Continuous-variable (CV) qubits can be created on an optical longitudinal mode in which quantum information is encoded by the superposition of even and odd Schroedinger's cat states with quadrature amplitude. Based on the analogous features of paraxial optics and quantum mechanics, we propose a system to generate and detect CV qubits on an optical transverse mode. As a proof-of-principle experiment, we generate six CV qubit states and observe their probability distributions in position and momentum space. This enabled us to prepare a non-Gaussian initial state for CV quantum computing. Other potential applications of the CV qubit include adiabatic control of a beam profile, phase shift keying on transverse modes, and quantum cryptography using CV qubit states.
Continuous-variable (CV) qubits can be created on an optical longitudinal mode in which quantum information is encoded by the superposition of even and odd Schroedinger's cat states with quadrature amplitude. Based on the analogous features of paraxial optics and quantum mechanics, we propose a system to generate and detect CV qubits on an optical transverse mode. As a proof-of-principle experiment, we generate six CV qubit states and observe their probability distributions in position and momentum space. This enabled us to prepare a non-Gaussian initial state for CV quantum computing. Other potential applications of the CV qubit include adiabatic control of a beam profile, phase shift keying on transverse modes, and quantum cryptography using CV qubit states.
Continuous-variables (CV) quantum optics is a natural formalism for neural networks (NNs) due to its ability to reproduce the information processing of such trainable interconnected systems. In quantum optics, Gaussian operators induce affine mappings on the quadratures of optical modes while non-Gaussian resources (the challenging piece for physical implementation) originate the nonlinear effects, unlocking quantum analogs of an artificial neuron. This work presents a novel experimentally-feasible framework for continuous-variable quantum optical neural networks (QONNs) developed with available photonic components: coherent states as input encoding, a general Gaussian transformation followed by multi-mode photon subtractions as the processing layer, and homodyne detection as outputs readout. The closed-form expressions of such architecture are derived demonstrating the family of adaptive activations and the quantum-optical neurons that emerge from the amount of photon-subtracted modes, proving that the proposed design satisfies the Universal Approximation Theorem within a single layer. To classically simulate the QONN training, the high-performance QuaNNTO library has been developed based on Wick-Isserlis expansion and Bogoliubov transformations, allowing multi-layer exact expectation values of non-Gaussian states without truncating the infinite-dimensional Hilbert space. Experiments on supervised learning and state-preparation tasks show balanced-resource efficiency with strong expressivity and generalization capabilities, illustrating the potential of the architecture for scalable photonic quantum machine learning and for quantum applications such as complex non-Gaussian gate synthesis.
This thesis deals with the study of quantum communication protocols with Continuous Variable (CV) systems. Continuous Variable systems are those described by canonical conjugated coordinates x and p endowed with infinite dimensional Hilbert spaces, thus involving a complex mathematical structure. A special class of CV states, are the so-called Gaussian states. With them, it has been possible to implement certain quantum tasks as quantum teleportation, quantum cryptography and quantum computation with fantastic experimental success. The importance of Gaussian states is two-fold; firstly, its structural mathematical description makes them much more amenable than any other CV system. Secondly, its production, manipulation and detection with current optical technology can be done with a very high degree of accuracy and control. Nevertheless, it is known that in spite of their exceptional role within the space of all Continuous Variable states, in fact, Gaussian states are not always the best candidates to perform quantum information tasks. Thus non-Gaussian states emerge as potentially good candidates for communication and computation purposes.
Quantum optics is central to emerging quantum technologies such as quantum metrology and quantum information. The continuous variable (CV) approach to encoding information in a physical system, for example the electromagnetic field quadratures has significant advantages over discrete variables (DV) encoding. CV offers higher density encoding in a single optical state and on-demand state preparation for example. However, techniques for CV preparation, manipulation and measurement are not as well developed as the corresponding DV approach. In this thesis we present methods to characterize quantum detectors that operate in the CV regime, and discuss their application to CV state preparation. A quantum detector is described by its positive operator valued measure (POVM) set, with one operator for each measurement outcome. We present an experimental scheme for detector tomography, that is reconstruction of the POVM set of an unknown detector by means of measurement outcomes for a set of tomographically complete input states. We use this scheme to experimentally determine the POVM set of an avalanche photodiode (APD) and a time-multiplexed-detector (TMD) and compare the results to models of the detectors. We introduce a weak-homodyne photon-number-resolving detector (PNRD) , which uses a weak local oscillator beam to set a phase reference for the detection process. We develop a theoretical description of the sensitivity regimes for this detector using the Wigner phase space picture. We also present experimental detector tomography for a weak-homodyne detector based on two APDs. In many cases it is sufficient to calibrate the efficiencies of previously characterized PNRDs. We experimentally demonstrate a scheme using correlated photons produced by spontaneous parametric downconversion (SPDC) to determine the efficiencies of PNRDs, based on the photon number statistics of the source. The same SPDC source is also used to demonstrate preparation of photonic states in the photon number basis and for a first proof-of-principle experiment with a weak-homodyne PNRD based on a TMD.
Observables of quantum systems can posses either a discrete or a continuous spectrum. For example, upon measurements of the photon number of a light state, discrete outcomes will result whereas measurements of the light's quadrature amplitudes result in continuous outcomes. If one uses the continuous degree of freedom of a quantum system either for encoding, processing or detecting information, one enters the field of continuous variable (CV) quantum information processing. In this paper we review the basic principles of CV quantum information processing with main focus on recent developments in the field. We will be addressing the three main stages of a quantum informational system; the preparation stage where quantum information is encoded into CVs of coherent states and single photon states, the processing stage where CV information is manipulated to carry out a specified protocol and a detection stage where CV information is measured using homodyne detection or photon counting.
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〉.
In this article we develop a continuous variable (CV) shadow tomography scheme with wide ranging applications in quantum optics. Our work is motivated by the increasing experimental and technological relevance of CV systems in quantum information, quantum communication, quantum sensing, quantum simulations, quantum computing and error correction. We introduce two experimentally realisable schemes for obtaining classical shadows of CV (possibly non-Gaussian) quantum states using only randomised Gaussian unitaries and easily implementable Gaussian measurements such as homodyne and heterodyne detection. For both schemes, we show thatN=O(poly (1 /ϵ, log (1/δ),Mr+αn, log(m) )) samples of an unknownm-mode state ρ suffice to learn the expected value of anyr-local polynomial in the canonical observables of degree α, both with high probability 1 - δ and accuracy ϵ, as long as the state ρ has moments of ordern> α bounded byMn. By simultaneously truncating states and operators in energy and phase space, we are able to overcome new mathematical challenges that arise due to the infinite-dimensionality of CV systems. We also provide a scheme to learn nonlinear functionals of the state, such as entropies over any small number of modes, by leveraging recent energy-constrained entropic continuity bounds. Finally, we provide numerical evidence of the efficiency of our protocols in the case of CV states of relevance in quantum information theory, including ground states of quadratic Hamiltonians of many-body systems and cat qubit states. We expect our scheme to provide good recovery in learning relevant states of 2D materials and photonic crystals.