5,422 research outputs found
An entanglement monotone derived from Grover's algorithm
This paper demonstrates that how well a state performs as an input to
Grover's search algorithm depends critically upon the entanglement present in
that state; the more entanglement, the less well the algorithm performs. More
precisely, suppose we take a pure state input, and prior to running the
algorithm apply local unitary operations to each qubit in order to maximize the
probability P_max that the search algorithm succeeds. We prove that, for pure
states, P_max is an entanglement monotone, in the sense that P_max can never be
decreased by local operations and classical communication.Comment: 7 page
Quantum Cellular Automata
Quantum cellular automata (QCA) are reviewed, including early and more recent
proposals. QCA are a generalization of (classical) cellular automata (CA) and
in particular of reversible CA. The latter are reviewed shortly. An overview is
given over early attempts by various authors to define one-dimensional QCA.
These turned out to have serious shortcomings which are discussed as well.
Various proposals subsequently put forward by a number of authors for a general
definition of one- and higher-dimensional QCA are reviewed and their properties
such as universality and reversibility are discussed.Comment: 12 pages, 3 figures. To appear in the Springer Encyclopedia of
Complexity and Systems Scienc
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