Quantum Computing Without Entanglement
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It is generally believed that entanglement is essential for quantum computing. We present here a few simple examples in which quantum computing without entanglement is better than anything classically achievable, in terms of the reliability of the outcome after a xed number of oracle calls. Using a separable (that is, unentangled) n-qubit state, we show that the Deutsch-Jozsa problem and the Simon problem can be solved more reliably by a quantum computer than by the best possible classical algorithm, even probabilistic. We conclude that: (a) entanglement is not essential for quantum computing; and (b) some advantage of quantum algorithms over classical algorithms persists even when the quantum state contains an arbitrarily small amount of information|that is, even when the state is arbitrarily close to being totally mixed.
18 pages. Presented at FoCM'02 (Aug 2002, see http://www.cs.technion.ac.il/~danken/pub/QCnoEnt.pdf), QIP'03 (Dec 2002, see http://www.msri.org/publications/ln/msri/2002/qip/brassard/1/), Qubit'03 (Apr 2003, see http://www.cs.technion.ac.il/~talmo/Qubitconf/QUBIT-2003/program/)
18 pages. Presented at FoCM'02 (Aug 2002, see http://www.cs.technion.ac.il/~danken/pub/QCnoEnt.pdf), QIP'03 (Dec 2002, see http://www.msri.org/publications/ln/msri/2002/qip/brassard/1/), Qubit'03 (Apr 2003, see http://www.cs.technion.ac.il/~talmo/Qubitconf/QUBIT-2003/program/)