Optimal fingerprinting strategies with one-sided error University of Calgary | Publication | 2007-01-01 | A. Scott, J. Walgate, B. C. Sanders |

Hypersensitivity and chaos signatures in the quantum baker's maps University of Calgary | Publication | 2006-01-01 | A. Scott, T. A. Brun, C. M. Caves, R. Schack |

Probabilities of failure for quantum error correction University of Calgary | Publication | 2005-01-01 | A. Scott |

Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions University of Calgary | Publication | 2004-05-01 | A. Scott |

Hamiltonian mappings and circle packing phase spaces: numerical investigations University of Calgary | Publication | 2003-01-01 | A. Scott |

Classical and quantum fingerprinting strategiesFingerprinting enables two parties to infer whether the messages they hold are the same or different when the cost of communication is high: each message is associated with a smaller fingerprint and comparisons between messages are made in terms of their fingerprints alone. When the two parties are forbidden access to a public coin, it is known that fingerprints composed of quantum information can be made exponentially smaller than those composed of classical information. We present specific constructions of classical fingerprinting strategies through the use of constant-weight codes and provide bounds on the worst-case error probability with the help of extremal set theory. These classical strategies are easily outperformed by quantum strategies constructed from equiangular tight frames. We also examine the case where access to a public coin is granted. University of Calgary | Presentation | 2005-01-16 | A. Scott |

Bounds on Classical Fingerprinting University of Calgary | Presentation | 2004-09-21 | A. Scott |

Classical and Quantum FingerprintingFingerprinting enables inference of whether two messages are the same
or different: each message is associated with a fingerprint and
comparisons between messages are made in terms of their fingerprints
alone. The number of fingerprints is always assumed less than the
number of messages, leading to savings in the communication and
storage of information. We derive lower bounds for the error
probability when the fingerprints consist of classical information and
the parties preparing the fingerprints have access to a correlated
random source. When the fingerprints consist of quantum information,
however, and the parties preparing the fingerprints share an entangled
resource, we give protocols which achieve the same error probability
with square-root fewer or less fingerprints. University of Calgary | Presentation | 2004-11-05 | A. Scott |

Classical and quantum fingerprinting with shared randomness and one-sided error University of Calgary | Publication | 2005-05-01 | R. T. Horn, A. Scott, J. Walgate, R. Cleve, A. Lvovsky, B. C. Sanders |

Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements University of Calgary | Presentation | 2007-06-18 | A. Roy, A. Scott |

Unitary t-designsIn this talk, we introduce the concept of unitary t-designs. A unitary design is a finite set of unitary matrices that nicely approximates the en-
tire unitary group, much as spherical design approximates the unit sphere. Unitary t-designs were introduced by Dankert, Cleve, Emerson, and Livine in 2006, and in 2007 Scott showed that unitary t-designs serve as optimal choices for quantum process tomography. Using representations of the unitary group, we give a Delsarte-style lower bound on the size of a unitary t-design and some necessary conditions for the bound to be tight. This is Unijoint work with Andrew Scott. University of Calgary | Presentation | 2008-07-08 | A. Roy, A. Scott |

Weighted complex projective 2-designs from basesWe introduce the problem of constructing weighted complex projective 2-designs from the union of a family of orthonormal bases. If the weight remains constant across elements of the same basis, then such designs can be interpreted as generalizations of complete sets of mutually unbiased bases, being equivalent whenever the design is composed of d+1 bases in dimension d. We show that, for the purpose of quantum state determination, these designs specify an optimal collection of orthogonal measurements. Using highly nonlinear functions on abelian groups, we construct explicit examples from d+2 orthonormal bases whenever d+1 is a prime power, covering dimensions d+d=6, 10, and 12, for example, where no complete sets of mutually unbiased bases have thus far been found.
University of Calgary | Presentation | 2007-06-02 | A. Roy, A. Scott |

Symmetric informationally complete quantum measurements University of Calgary | Publication | 2004-01-01 | J. M. Renes, R. Blume-Kohout, A. Scott, C. M. Caves |