A versatile entanglement synthesizer in the spatial domain David Barral, 1, ∗ Nadia Belabas, 1, † Kamel Bencheikh, 1 Juan Ariel Levenson, 1 Mattia Walschaers, 2 Valentina Parigi, 2 and Nicolas Treps 2 1 Centre de Nanosciences et de Nanotechnologies C2N, CNRS, Universit´ e Paris-Saclay, 10 boulevard Thomas Gobert, 91120 Palaiseau, France 2 Laboratoire Kastler Brossel, Sorbonne Universit´ e, CNRS, ENS-PSL Research University, Coll` ege de France, 4 place Jussieu, F-75252 Paris, France (Dated: December 24, 2019) Multimode entanglement is an essential resource for quantum information in continuous-variable systems. Quantum light-based mainstream technologies will arguably not be built upon table-top bulk optics-based setups. Integrated optics is a leading substrate technology for real-world light- based quantum information technologies. Sequential bulk optics-like proposals based on cascaded interferometers are not scalable with the current state-of-the-art low-loss materials used for con- tinuous variables. In this work we analyze the multimode continuous-variable entanglement capa- bilities of a compact currently-available integrated device without bulk-optics analogous: the array of nonlinear waveguides. We demonstrate that this simple and compact structure, together with a reconfigurable input pump distribution and multimode coherent detection of the output modes, is a versatile entanglement synthesizer in the spatial domain. We demonstrate this versatility through analytical and numerically optimized examples of multimode squeezing, entanglement, and cluster state generation in different encodings. Our results establish back spatial encoding as a contender in the game of continuous-variable quantum information processing. I. INTRODUCTION Two key phenomena underpin current quantum tech- nologies: quantum superposition and quantum correla- tions –entanglement– [1]. The paradigmatic example of entanglement is the case of two spatially separated quan- tum particles that have both maximally correlated mo- menta and maximally anticorrelated positions [2]. Posi- tion and momentum are continuous variables (CV), i.e. variables that take a continuous spectrum of eigenvalues [3]. In the optical domain CV-based quantum informa- tion can be encoded in the fluctuations of the electro- magnetic field quadratures. Features like deterministic resources, unconditional operations and near-unity effi- ciency homodyne detectors make CV a powerful frame- work for the development of quantum technologies [4]. Remarkably, entanglement between more than two par- ties is also possible. Particularly, large-scale CV entan- gled states are the resources of a promising class of quan- tum computing, measurement-based quantum comput- ing (MBQC) [5, 6]. Multipartite entangled states are usually produced in table-top experiments with specific designs generating only specific entanglement geometries or quantum networks. Such large-scale entanglement has been exhibited through frequency [7] and temporal [8] encoding of squeezed light. Multimode spatially-encoded CV entangled states have been likewise prepared by mix- ing single-mode squeezed states in large networks of beam splitters [9, 10]. The generation on-demand of different multimode en- tangled states with the same optical setup –an entan- * david.barral@c2n.upsaclay.fr † nadia.belabas@c2n.upsaclay.fr glement synthesizer– is a challenging task. Transverse spatial and frequency modes entanglement synthesizers based respectively on postprocessing measurement re- sults and on measurement basis shaping have been in- troduced in [11–13]. These approaches, being interesting for MBQC, are however not fully equivalent to a quan- tum network, since the quantum information can only be processed locally, but not in a distributed way. Recently, an entanglement synthesizer with the possibility to dis- tribute the nodes has been introduced in the time do- main [14]. Entanglement synthesizers find application in quantum computing, quantum communication and quan- tum simulation [15–17]. A versatile entanglement synthe- sizer in the spatial domain is nevertheless still missing mainly due to the lack of scalability of bulk-optics sys- tems. Specifically, distribution of signal in networks is naturally accomplished in this domain, making communi- cation through quantum secret sharing straightforwardly benefited from such development [18]. The scalability bottleneck can be solved with inte- grated optics by means of on-chip integration of squeez- ing sources and reconfigurable interferometers, minia- turization, and subwavelength stability [19]. The first source of CV entangled states fully on-chip has been in- troduced recently [20]. However, the extension of that scheme to dimensions N> 2 is very demanding with current technology. We establish here that arrays of nonlinear waveguides (ANWs) are a good contender for versatile and scalable generation of entanglement. Non- classical biphoton states for discrete-variable (DV) ap- plications have been demonstrated in periodically poled lithium niobate (PPLN) arrays in the last few years [21, 22]. Bipartite and tripartite CV entanglement have been predicted in arrays of nonlinear waveguides in the spontaneous (SPDC) and stimulated parametric down- arXiv:1912.11154v1 [quant-ph] 24 Dec 2019