97 research outputs found
Weak value amplification is suboptimal for estimation and detection
We show using statistically rigorous arguments that the technique of weak
value amplification (WVA) does not perform better than standard statistical
techniques for the tasks of single parameter estimation and signal detection.
Specifically we prove that post-selection, a necessary ingredient for WVA,
decreases estimation accuracy and, moreover, arranging for anomalously large
weak values is a suboptimal strategy. In doing so, we explicitly provide the
optimal estimator, which in turn allows us to identify the optimal experimental
arrangement to be the one in which all outcomes have equal weak values (all as
small as possible) and the initial state of the meter is the maximal eigenvalue
of the square of the system observable. Finally, we give precise quantitative
conditions for when weak measurement (measurements without post-selection or
anomalously large weak values) can mitigate the effect of uncharacterized
technical noise in estimation.Comment: This is a significant revision which is closer to the published
versio
How the result of a single coin toss can turn out to be 100 heads
We show that the phenomenon of anomalous weak values is not limited to
quantum theory. In particular, we show that the same features occur in a simple
model of a coin subject to a form of classical backaction with pre- and
post-selection. This provides evidence that weak values are not inherently
quantum, but rather a purely statistical feature of pre- and post-selection
with disturbance.Comment: published versio
Quantum feedback for rapid state preparation in the presence of control imperfections
Quantum feedback control protocols can improve the operation of quantum
devices. Here we examine the performance of a purification protocol when there
are imperfections in the controls. The ideal feedback protocol produces an
eigenstate from a mixed state in the minimum time, and is known as rapid state
preparation. The imperfections we examine include time delays in the feedback
loop, finite strength feedback, calibration errors, and inefficient detection.
We analyse these imperfections using the Wiseman-Milburn feedback master
equation and related formalism. We find that the protocol is most sensitive to
time delays in the feedback loop. For systems with slow dynamics, however, our
analysis suggests that inefficient detection would be the bigger problem. We
also show how system imperfections, such as dephasing and damping, can be
included in model via the feedback master equation.Comment: 15 pages, 6 figures and 2 tables. V2 the published version, fig. 1
corrected and some minor changes to the tex
Maximum information gain in weak or continuous measurements of qudits: complementarity is not enough
To maximize average information gain for a classical measurement, all
outcomes of an observation must be equally likely. The condition of equally
likely outcomes may be enforced in quantum theory by ensuring that one's state
is maximally different, or complementary, to the measured observable.
This requires the ability to perform unitary operations on the state,
conditioned on the results of prior measurements. We consider the case of
measurement of a component of angular momentum for a qudit (a -dimensional
system, with ). For weak or continuous-in-time (i.e. repeated weak)
measurements, we show that the complementarity condition ensures an average
improvement, in the rate of purification, of only 2. However, we show that by
choosing the optimal control protocol of this type, one can attain the best
possible scaling, , for the average improvement. For this protocol
the acquisition of information is nearly deterministic. Finally we contrast
these results with those for complementarity-based protocols in a register of
qbits.Comment: 21 pages, 21 figures. V2 published versio
Quantum trajectories for propagating Fock states
We derive quantum trajectories (also known as stochastic master equations)
that describe an arbitrary quantum system probed by a propagating wave packet
of light prepared in a continuous-mode Fock state. We consider three detection
schemes of the output light: photon counting, homodyne detection, and
heterodyne detection. We generalize to input field states that are
superpositions and or mixtures of Fock states and illustrate the formalism with
several examples.Comment: 20 pages, 4 figure
The SLH framework for modeling quantum input-output networks
Many emerging quantum technologies demand precise engineering and control
over networks consisting of quantum mechanical degrees of freedom connected by
propagating electromagnetic fields, or quantum input-output networks. Here we
review recent progress in theory and experiment related to such quantum
input-output networks, with a focus on the SLH framework, a powerful modeling
framework for networked quantum systems that is naturally endowed with
properties such as modularity and hierarchy. We begin by explaining the
physical approximations required to represent any individual node of a network,
eg. atoms in cavity or a mechanical oscillator, and its coupling to quantum
fields by an operator triple . Then we explain how these nodes can be
composed into a network with arbitrary connectivity, including coherent
feedback channels, using algebraic rules, and how to derive the dynamics of
network components and output fields. The second part of the review discusses
several extensions to the basic SLH framework that expand its modeling
capabilities, and the prospects for modeling integrated implementations of
quantum input-output networks. In addition to summarizing major results and
recent literature, we discuss the potential applications and limitations of the
SLH framework and quantum input-output networks, with the intention of
providing context to a reader unfamiliar with the field.Comment: 60 pages, 14 figures. We are still interested in receiving
correction
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