Efficient factorization with a single pure qubit and $log N$ mixed qubits

Physics – Quantum Physics

Scientific paper

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5 pages including 2 figures. Final version submitted to PRL. Now includes additional comments on entanglement and mixedness as

Scientific paper

10.1103/PhysRevLett.85.3049

It is commonly assumed that Shor's quantum algorithm for the efficient
factorization of a large number $N$ requires a pure initial state. Here we
demonstrate that a single pure qubit together with a collection of $log_2 N$
qubits in an arbitrary mixed state is sufficient to implement Shor's
factorization algorithm efficiently.

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