Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Groverian Measure of Entanglement for Mixed States   The Groverian entanglement measure introduced earlier for pure quantum states
[O. Biham, M.A. Nielsen and T. Osborne, Phys. Rev. A 65, 062312 (2002)] is
generalized to the case of mixed states, in a way that maintains its
operational interpretation. The Groverian measure of a mixed state of n qubits
is obtained by a purification procedure into a pure state of 2n qubits,
followed by an optimization process based on Uhlmann's theorem, before the
resulting state is fed into Grover's search algorithm. The Groverian measure,
expressed in terms of the maximal success probability of the algorithm,
provides an operational measure of entanglement of both pure and mixed quantum
states of multiple qubits. These results may provide further insight into the
role of entanglement in making quantum algorithms powerful.

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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: math
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th