Sophisticated quantum search without entanglement

Details Sophisticated quantum search without entanglement Sophisticated quantum search without entanglement

2000-07-19

arxiv.org/abs/quant-ph/0007070v1

Physics

Quantum Physics

8 pages, plain TeX, 2 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages); for related

Scientific paper

10.1103/PhysRevLett.85.2014

Although entanglement is widely considered to be necessary for quantum algorithms to improve on classical ones, Lloyd has observed recently that Grover's quantum search algorithm can be implemented without entanglement, by replacing multiple particles with a single particle having exponentially many states. We explain that this maneuver removes entanglement from any quantum algorithm. But all physical resources must be accounted for to quantify algorithm complexity, and this scheme typically incurs exponential costs in some other resource(s). In particular, we demonstrate that a recent experimental realization requires exponentially increasing precision. There is, however, a quantum algorithm which searches a `sophisticated' database (not unlike a Web search engine) with a single query, but which we show does not require entanglement even for multiparticle implementations.

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