224,181 research outputs found
Estimation in the group action channel
We analyze the problem of estimating a signal from multiple measurements on a
\mbox{group action channel} that linearly transforms a signal by a random
group action followed by a fixed projection and additive Gaussian noise. This
channel is motivated by applications such as multi-reference alignment and
cryo-electron microscopy. We focus on the large noise regime prevalent in these
applications. We give a lower bound on the mean square error (MSE) of any
asymptotically unbiased estimator of the signal's orbit in terms of the
signal's moment tensors, which implies that the MSE is bounded away from 0 when
is bounded from above, where is the number of observations,
is the noise standard deviation, and is the so-called
\mbox{moment order cutoff}. In contrast, the maximum likelihood estimator is
shown to be consistent if diverges.Comment: 5 pages, conferenc
A generalization of Schur-Weyl duality with applications in quantum estimation
Schur-Weyl duality is a powerful tool in representation theory which has many
applications to quantum information theory. We provide a generalization of this
duality and demonstrate some of its applications. In particular, we use it to
develop a general framework for the study of a family of quantum estimation
problems wherein one is given n copies of an unknown quantum state according to
some prior and the goal is to estimate certain parameters of the given state.
In particular, we are interested to know whether collective measurements are
useful and if so to find an upper bound on the amount of entanglement which is
required to achieve the optimal estimation. In the case of pure states, we show
that commutativity of the set of observables that define the estimation problem
implies the sufficiency of unentangled measurements.Comment: The published version, Typos corrected, 40 pages, 2 figure
Confusability graphs for symmetric sets of quantum states
For a set of quantum states generated by the action of a group, we consider
the graph obtained by considering two group elements adjacent whenever the
corresponding states are non-orthogonal. We analyze the structure of the
connected components of the graph and show two applications to the optimal
estimation of an unknown group action and to the search for decoherence free
subspaces of quantum channels with symmetry.Comment: 7 pages, no figures, contribution to the Proceedings of the XXIX
International Colloquium on Group-Theoretical Methods in Physics, August
22-26, Chern Institute of Mathematics, Tianjin, Chin
Modeled channel distributions explain extracellular recordings from cultured neurons sealed to microelectrodes
Amplitudes and shapes of extracellular recordings from single neurons cultured on a substrate embedded microelectrode depend not only on the volume conducting properties of the neuron-electrode interface, but might also depend on the distribution of voltage-sensitive channels over the neuronal membrane. In this paper, finite-element modeling is used to quantify the effect of these channel distributions on the neuron-electrode contact. Slight accumulation or depletion of voltage-sensitive channels in the sealing membrane of the neuron results in various shapes and amplitudes of simulated extracellular recordings. However, estimation of channel-specific accumulation factors from extracellular recordings can be obstructed by co-occuring ion currents and defect sealing. Experimental data from cultured neuron-electrode interfaces suggest depletion of sodium channels and accumulation of potassium channels
Process reconstruction from incomplete and/or inconsistent data
We analyze how an action of a qubit channel (map) can be estimated from the
measured data that are incomplete or even inconsistent. That is, we consider
situations when measurement statistics is insufficient to determine consistent
probability distributions. As a consequence either the estimation
(reconstruction) of the channel completely fails or it results in an unphysical
channel (i.e., the corresponding map is not completely positive). We present a
regularization procedure that allows us to derive physically reasonable
estimates (approximations) of quantum channels. We illustrate our procedure on
specific examples and we show that the procedure can be also used for a
derivation of optimal approximations of operations that are forbidden by the
laws of quantum mechanics (e.g., the universal NOT gate).Comment: 9pages, 5 figure
Deep Reinforcement Learning for Real-Time Optimization in NB-IoT Networks
NarrowBand-Internet of Things (NB-IoT) is an emerging cellular-based
technology that offers a range of flexible configurations for massive IoT radio
access from groups of devices with heterogeneous requirements. A configuration
specifies the amount of radio resource allocated to each group of devices for
random access and for data transmission. Assuming no knowledge of the traffic
statistics, there exists an important challenge in "how to determine the
configuration that maximizes the long-term average number of served IoT devices
at each Transmission Time Interval (TTI) in an online fashion". Given the
complexity of searching for optimal configuration, we first develop real-time
configuration selection based on the tabular Q-learning (tabular-Q), the Linear
Approximation based Q-learning (LA-Q), and the Deep Neural Network based
Q-learning (DQN) in the single-parameter single-group scenario. Our results
show that the proposed reinforcement learning based approaches considerably
outperform the conventional heuristic approaches based on load estimation
(LE-URC) in terms of the number of served IoT devices. This result also
indicates that LA-Q and DQN can be good alternatives for tabular-Q to achieve
almost the same performance with much less training time. We further advance
LA-Q and DQN via Actions Aggregation (AA-LA-Q and AA-DQN) and via Cooperative
Multi-Agent learning (CMA-DQN) for the multi-parameter multi-group scenario,
thereby solve the problem that Q-learning agents do not converge in
high-dimensional configurations. In this scenario, the superiority of the
proposed Q-learning approaches over the conventional LE-URC approach
significantly improves with the increase of configuration dimensions, and the
CMA-DQN approach outperforms the other approaches in both throughput and
training efficiency
Selective and Efficient Quantum Process Tomography
In this paper we describe in detail and generalize a method for quantum
process tomography that was presented in [A. Bendersky, F. Pastawski, J. P.
Paz, Physical Review Letters 100, 190403 (2008)]. The method enables the
efficient estimation of any element of the --matrix of a quantum process.
Such elements are estimated as averages over experimental outcomes with a
precision that is fixed by the number of repetitions of the experiment.
Resources required to implement it scale polynomically with the number of
qubits of the system. The estimation of all diagonal elements of the
--matrix can be efficiently done without any ancillary qubits. In turn,
the estimation of all the off-diagonal elements requires an extra clean qubit.
The key ideas of the method, that is based on efficient estimation by random
sampling over a set of states forming a 2--design, are described in detail.
Efficient methods for preparing and detecting such states are explicitly shown.Comment: 9 pages, 5 figure
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