Abstract
Full text: We present an analysis of reading out the state of an electron tunneling between two coherently coupled quantum dots using two low transparency point contact (PC) or tunnel junction detectors, one on either side of the two dots. The double dot system forms a single charge quantum bit (qubit), and the readout corresponds to a continuous in time measurement of the occupancy of the two dots. The correlated outputs of the two detectors reduce the effect of random charge noise and improve the signal-to-noise ratio as compared to the case that only one detector is employed. We provide a unified view for the master equation approach and the so-called quantum trajectory (or stochastic Schrodinger equation) approach to the measurement problem. We show that the master equation for the reduced or 'partially' reduced density matrix can be obtained when an average or partial average is taken on the conditional, stochastic density matrix over the possible outcomes of the measurement. We then simulate P(N,t), the probability of finding N electron that have tunneled through the PC barriers in time t, using 10000 quantum trajectories and measurement records. In this approach, each quantum trajectory resembles a single history of the qubit
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Goan, H -S
[1]
- University of New South Wales, Sydney, NSW (Australia). Center for Quantum Computer Technology
Citation Formats
Goan, H -S.
Quantum trajectories and quantum measurement theory in solid-state mesoscopics.
Australia: N. p.,
2002.
Web.
Goan, H -S.
Quantum trajectories and quantum measurement theory in solid-state mesoscopics.
Australia.
Goan, H -S.
2002.
"Quantum trajectories and quantum measurement theory in solid-state mesoscopics."
Australia.
@misc{etde_20619925,
title = {Quantum trajectories and quantum measurement theory in solid-state mesoscopics}
author = {Goan, H -S}
abstractNote = {Full text: We present an analysis of reading out the state of an electron tunneling between two coherently coupled quantum dots using two low transparency point contact (PC) or tunnel junction detectors, one on either side of the two dots. The double dot system forms a single charge quantum bit (qubit), and the readout corresponds to a continuous in time measurement of the occupancy of the two dots. The correlated outputs of the two detectors reduce the effect of random charge noise and improve the signal-to-noise ratio as compared to the case that only one detector is employed. We provide a unified view for the master equation approach and the so-called quantum trajectory (or stochastic Schrodinger equation) approach to the measurement problem. We show that the master equation for the reduced or 'partially' reduced density matrix can be obtained when an average or partial average is taken on the conditional, stochastic density matrix over the possible outcomes of the measurement. We then simulate P(N,t), the probability of finding N electron that have tunneled through the PC barriers in time t, using 10000 quantum trajectories and measurement records. In this approach, each quantum trajectory resembles a single history of the qubit state in a single run of the continuous measurement experiment, and thus aids in the interpretation of ensemble and time averaged properties. The simulation results of P(N,t) are in very good agreement with those obtained from the Fourier analysis of the partially reduced density matrix. Finally, we discuss the possibility of reading out the state of the qubit system in a single-shot experiment.}
place = {Australia}
year = {2002}
month = {Jul}
}
title = {Quantum trajectories and quantum measurement theory in solid-state mesoscopics}
author = {Goan, H -S}
abstractNote = {Full text: We present an analysis of reading out the state of an electron tunneling between two coherently coupled quantum dots using two low transparency point contact (PC) or tunnel junction detectors, one on either side of the two dots. The double dot system forms a single charge quantum bit (qubit), and the readout corresponds to a continuous in time measurement of the occupancy of the two dots. The correlated outputs of the two detectors reduce the effect of random charge noise and improve the signal-to-noise ratio as compared to the case that only one detector is employed. We provide a unified view for the master equation approach and the so-called quantum trajectory (or stochastic Schrodinger equation) approach to the measurement problem. We show that the master equation for the reduced or 'partially' reduced density matrix can be obtained when an average or partial average is taken on the conditional, stochastic density matrix over the possible outcomes of the measurement. We then simulate P(N,t), the probability of finding N electron that have tunneled through the PC barriers in time t, using 10000 quantum trajectories and measurement records. In this approach, each quantum trajectory resembles a single history of the qubit state in a single run of the continuous measurement experiment, and thus aids in the interpretation of ensemble and time averaged properties. The simulation results of P(N,t) are in very good agreement with those obtained from the Fourier analysis of the partially reduced density matrix. Finally, we discuss the possibility of reading out the state of the qubit system in a single-shot experiment.}
place = {Australia}
year = {2002}
month = {Jul}
}