Random Bipartite Entanglement from W and W -Like States University of Calgary | Publication | 2007-06-01 | B. Fortescue, H. Lo |

Inefficiency and classical communication bounds for conversion between partially entangled pure bipartite states University of Calgary | Publication | 2005-09-01 | B. Fortescue, H. Lo |

Random-party entanglement distillation in multiparty states University of Calgary | Publication | 2008-07-01 | B. Fortescue, H. Lo |

Reducing the Quantum Communication Cost of Quantum Secret Sharing University of Calgary, University of California, San Diego | Publication | 2012-10-01 | B. Fortescue, G. Gour |

Graph states and ramp schemes for quantum secret sharingI will discuss our recent work in developing new protocols for quantum secret sharing (QSS), a cryptographic scheme in which an encoded quantum "secret" is divided between several "players" such that only certain subsets of players may recover it. We have found a class of protocols based on graph states which allow for efficient (i.e. player states of the same dimension as the secret) QSS for states of prime dimension. We have also found examples of "ramp" schemes for QSS, in which the efficiency can be improved by sacrificing some security. I will discuss these and the use of shared entanglement as a measure of the players' information about the secret.
University of Calgary | Presentation | 2011-02-24 | B. Fortescue, A. Keet, D. Markham, G. Gour, B. C. Sanders |

Going beyond the share size bound in quantum secret sharingQuantum secret sharing (QSS) is an important cryptographic protocol which allows a quantum secret to be split between multiple "players", such that only certain authorised player subsets may recover the secret. It is, however, costly in terms of quantum communication and storage; perfect QSS using quantum states requires every player's share to be at least as large as the original secret.
I will discuss some of our recent results in which we improve upon this bound through the use of imperfect "ramp" secret sharing, which allows for smaller shares at the cost of weaker security. We find a specific class of "entanglement sharing" ramp protocols, which allow for smaller shares while still broadly restricting the protocols' information leakage.
Finally I will demonstrate how, by incorporating classical encryption into "hybrid" QSS protocols, quantum share size can be reduced (sometimes
drastically) without requiring any reduction in security.
University of Calgary | Presentation | 2011-06-28 | B. Fortescue, G. Gour, B. C. Sanders |

Random distillation of multiparty states University of Calgary | Presentation | 2007-08-30 | B. Fortescue, H. Lo |

Quantum secret sharing with qudit graph statesWe present a formalism for quantum secret sharing using graph states of systems with prime dimension. As we show, such states allow for a unified structure for the sharing of classical and quantum secrets over both classical and quantum channels. We give explicit protocols for three varieties of threshold secret sharing within this formalism. Joint work with Adrian Keet and Barry C. Sanders. University of Calgary | Presentation | 2010-02-20 | B. Fortescue, A. Keet, B. C. Sanders, D. Markham |

Threshold quantum secret sharing using graph states of prime-dimensional systemsSecret sharing schemes allow a classical or quantum secret to be divided among many parties such that it can be recovered only by some specified set of parties collaborating in order to do so. It is known that arbitrary secret sharing schemes may be constructed by concatenating threshold schemes, in which the secret can be recovered by any sufficiently large number of parties, and the remainder are denied any knowledge of the secret
I will discuss a formalism within which, using entangled graph states of prime-dimensional systems, a variety of different threshold secret sharing schemes (involving both quantum and classical secrets and quantum and classical channels shared between parties) may be unified. I will give explicit protocols for three varieties of secret sharing within this formalism, including some for which the analogous formalism using graph states of two-dimensional systems is not sufficient. University of Calgary | Presentation | 2010-07-19 | B. Fortescue, A. Keet, D. Markham, B. C. Sanders |

Secret sharing with higher-dimensional graph states University of Calgary | Presentation | 2010-08-26 | B. Fortescue, A. Keet, D. Markham, B. C. Sanders |

New directions in quantum secret sharing University of Calgary | Presentation | 2010-11-19 | B. Fortescue, A. Keet, D. Markham, G. Gour, B. C. Sanders |

Entanglement Sharing SchemeEntanglement is a necessary resource for quantum information tasks such as teleportation, dense coding, and Ekert QKD scheme. In entanglement sharing scheme, one share of a bipartite entangled pair is encoded and distributed to untrusted players in a way that they must collaborate in groups to unlock the entanglement. I show how to use quantum error correcting codes to share maximally entangled states between a dealer and collaborating groups of players by exploiting quantum secret sharing concepts and techniques.
University of Calgary | Presentation | 2012-02-09 | H. R. Choi, B. Fortescue, G. Gour, B. C. Sanders |

Quantifying the resourcefulness of quantum reference frames University of Calgary | Presentation | 2010-05-26 | Y. Sanders, B. Fortescue, G. Gour |

Entanglement sharing schemes via quantum error-correcting codes University of Calgary | Presentation | 2011-06-17 | H. R. Choi, B. Fortescue, G. Gour, B. C. Sanders |

Entanglement sharing protocolsEntanglement sharing schemes are important as a tool for secure quantum communication in a
network where some subsets of players are authorized to access the transmitted quantum information and other subsets must be denied any quantum information. We conjecture that every stabilizer error correcting code is an entanglement sharing scheme. We test this conjecture with known codes including Shor's 9-qubit code, Steane's 7-qubit code and the 5-qubit code. If our conjecture is true, then we can use existing stabilizer error correcting codes as candidates for entanglement sharing rather than having to construct entanglement sharing schemes ab initio. University of Calgary | Presentation | 2011-11-04 | H. R. Choi, B. Fortescue, G. Gour, B. C. Sanders |