51,596 research outputs found
Controlled Sensing for Multihypothesis Testing
The problem of multiple hypothesis testing with observation control is
considered in both fixed sample size and sequential settings. In the fixed
sample size setting, for binary hypothesis testing, the optimal exponent for
the maximal error probability corresponds to the maximum Chernoff information
over the choice of controls, and a pure stationary open-loop control policy is
asymptotically optimal within the larger class of all causal control policies.
For multihypothesis testing in the fixed sample size setting, lower and upper
bounds on the optimal error exponent are derived. It is also shown through an
example with three hypotheses that the optimal causal control policy can be
strictly better than the optimal open-loop control policy. In the sequential
setting, a test based on earlier work by Chernoff for binary hypothesis
testing, is shown to be first-order asymptotically optimal for multihypothesis
testing in a strong sense, using the notion of decision making risk in place of
the overall probability of error. Another test is also designed to meet hard
risk constrains while retaining asymptotic optimality. The role of past
information and randomization in designing optimal control policies is
discussed.Comment: To appear in the Transactions on Automatic Contro
Flexible resources for quantum metrology
Quantum metrology offers a quadratic advantage over classical approaches to
parameter estimation problems by utilizing entanglement and nonclassicality.
However, the hurdle of actually implementing the necessary quantum probe states
and measurements, which vary drastically for different metrological scenarios,
is usually not taken into account. We show that for a wide range of tasks in
metrology, 2D cluster states (a particular family of states useful for
measurement-based quantum computation) can serve as flexible resources that
allow one to efficiently prepare any required state for sensing, and perform
appropriate (entangled) measurements using only single qubit operations.
Crucially, the overhead in the number of qubits is less than quadratic, thus
preserving the quantum scaling advantage. This is ensured by using a
compression to a logarithmically sized space that contains all relevant
information for sensing. We specifically demonstrate how our method can be used
to obtain optimal scaling for phase and frequency estimation in local
estimation problems, as well as for the Bayesian equivalents with Gaussian
priors of varying widths. Furthermore, we show that in the paradigmatic case of
local phase estimation 1D cluster states are sufficient for optimal state
preparation and measurement.Comment: 9+18 pages, many figure
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