title: Achievable Polarization for Heat-Bath Algorithmic Cooling.
abstract: Pure quantum states play a central role in applications of quantum information, both as initial states for quantum algorithms and as resources for quantum error correction. Preparation of highly pure states that satisfy the threshold for quantum error correction remains a challenge, not only for ensemble implementations like NMR or ESR but also for other technologies. Heat-bath algorithmic cooling is a method to increase the purity of a set of qubits coupled to a bath. We investigated the achievable polarization by analyzing the limit when no more entropy can be extracted from the system. In particular, we give an analytic form for the maximum polarization achievable for the case when the initial state of the qubits is totally mixed, and the corresponding steady state of the whole system. It is, however, possible to reach higher polarization while starting with certain states; thus, our result provides an achievable bound. We also give the number of steps needed to get a specific required polarization.
authors.affiliation: Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.|Department of Physics & Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
authors.forename: Nayeli Azucena
authors.initials: NA
authors.lastname: Rodríguez-Briones
authors.affiliation: Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.|Department of Physics & Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.|Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada.|Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada.
authors.forename: Raymond
authors.initials: R
authors.lastname: Laflamme