The main topic of this thesis revolves around quantum measurement. We illustrate how two different views of quantum objects, the discrete-and continuous-variable views, can be combined to more effectively distinguish between orthogonal states. Such combined measurements are referred to as hybrid. The discrete-variable view is more appropriate to probe energy eigenstates. However, when two or more energy eigenstates are superposed, accurate measurements in the energy eigenbasis require rotations in phase space which are very unwieldy as they require strong nonlinearities and elaborate interactions between light and matter. On the other hand, energy eigenstate superpositions carry a continuous relative phase which is easily probed by continuous-variable interference measurements such as homodyning. The tradeoff between photon counting and homodyning is in practice determined by feasibility studies. This is what we do for two particular applications of quantum measurements: Bell tests and the amplication of Schrödinger cat states. This project also had an experimental component which was supposed to produce high-fidelity Schrödinger cat states. This goal turned out to be hampered by noise from the laser as well as a series of anomalous behavior of the nonlinear crystal whereby no classical de-amplification, and therefore no squeezing, could be observed.
The main topic of this thesis revolves around quantum measurement. We illustrate how two different views of quantum objects, the discrete-and continuous-variable views, can be combined to more effectively distinguish between orthogonal states. Such combined measurements are referred to as hybrid. The discrete-variable view is more appropriate to probe energy eigenstates. However, when two or more energy eigenstates are superposed, accurate measurements in the energy eigenbasis require rotations in phase space which are very unwieldy as they require strong nonlinearities and elaborate interactions between light and matter. On the other hand, energy eigenstate superpositions carry a continuous relative phase which is easily probed by continuous-variable interference measurements such as homodyning. The tradeoff between photon counting and homodyning is in practice determined by feasibility studies. This is what we do for two particular applications of quantum measurements: Bell tests and the amplication of Schrödinger cat states. This project also had an experimental component which was supposed to produce high-fidelity Schrödinger cat states. This goal turned out to be hampered by noise from the laser as well as a series of anomalous behavior of the nonlinear crystal whereby no classical de-amplification, and therefore no squeezing, could be observed.
The implementation of optical quantum technologies requires precise and complete characterisation tools for multi-mode nonclassical states of light. In this thesis, we propose and we implement experimentally three applications of optical quantum measurements, which combine aspects of light that are described by both discrete and continuous variables. In the rst part of this thesis, we present a new scheme for interferometric phase estimation, which uses double homodyne measurements as an alternative to photon counting. We show that, without requiring a phase reference, this scheme can achieve the optimum phase estimation precision for all path-symmetric probe states with a de ned number of photons. Furthermore, the estimation procedure is robust against state preparation imperfections, and naturally yields the same precision for all values of the estimated phase. We implement the proposed scheme experimentally, using a polarisation interferometer probed by a single-photon signal, and temporally multiplexing a single homodyne detector. We repeat the experiment with classical probe states. For both cases, we demonstrate the accuracy and precision of the proposed method, our implementation deviating by 5% from the fundamental precision bound. We demonstrate that, in our scheme, single-photon probe states can provide better precision than weak coherent ones. These results indicate that hybrid quantum resources, which combine tools from the discrete and continuous-variable paradigms, can play a signi cant role in practical sensing scenarios. In the second part of this thesis, we present an application in the eld of information thermodynamics, reporting an experimental realisation, in a photonic setup, of Maxwell's demon. We show that a measurement at the few-photons level, followed by a feed-forward operation, allows the extraction of work from intense thermal light into an electric circuit. The interpretation of the experiment leads us to the derivation of an equality relating work extraction to information acquired by measurement. We prove a bound using this relation, and show that it is in agreement with the experimental results. Our work puts forward photonic systems as a platform for experiments in the eld of information thermodynamics. In the third part of this thesis, we present a new method for the characterisation of broadband parametric down-conversion, based on stimulated frequency generation. In particular, we analyse the information contained in the frequency generation produced in the same mode as a seeding beam, for a type-II down-conversion process. We derive a model for this signal and argue that its detection can provide a useful characterisation tool in the high-gain regime, allowing for a self-referenced estimation of squeezing gain. We propose a method for measuring this signal and present an experimental realisation, based on a wave-guided source, at telecommunication wavelengths. Our experimental results demonstrate that the proposed measurement is an e ective experimental handle for discerning the intricate structure of broadband parametric down-conversion.
The thesis focuses on the experimental investigation of the optical hybrid approach forquantum information processing. Specifically, two traditionally separated approaches, i.e.the discrete and the continuous-variable ones, are combined in the same experiment with twodistinct quantum measurements based on photon counting (photon number) and homodynedetection (quadrature components).The optical hybrid approach is first applied to generate high-fidelity non-Gaussian states,e.g. Fock states and Schrödinger cat states, which correspond to two types of qubit encodingsused in optical quantum information. The use of high-efficiency superconducting nanowiresingle-photon detectors leads to an unprecedented preparation rate, which facilitates thesubsequent use of these states. For instance, the two types of states are combined to generatefor the first time a hybrid entanglement between particle-like and wave-like optical qubits, aswell as the extension to hybrid qutrit entanglement. These novel resources may pave the wayto implement heterogeneous networks where discrete and continuous-variable operations andtechniques can be efficiently combined. Additionally, we also experimentally demonstratefor the first time the so-called squeezing-induced micro-macro entangled states.During this PhD, efforts have also been dedicated to implement a high-efficiency andlow-noise frequency up-conversion system based on two synchronized fiber lasers. Suchquantum frequency converter not only permits to extend the spectra of quantum statesto difficultly accessible wavelengths with current technology, but also constitutes a highperformancephoton detector especially in the infrared regime. Based on the conversionsystem, several applications are demonstrated, such as infrared photon-number-resolvingdetection, and few-photon-level infrared imaging.
In the present PhD work, we focus on a specific class of quantum states of light: the non-Gaussian states. These states have the particularity of exhibiting Wigner functions with some negative values. This quantum feature is a necessary condition to perform some quantum computation task; furthermore it is also useful for various other applications, including quantum communication and metrology. Different strategies can be used to generate these states. Here, we start from Gaussian states produced by optical parametric oscillators in the continuous wave regime, (i.e. single-mode and two-mode squeezed vacuum states). The non-Gaussian feature can only be obtained by non-linear phenomena (over-quadratic Hamiltonian). In our case, the non-linearity is induced by photon-counting-based measurements (also called non-Gaussian measurements). This study is mainly divided into two parts. First, the generation of non-classical states associated with two types of qubit encoding: the single-photon state, used for quantum information with discrete variables, and the coherent state superposition (the so-called optical Schrodinger cat state), used for quantum information with continuous variables. These two states have then been used to perform some quantum information protocols. The first one addresses the problem of single-photon entanglement witness, and the other the generation of entanglement between the two encodings (also called hybrid entanglement).
In optical quantum information, one can distinguish two approaches: the discrete-variable (DV), involving single photons, for example c0|0〉 + c1|1〉, and the continuous-variable alternative (CV) encoding information into the quadrature components of the light field. In this CV approach, qubits can be implemented as superposition of coherent states of opposite phases, |cat ±〉 = |α〉 ± |−α〉, also called optical Schrodinger cat states. Combining these two approaches has recently led to a so-called optical hybrid quantum information aiming at merging the properties of both [1]. As both encodings have their own advantages and drawbacks, transferring information between them is a requirement which can be fulfill by teleportation using hybrid entanglement between particle-like qubits and wave-like qubits, i.e. entanglement of the form |0〉|α〉 + |1〉|−α〉.
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.
In the present PhD work, we focus on a specific class of quantum states of light: the non-Gaussian states. These states have the particularity of exhibiting Wigner functions with some negative values. This quantum feature is a necessary condition to perform some quantum computation task; furthermore it is also useful for various other applications, including quantum communication and metrology. Different strategies can be used to generate these states. Here, we start from Gaussian states produced by optical parametric oscillators in the continuous wave regime, (i.e. single-mode and two-mode squeezed vacuum states). The non-Gaussian feature can only be obtained by non-linear phenomena (over-quadratic Hamiltonian). In our case, the non-linearity is induced by photon-counting-based measurements (also called non-Gaussian measurements). This study is mainly divided into two parts. First, the generation of non-classical states associated with two types of qubit encoding: the single-photon state, used for quantum information with discrete variables, and the coherent state superposition (the so-called optical Schrödinger cat state), used for quantum information with continuous variables. These two states have then been used to perform some quantum information protocols. The first one addresses the problem of single-photon entanglement witness, and the other the generation of entanglement between the two encodings (also called hybrid entanglement).