Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: `Lazy' quantum ensembles   We compare different strategies aimed to prepare an ensemble with a given
density matrix $\rho$. Preparing the ensemble of eigenstates of $\rho$ with
appropriate probabilities can be treated as `generous' strategy: it provides
maximal accessible information about the state. Another extremity is the
so-called `Scrooge' ensemble, which is mostly stingy to share the information.
We introduce `lazy' ensembles which require minimal efforts to prepare the
density matrix by selecting pure states with respect to completely random
choice.
  We consider two parties, Alice and Bob, playing a kind of game. Bob wishes to
guess which pure state is prepared by Alice. His null hypothesis, based on the
lack of any information about Alice's intention, is that Alice prepares any
pure state with equal probability. Then, the average quantum state measured by
Bob turns out to be $\rho$, and he has to make a new hypothesis about Alice's
intention solely based on the information that the observed density matrix is
$\rho$. The arising `lazy' ensemble is shown to be the alternative hypothesis
which minimizes the Type I error.

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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: nlin
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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: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg