This paper theoretically demonstrates a compact method for the production of cluster states, based on recent experiments with multimode cavities, by using a so-called multi-pixel homodyne detection (MPHD) system and classical post-processing. This effectively allows to incorporate the linear optic network in the stage of the measurement. The physical transformations which the modes undergo due to the measurement (i.e., propagation from the cavity to the multipixel homodyne detector and multipixel homodyne detection) can be modeled by symplectic matrices, acting on the vector which regroups the annihilation operators associated to the various input squeezed mode. The method proposed can mimic the action of a desired matrix Uthif there exists a suitable combination of the experimental parameters such that UMPHD= Uth. It is therefore important to characterize from a theoretical point of view the class of unitary operations which are experimentally implementable by the use of this method. A condition which allows to test the implementability of a given unitary matrix Uth, and to find the experimental parameters to use in order to emulate it is determined. Some examples of cluster state generation by this method are presented. Finally, how this procedure can be generalized to perform Gaussian quantum computation is further analyzed. In particular, the possibility of implementing the elementary operations which compose a Gaussian universal set, including the Fourier transform of a single-mode input state and a two-mode CZinteraction, is studied.
This paper theoretically demonstrates a compact method for the production of cluster states, based on recent experiments with multimode cavities, by using a so-called multi-pixel homodyne detection (MPHD) system and classical post-processing. This effectively allows to incorporate the linear optic network in the stage of the measurement. The physical transformations which the modes undergo due to the measurement (i.e., propagation from the cavity to the multipixel homodyne detector and multipixel homodyne detection) can be modeled by symplectic matrices, acting on the vector which regroups the annihilation operators associated to the various input squeezed mode. The method proposed can mimic the action of a desired matrix Uthif there exists a suitable combination of the experimental parameters such that UMPHD= Uth. It is therefore important to characterize from a theoretical point of view the class of unitary operations which are experimentally implementable by the use of this method. A condition which allows to test the implementability of a given unitary matrix Uth, and to find the experimental parameters to use in order to emulate it is determined. Some examples of cluster state generation by this method are presented. Finally, how this procedure can be generalized to perform Gaussian quantum computation is further analyzed. In particular, the possibility of implementing the elementary operations which compose a Gaussian universal set, including the Fourier transform of a single-mode input state and a two-mode CZinteraction, is studied.
We study the possibility of producing and detecting continuous variable cluster states in an extremely compact optical setup. This method is based on a multi-pixel homodyne detection system recently demonstrated experimentally, which includes classical data post-processing. It allows the incorporation of the linear optics network, usually employed in standard experiments for the production of cluster states, in the stage of the measurement. After giving an example of cluster state generation by this method, we further study how this procedure can be generalized to perform Gaussian quantum computation.
We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multimode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations.
Multimode Gaussian states are a versatile resource for quantum information technologies and have been realized across a wide range of physical platforms. Recent progress in the large-scale generation of such states provides a key ingredient for scalable quantum technologies. Despite the importance of accurately characterizing these states, conventional tomography methods are often impractical because they require large sample sizes and can yield unphysical states. Here we present a reliable and efficient tomography method for multimode Gaussian states based on maximum-likelihood estimation. By directly operating on covariance matrices, the method avoids the exponential overhead associated with density-matrix reconstruction. We consider two commonly used detection schemes--single and joint homodyne detection--and systematically analyze the reconstruction performance. Our method outperforms conventional approaches by ensuring physical covariance matrices and achieving better agreement with the true states. To demonstrate the experimental applicability of the method, we experimentally generate various multipartite entangled states--six-mode graph states with different connectivity, a six-mode GHZ state, and a fully connected ten-mode graph state--and reconstruct their covariance matrices. Using the reconstructed covariance matrices, we quantify fidelities, detect entanglement, and reveal the multimode structure of squeezing and noise. Our technique offers a practical diagnostic tool for developing scalable quantum technologies.
ABSTRACT Measurement‐based quantum computing relies on the preparation of large‐scale multipartite entanglement, typically realized through cluster states. Quantum frequency combs provide a naturally multimode platform for constructing such states, yet prior pulse‐shaping methods are inherently sequential, thereby hindering scalability and making the reconstructed state vulnerable to system drifts. Here, we address this limitation by developing a multipixel homodyne detection scheme that enables the parallel characterization of quantum noise across multiple frequency modes and the single‐step reconstruction of the full covariance matrix, ensuring high measurement stability independent of long‐term system drifts. In an eight‐mode quantum frequency comb system, we experimentally determine sixteen entangled bipartitions (out of 127 possible bipartitions) and extract three squeezed supermodes via eigenmode decomposition of the covariance matrix. Through constructing linear optical networks in classical post‐processing, these resources enable the deterministic construction of cluster states ranging from one‐dimensional chains based on supermodes to three‐dimensional topological graphs formed by bipartite entangled pairs. The synergy between the parallel measurement capability of multipixel homodyne detection and the scalability of quantum frequency combs provides a compact and versatile platform for large‐scale, reconfigurable quantum information processing.
We present in this thesis a study of the spatial properties of light at the quantum level. More specifically, we focus on techniques to manipulate the quantum fluctuations of different degrees of freedom in a beam's transverse plane, and on the quantum protocols we can implement using these specific fluctuations. We begin by providing an experimental characterization of different methods to manipulate the quantum fluctuations of multiple transverse profiles, or modes, in one beam. While manipulating the quantum fluctuations of a mode, a process known as squeezing, for a single mode beam can be performed very efficiently using a conventional optical parametric oscillator, we present implementations of different, less conventional techniques able to generate a beam carrying multiple squeezed modes. Conventionally, the squeezed modes we can generate using these techniques are fixed by the optical design. We present a new optical system, called a Unitary Programmable Mode Converter (UPMC), able to reshape these modes at will. We show theoretically that such a UPMC can in principle perform any desired reshaping of the modes. We present the performances of an experimental implementation of the UPMC, both in a classical and quantum context. We find that the UPMC performs as predicted, and we present a method to optimize the UPMC settings taking into account experimental restrictions. The UPMC, combined with a technique to build a beam carrying multiple squeezed modes, allows us to generate a beam with squeezing in any desired set of spatial modes. In order to detect these fluctuations, we built a multipixel homodyne detection, a detection system able to record simultaneously the quantum fluctuations in all these modes. We provide in this thesis our solutions to overcome the electronic challenges associated with such a device, and present an experimental characterization of the performances of our multipixel homodyne detection. Finally, we combine these experimental characterizations to discuss how these techniques help us implement different quantum protocols involving multiple spatial modes, more specifically quantum enhanced detections and cluster states quantum computation.
Continuous-variable quantum networks constitute a valuable resource for a wide range of quantum communication and information protocols. While frequency- and fast time-multiplexing enable the implementation of scalable quantum architectures, a precise characterization of multimode squeezed-light sources is essential. In this work, we increase both the spectral resolution and the measured squeezing values. Both parameters are relevant for the improved generation of so-called cluster states, a key resource for measurement-based quantum computing. Our source is based on parametric down-conversion in a periodically poled KTP waveguide pumped by a pulsed laser. The source produces squeezed states over a specific set of optical spectra. Increased spectral resolution in spectrally resolved homodyne detection allowed us to enhance the squeezing per spectral mode, increasing it from 1 dB to more than 2.4 dB in the first mode when measuring with a homodyne detector with a bandwidth of a few MHz. Secondly, we implemented a pulse-by-pulse characterization of the resource using a fast homodyne detector with an electronic bandwidth on the order of the laser repetition rate (100 MHz). Using this approach, the fast measurements revealed squeezing values of up to 1.5 dB in the first few spectral modes. To fully access the multimode quantum resource and ultimately improve the amount of squeezing, a high quantum efficiency is required. To avoid limitations imposed by poor spatial mode matching between the quantum resource and the local oscillator in homodyne detection, we implemented a wavefront-shaping scheme to characterize and control both the intensity profile and phase of the local oscillator. In preliminary tests this approach increased the mode-matching between the reference beam and the quantum signal by more than 8% while simultaneously providing a detailed characterization of the beam shape and of the influence of waveguide transmission on the beam profile. To achieve a genuine advantage in quantum information processing over classical protocols, the generation of non-Gaussian states is necessary. We therefore present a complete scheme for the creation of non-Gaussian states in a multimode system via mode-selective single-photon addition and subtraction, implemented through nonlinear optical processes in second-order nonlinear materials. We introduce a simulation framework applied to our squeezing source, which can be adapted to other regimes as well. Based on this framework, we are able to predict specific waveguide configurations that enable full control over the generated quantum states while maintaining high purity, with each process exhibiting a Schmidt number close to K=1, corresponding to effective single-mode addressing. generated quantum states while maintaining high purity, with each process exhibiting a Schmidt number close to K=1, corresponding to effective single-mode addressing.