92 research outputs found
The best Fisher is upstream: data processing inequalities for quantum metrology
We apply the classical data processing inequality to quantum metrology to
show that manipulating the classical information from a quantum measurement
cannot aid in the estimation of parameters encoded in quantum states. We
further derive a quantum data processing inequality to show that coherent
manipulation of quantum data also cannot improve the precision in estimation.
In addition, we comment on the assumptions necessary to arrive at these
inequalities and how they might be avoided providing insights into enhancement
procedures which are not provably wrong.Comment: Comments encourage
Self-guided quantum tomography
We introduce a self-learning tomographic technique in which the experiment
guides itself to an estimate of its own state. Self-guided quantum tomography
(SGQT) uses measurements to directly test hypotheses in an iterative algorithm
which converges to the true state. We demonstrate through simulation on many
qubits that SGQT is a more efficient and robust alternative to the usual
paradigm of taking a large amount of informationally complete data and solving
the inverse problem of post-processed state estimation.Comment: v2: published versio
Quantum Model Averaging
Standard tomographic analyses ignore model uncertainty. It is assumed that a
given model generated the data and the task is to estimate the quantum state,
or a subset of parameters within that model. Here we apply a model averaging
technique to mitigate the risk of overconfident estimates of model parameters
in two examples: (1) selecting the rank of the state in tomography and (2)
selecting the model for the fidelity decay curve in randomized benchmarking.Comment: For a summary, see http://i.imgur.com/nMJxANo.pn
High posterior density ellipsoids of quantum states
Regions of quantum states generalize the classical notion of error bars. High
posterior density (HPD) credible regions are the most powerful of region
estimators. However, they are intractably hard to construct in general. This
paper reports on a numerical approximation to HPD regions for the purpose of
testing a much more computationally and conceptually convenient class of
regions: posterior covariance ellipsoids (PCEs). The PCEs are defined via the
covariance matrix of the posterior probability distribution of states. Here it
is shown that PCEs are near optimal for the example of Pauli measurements on
multiple qubits. Moreover, the algorithm is capable of producing accurate PCE
regions even when there is uncertainty in the model.Comment: TL;DR version: computationally feasible region estimator
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
Accelerated Randomized Benchmarking
Quantum information processing offers promising advances for a wide range of
fields and applications, provided that we can efficiently assess the
performance of the control applied in candidate systems. That is, we must be
able to determine whether we have implemented a desired gate, and refine
accordingly. Randomized benchmarking reduces the difficulty of this task by
exploiting symmetries in quantum operations.
Here, we bound the resources required for benchmarking and show that, with
prior information, we can achieve several orders of magnitude better accuracy
than in traditional approaches to benchmarking. Moreover, by building on
state-of-the-art classical algorithms, we reach these accuracies with
near-optimal resources. Our approach requires an order of magnitude less data
to achieve the same accuracies and to provide online estimates of the errors in
the reported fidelities. We also show that our approach is useful for physical
devices by comparing to simulations.
Our results thus enable the application of randomized benchmarking in new
regimes, and dramatically reduce the experimental effort required to assess
control fidelities in quantum systems. Finally, our work is based on
open-source scientific libraries, and can readily be applied in systems of
interest.Comment: 10 pages, full source code at
https://github.com/cgranade/accelerated-randomized-benchmarking #quantuminfo
#benchmarkin
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