2,556 research outputs found
Protocols for optimal readout of qubits using a continuous quantum nondemolition measurement
We study how the spontaneous relaxation of a qubit affects a continuous
quantum non-demolition measurement of the initial state of the qubit. Given
some noisy measurement record , we seek an estimate of whether the qubit
was initially in the ground or excited state. We investigate four different
measurement protocols, three of which use a linear filter (with different
weighting factors) and a fourth which uses a full non-linear filter that gives
the theoretically optimal estimate of the initial state of the qubit. We find
that relaxation of the qubit at rate strongly influences the fidelity
of any measurement protocol. To avoid errors due to this decay, the measurement
must be completed in a time that decrease linearly with the desired fidelity
while maintaining an adequate signal to noise ratio. We find that for the
non-linear filter the predicted fidelity, as expected, is always better than
the linear filters and that the fidelity is a monotone increasing function of
the measurement time. For example, to achieve a fidelity of 90%, the box car
linear filter requires a signal to noise ratio of in a time
whereas the non-linear filter only requires a signal to noise ratio of .Comment: 12 pages, 6 figure
Non Markovian Quantum Repeated Interactions and Measurements
A non-Markovian model of quantum repeated interactions between a small
quantum system and an infinite chain of quantum systems is presented. By
adapting and applying usual pro jection operator techniques in this context,
discrete versions of the integro-differential and time-convolutioness Master
equations for the reduced system are derived. Next, an intuitive and rigorous
description of the indirect quantum measurement principle is developed and a
discrete non Markovian stochastic Master equation for the open system is
obtained. Finally, the question of unravelling in a particular model of
non-Markovian quantum interactions is discussed.Comment: 22 page
Non-Markovian stochastic Schr\"odinger equations: Generalization to real-valued noise using quantum measurement theory
Do stochastic Schr\"odinger equations, also known as unravelings, have a
physical interpretation? In the Markovian limit, where the system {\em on
average} obeys a master equation, the answer is yes. Markovian stochastic
Schr\"odinger equations generate quantum trajectories for the system state
conditioned on continuously monitoring the bath. For a given master equation,
there are many different unravelings, corresponding to different sorts of
measurement on the bath. In this paper we address the non-Markovian case, and
in particular the sort of stochastic \sch equation introduced by Strunz, Di\'
osi, and Gisin [Phys. Rev. Lett. 82, 1801 (1999)]. Using a quantum measurement
theory approach, we rederive their unraveling which involves complex-valued
Gaussian noise. We also derive an unraveling involving real-valued Gaussian
noise. We show that in the Markovian limit, these two unravelings correspond to
heterodyne and homodyne detection respectively. Although we use quantum
measurement theory to define these unravelings, we conclude that the stochastic
evolution of the system state is not a true quantum trajectory, as the identity
of the state through time is a fiction.Comment: 17 pages, 3 figure
Jump-like unravelings for non-Markovian open quantum systems
Non-Markovian evolution of an open quantum system can be `unraveled' into
pure state trajectories generated by a non-Markovian stochastic (diffusive)
Schr\"odinger equation, as introduced by Di\'osi, Gisin, and Strunz. Recently
we have shown that such equations can be derived using the modal (hidden
variable) interpretation of quantum mechanics. In this paper we generalize this
theory to treat jump-like unravelings. To illustrate the jump-like behavior we
consider a simple system: A classically driven (at Rabi frequency )
two-level atom coupled linearly to a three mode optical bath, with a central
frequency equal to the frequency of the atom, , and the two side
bands have frequencies . In the large limit we
observed that the jump-like behavior is similar to that observed in this system
with a Markovian (broad band) bath. This is expected as in the Markovian limit
the fluorescence spectrum for a strongly driven two level atom takes the form
of a Mollow triplet. However the length of time for which the Markovian-like
behaviour persists depends upon {\em which} jump-like unraveling is used.Comment: 11 pages, 5 figure
A proposal for implementing an n-qubit controlled-rotation gate with three-level superconducting qubit systems in cavity QED
We present a way for implementing an n-qubit controlled-rotation gate with
three-level superconducting qubit systems in cavity QED. The two logical states
of a qubit are represented by the two lowest levels of each system while a
higher-energy level is used for the gate implementation. The method operates
essentially by preparing a state conditioned on the states of the control
qubits, creating a single photon in the cavity mode, and then performing an
arbitrary rotation on the states of the target qubit with assistance of the
cavity photon. It is interesting to note that the basic operational steps for
implementing the proposed gate do not increase with the number of qubits,
and the gate operation time decreases as the number of qubits increases. This
proposal is quite general, which can be applied to various types of
superconducting devices in a cavity or coupled to a resonator.Comment: Six figures, accepted by Journal of Physics: Condensed Matte
Dissipation and Ultrastrong Coupling in Circuit QED
Cavity and circuit QED study light-matter interaction at its most fundamental
level. Yet, this interaction is most often neglected when considering the
coupling of this system with an environment. In this paper, we show how this
simplification, which leads to the standard quantum optics master equation, is
at the root of unphysical effects. Including qubit relaxation and dephasing,
and cavity relaxation, we derive a master equation that takes into account the
qubit-resonator coupling. Special attention is given to the ultrastrong
coupling regime, where the failure of the quantum optical master equation is
manifest. In this situation, our model predicts an asymmetry in the vacuum Rabi
splitting that could be used to probe dephasing noise at unexplored
frequencies. We also show how fluctuations in the qubit frequency can cause
sideband transitions, squeezing, and Casimir-like photon generation.Comment: 16 pages, 6 figure
Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect
We present a theoretical study of a superconducting charge qubit dispersively
coupled to a transmission line resonator. Starting from a master equation
description of this coupled system and using a polaron transformation, we
obtain an exact effective master equation for the qubit. We then use quantum
trajectory theory to investigate the measurement of the qubit by continuous
homodyne measurement of the resonator out-field. Using the same porlaron
transformation, a stochastic master equation for the conditional state of the
qubit is obtained. From this result, various definitions of the measurement
time are studied. Furthermore, we find that in the limit of strong homodyne
measurement, typical quantum trajectories for the qubit exhibit a crossover
from diffusive to jump-like behavior. Finally, in the presence of Rabi drive on
the qubit, the qubit dynamics is shown to exhibit quantum Zeno behavior.Comment: 20 pages, 12 figure
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