurement and
intrinsic qubit dynamics. We discuss the relation between our analysis and the
stochastic master equation that describes the evolution of the qubit's state
under the influence of measurement and decoherence. In particular, we write
down a stochastic equation that encompasses the usual stochastic master
equation for the evolution of the qubit's density matrix and additionally
contains the measurement information that can be extracted from the observed
signal.Comment: 21 pages (two column), 8 figure