Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Beyond the density operator and Tr(\rho A): Exploiting the higher-order
  statistics of random-coefficient pure states for quantum information
  processing   Two types of states are widely used in quantum mechanics, namely
(deterministic-coefficient) pure states and statistical mixtures. A density
operator can be associated with each of them. We here address a third type of
states, that we previously introduced in a more restricted framework. These
states generalize pure ones by replacing each of their deterministic ket
coefficients by a random variable. We therefore call them Random-Coefficient
Pure States, or RCPS. We analyze their properties and their relationships with
both types of usual states. We show that RCPS contain much richer information
than the density operator and mean of observables that we associate with them.
This occurs because the latter operator only exploits the second-order
statistics of the random state coefficients, whereas their higher-order
statistics contain additional information. That information can be accessed in
practice with the multiple-preparation procedure that we propose for RCPS, by
using second-order and higher-order statistics of associated random
probabilities of measurement outcomes. Exploiting these higher-order statistics
opens the way to a very general approach for performing advanced quantum
information processing tasks. We illustrate the relevance of this approach with
a generic example, dealing with the estimation of parameters of a quantum
process and thus related to quantum process tomography. This parameter
estimation is performed in the non-blind (i.e. supervised) or blind (i.e.
unsupervised) mode. We show that this problem cannot be solved by using only
the density operator \rho of an RCPS and the associated mean value Tr(\rho A)
of the operator A that corresponds to the considered physical quantity. We
succeed in solving this problem by exploiting a fourth-order statistical
parameter of state coefficients, in addition to second-order statistics.
Numerical tests validate this result.

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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: math
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph