974 research outputs found
Quantum Bayesian approach to circuit QED measurement with moderate bandwidth
We consider continuous quantum measurement of a superconducting qubit in the
circuit QED setup with a moderate bandwidth of the measurement resonator, i.e.,
when the "bad cavity" limit is not applicable. The goal is a simple description
of the quantum evolution due to measurement, i.e., the measurement back-action.
Extending the quantum Bayesian approach previously developed for the "bad
cavity" regime, we show that the evolution equations remain the same, but now
they should be applied to the entangled qubit-resonator state, instead of the
qubit state alone. The derivation uses only elementary quantum mechanics and
basic properties of coherent states, thus being accessible to non-experts.Comment: 26 page
Quantum Bayesian approach to circuit QED measurement
We present a simple formalism describing evolution of a qubit in the process
of its measurement in a circuit QED setup. When a phase-sensitive amplifier is
used, the evolution depends on only one output quadrature, and the formalism is
the same as for a broadband setup. When a phase-preserving amplifier is used,
the qubit evolution depends on two output quadratures. In both cases a perfect
monitoring of the qubit state and therefore a perfect quantum feedback is
possible.Comment: 11 pages; Contribution to Proceedings of Les Houches summer school
"Quantum Machines" (2011
Density matrix purification due to continuous quantum measurement
We consider the continuous quantum measurement of a two-level system, for
example, a single-Cooper-pair box measured by a single-electron transistor or a
double-quantum dot measured by a quantum point contact. While the approach most
commonly used describes the gradual decoherence of the system due to the
measurement, we show that when taking into account the detector output, we get
the opposite effect: gradual purification of the density matrix. The
competition between purification due to measurement and decoherence due to
interaction with the environment can be described by a simple Langevin equation
which couples the random evolution of the system density matrix and the
stochastic detector output. The gradual density matrix purification due to
continuous measurement may be verified experimentally using present-day
technology. The effect can be useful for quantum computing.Comment: 2 pages, 1 figure; submitted to LT'2
Error matrices in quantum process tomography
We discuss characterization of experimental quantum gates by the error
matrix, which is similar to the standard process matrix in the Pauli
basis, except the desired unitary operation is factored out, by formally
placing it either before or after the error process. The error matrix has only
one large element, which is equal to the process fidelity, while other elements
are small and indicate imperfections. The imaginary parts of the elements along
the left column and/or top row directly indicate the unitary imperfection and
can be used to find the needed correction. We discuss a relatively simple way
to calculate the error matrix for a composition of quantum gates. Similarly, it
is rather straightforward to find the first-order contribution to the error
matrix due to the Lindblad-form decoherence. We also discuss a way to identify
and subtract the tomography procedure errors due to imperfect state preparation
and measurement. In appendices we consider several simple examples of the
process tomography and also discuss an intuitive physical interpretation of the
Lindblad-form decoherence.Comment: 21 pages (slightly revised version
Continuous quantum measurement with observer: pure wavefunction evolution instead of decoherence
We consider a continuous measurement of a two-level system (double-dot) by
weakly coupled detector (tunnel point contact nearby). While usual treatment
leads to the gradual system decoherence due to the measurement, we show that
the knowledge of the measurement result can restore the pure wavefunction at
any time (this can be experimentally verified). The formalism allows to write a
simple Langevin equation for the random evolution of the system density matrix
which is reflected and caused by the stochastic detector output. Gradual
wavefunction ``collapse'' and quantum Zeno effect are naturally described by
the equation.Comment: 6 pages, 2 figure
Continuous quantum measurement with particular output: pure wavefunction evolution instead of decoherence
We consider a continuous measurement of a two-level system (double-dot) by
weakly coupled detector (tunnel point contact nearby). While usual treatment
leads to the gradual system decoherence due to the measurement, we show that
the knowledge of the measurement result can restore the pure wavefunction at
any time (this can be experimentally verified). The formalism allows to write a
simple Langevin equation for the random evolution of the system density matrix
which is reflected and caused by the stochastic detector output. Gradual
wavefunction ``collapse'' and quantum Zeno effect are naturally described by
the equation.Comment: short version of quant-ph/9807051 (4 pages, 2 figures
Quasi-Langevin method for shot noise calculation in single-electron tunneling
It is shown that quasi-Langevin method can be used for the calculation of the
shot noise in correlated single-electron tunneling. We generalize the existing
Fokker-Plank-type approach and show its equivalence to quasi-Langevin approach.
The advantage of the quasi-Langevin method is a natural possibility to describe
simultaneously the high (``quantum'') frequency range.Comment: 13 pages (RevTeX), 1 figur
- …