title: Efficient factorization with a single pure qubit and logN mixed qubits.
abstract: 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 2N qubits in an arbitrary mixed state, is sufficient to implement Shor's factorization algorithm efficiently.
authors.affiliation: Optics Section, The Blackett Laboratory, Imperial College, London SW7 2BW, England.
authors.forename: S
authors.initials: S
authors.lastname: Parker
authors.forename: M B
authors.initials: MB
authors.lastname: Plenio