Vector coherent state theory of the generic representations of so(5) in an so(3) basis University of Calgary | Publication | 2006-01-01 | P. Turner, D. J. Rowe, J. Repka |

Phase transitions and quasidynamical symmetry in nuclear collective models. II. The spherical vibrator to gamma-soft rotor transition in an SO(5)-invariant Bohr model University of Calgary | Publication | 2005-07-01 | P. Turner, D. J. Rowe |

Vector coherent state theory of the generic representations of [fraktur so](5) in an [fraktur so](3) basis University of Calgary | Publication | 2006-01-01 | P. Turner, D. J. Rowe, J. Repka |

Phase transitions and quasidynamical symmetry in nuclear collective models: II. The spherical vibrator to gamma soft rotor phase transition in an SO(5)-invariant Bohr model University of Calgary | Publication | 2005-01-01 | P. Turner, D. J. Rowe |

Degradation of a quantum reference frame University of Calgary | Presentation | 2006-02-17 | P. Turner |

Hidden degrees of freedom and distinguishability University of Calgary | Presentation | 2007-03-29 | P. Turner |

The problem of quantum gravity University of Calgary | Presentation | 2005-10-27 | P. Turner |

State estimation and quantum reference frames University of Calgary | Presentation | 2005-08-31 | P. Turner |

Multimode squeezing in quantum networks University of Calgary | Presentation | 2007-04-01 | P. Turner |

The algebraic collective model University of Calgary | Publication | 2005-05-01 | D. J. Rowe, P. Turner |

SU(1,1) symmetry of multimode squeezed states University of Calgary | Publication | 2008-01-01 | Z. Shaterzadeh-Yazdi, P. Turner, B. C. Sanders |

Detecting hidden differences via permutation symmetries University of Calgary | Publication | 2008-09-01 | R. B. Adamson, P. Turner, M. W. Mitchell, A. M. Steinberg |

Spherical harmonics and basic coupling coefficients for the group SO(5) in an SO(3) basis University of Calgary | Publication | 2004-01-01 | D. J. Rowe, P. Turner, J. Repka |

Three-mode squeezing: SU(1,1) symmetry University of Calgary | Publication | 2007-01-01 | Z. Shaterzadeh-Yazdi, P. Turner, B. C. Sanders |

A three boson su(1,1) realisation for linear optical quantum information University of Calgary | Presentation | 2006-07-25 | Z. Shaterzadeh-Yazdi, P. Turner, B. C. Sanders |

A new approach to mutlipartite squeezed statesAn efficient technique to characterize complex linear quantum optical networks comprised by passive and active optical devices is the use of the symplectic Lie group, Sp(2n, R). Such optical networks play a significant role in the context of quantum information processing, and have been used in a variety of quantum schemes such as quantum teleportation [1] and quantum state/secret sharing [2]. In general, the operation of a multiport network of this type on a Gaussian input state can be described by Sp(2n, R) transformations, which preserve Gaussian states. The key tool in such quantum optical experiments is the generation and application of squeezed states. Recently, three-mode squeezed states have been produced in several quantum schemes. For characterizing such schemes, we have established a three-mode realization of SU(1, 1), which is a subgroup of Sp(6, R), and consequently the three-mode squeezed states are the coherent states of SU(1, 1). The elegance of this approach helps us to generalize it to multi-mode realizations of SU(1, 1), and to use them for characterizing any multiport quantum optical network constructed by concatenating sections, each with one two-mode squeezer and several passive optical devices. Such realizations give us a new insight into the interesting properties of the multimode squeezed states generated by any complex quantum optical network of this type. References: [1] N. Takei et al., Phys. Rev. A, 72, 042304 (2005). [2] A.M. Lance et al, Phys. Rev. A, 92, 177903 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This work is being supported by iCORE University of Calgary | Presentation | 2007-06-19 | Z. Shaterzadeh-Yazdi, P. Turner, B. C. Sanders |

Multi-partite squeezed states and SU(1,1) symmetryOne goal of quantum information science is quantum information processing using complex quantum optical networks comprising passive and active linear optical elements, such as beam splitters and squeezers. Such networks can be described mathematically as Sp(2n, R) transformations on n modes, which correspond to mappings that preserve Gaussian states.
Recently, tripartite squeezed states have been produced experimentally and are quite useful for quantum information tasks such as quantum state sharing and quantum teleportation. Theoretically, such states have been characterized based on the type of input states, but we have developed a simple and elegant mathematical framework, which is three-boson realization of SU(1, 1), and characterized all squeezed states of this type as SU(1, 1) coherent states. Inspired by the elegance of this theory, we have generalized it to multiboson realization of SU(1, 1) that characterizes any multi-port linear optical system constructed from a two-mode squeezer and several passive optical elements, or by concatenating such multi-port systems to each other. Thus, this theory gives us new insight into the properties of a large class of multipartite squeezed states generated in any complex optical network with concatenated sections each with one two-mode squeezer.
University of Calgary | Presentation | 2007-09-09 | Z. Shaterzadeh-Yazdi, P. Turner, B. C. Sanders |

Unambiguous discrimination of mixed states University of Calgary | Publication | 2003-01-01 | T. Rudolph, R. W. Spekkens, P. Turner |

Multi-partite entangled Gaussian states and su (1,1) symmetry University of Calgary | Presentation | 2007-05-23 | B. C. Sanders, Z. Shaterzadeh-Yazdi, P. Turner |

The su(1,1) symmetry of tripartite entangled Gaussian statesTwo-mode squeezed light has been central to theoretical and experimental studies of continuous variable quantum information processing and to quantum foundations. More recently the generalization of these states to three-mode squeezed light has been achieved in the context of quantum teleportation [1] and state sharing [2]. Theories are typically developed in Gaussian or position representations, but we have discovered that all tripartite entangled Gaussians states of these types are in fact su(1,1) coherent states with respect to an intriguing three-boson realization of su(1,1) first noticed by Sebawe Abdalla et al [3]. This symmetry provides insights into the useful properties of these states and suggests ways to generalize theories and applications of multipartite entangled Gaussian states. [1] A. Furusawa et al, Science \textbf{282}, 706 (1998). [2] A. M. Lance et al, Phys. Rev. Lett. \textbf{92}, 177903 (2004). [3] M. Sebawe Abdalla et al, Eur. Phys. J. D \textbf{13}, 423 (2001).
University of Calgary | Presentation | 2007-03-08 | B. C. Sanders, Z. Shaterzadeh-Yazdi, P. Turner |

Degradation of a quantum directional reference frame as a random walk University of Calgary | Publication | 2007-01-01 | S. D. Bartlett, T. Rudolph, B. C. Sanders, P. Turner |

Resource theories, SU(2) super selection rule, and time inversion University of Calgary | Presentation | 2008-08-24 | G. Gour, W. R. Spekkens, B. C. Sanders, P. Turner |