New Frontiers in Continuous-Variable Quantum Systems

Takaya Matsuura

X-F Qian, Curtis J. Broadbent, Joseph H. Eberly

We describe a new Bell test for two-particle entangled systems that engages an unbounded continuous variable. The continuous variable state is allowed to be arbitrary and inaccessible to direct measurements. A systematic method is introduced to perform the required measurements indirectly. Our results provide new perspectives on both the study of local realistic theory for continuous-variable systems and on the non-local control theory of quantum information.

Takaya Matsuura

Tonipe Anuradha, Amit Rai

Abstract Integrated optical systems have evolved into suitable platforms in the field of photonic quantum technologies. New technologies open up new possibilities for multimode quantum operations. Here we study how circularly coupled waveguide arrays generate bipartite and tripartite continuous-variable (CV) entanglement. We focus on the single-mode squeezed state as input to the circular array of the waveguide system. Our findings suggest that the circularly coupled arrays can be used to generate entangled sources in CV quantum technologies. So the generation of entanglement makes the circular arrays more critical for further investigation and in the applications of photonic CV quantum-information processing.

Darran F. Milne

In this thesis we explore the possibility of creating continuousvariable \nquantum systems that are capable of supporting universal \nquantum computation. We begin by examining the measurement-based \nmodel, which employs sequences of measurements on highly entangled \nresource states, known as a cluster states. We suggest a method for \nthe construction of Gaussian cluster states based on ensembles of atoms \nand quantum non-demolition interactions. We then go on to expand \nour model to allow for the inclusion of light modes as part of the cluster. \nThis yields a new class of states, the composite cluster states. \nThis leads us to propose a new architecture for the measurement-based \nmodel that uses these composite clusters to increase resource e ciency \nand reduce computational errors. \nThe second part of this thesis concerns topological quantum computation. \nIn states exhibiting topological degrees of freedom, quantum \ninformation can be stored as a non-local property of the physical system \nand manipulated by braiding quasiparticles known as anyons. Here \nwe show how these ideas can be extended to continuous variables. We \nestablish a continuous variable analogue of the Kitaev toric code, show \nthat excitations correspond to continuous versions of Abelian anyons \nand investigate their behaviour under the condition of nite squeezing \nof the resource state. \nFinally, we expand our continuous variable topological model to \ninclude non-abelian excitations by constructing superpositions of CV \ntoric code anyons. We derive the fusion and braiding behaviour of \nthese non-abelian excitations and nd that they correspond to a CV \nanalog of Ising anyons. Using these resources, we go on to suggest \na computational scheme that encodes qubits within the fusion spaces \nof the CV Ising anyons and derive one- and two-qubit quantum gates \noperations that are implemented in a topological manner.

Ola Bratteli, Derek W. Robinson