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Modular variables in quantum information

Abstract : Quantum information can be processed in two fundamentally different ways, using either discrete or continuous variable implementations. Each one of them provides different practical advantages and drawbacks. In this thesis we study theoretical means allowing to implement quantum information protocols originally formulated for discrete quantum systems in physical objects characterized by continuous variables. At the heart of our considerations is the use of modular variables as helpful technique to reveal discrete structure in continuous-variable states, operations and observables. The present work is strongly guided by the experimental applicability of our ideas in quantum optics experiments, with a particular focus on the transverse degrees of freedom of single photons. One of the main themes of this thesis is the formulation of a framework for quantum information processing in phase-space based on the use of modular variables. The term modular variables refers to a specific class of observables that are periodic with respect to some pair of conjugate variables. In our framework we use these periodic observables in order to encode discrete quantum information in Hilbert spaces of infinite dimension. In particular, we consider protocols that involve measurements of judiciously chosen logical observables enabling the readout of the encoded discrete quantum information from the corresponding logical states. Using this framework we show how to perform tests of fundamental properties of quantum mechanics, such as entanglement, Bell nonlocality and contextuality, in Hilbert spaces of various dimensions. Particularly, we generalize known tests of each of these properties, that were originally formulated for measurements with discrete outcomes, to more general measurement contexts comprising the case of bounded continuous outcomes. Concerning experimental implementations of the presented theoretical elaborations we discuss the transverse degrees of freedom of single photons as a natural platform to manipulate and measure modular variables. In particular, we demonstrate how to process discrete quantum information encoded in the spatial distribution of single photons via the optical Talbot effect - a near-field interference effect. Finally, we show how to produce d-dimensional entangled Talbot photon pairs without post-selection, using spontaneous parametric down-conversion and linear optical elements only. As last topic we explore the nonlocal properties of a specific class of hybrid entanglement between particle-like and wave-like optical qubits. Using a hybrid measurement scheme of Pauli and displaced parity measurements we show that, even after including realistic experimental losses, a violation of local-realism is theoretically possible.
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Contributor : Andreas Ketterer <>
Submitted on : Wednesday, April 5, 2017 - 4:35:59 PM
Last modification on : Thursday, April 6, 2017 - 5:04:04 PM
Long-term archiving on: : Thursday, July 6, 2017 - 1:54:01 PM


  • HAL Id : tel-01502539, version 1


Andreas Ketterer. Modular variables in quantum information. Quantum Physics [quant-ph]. Université Paris 7, Sorbonne Paris Cité, 2016. English. ⟨tel-01502539⟩



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