FET: Small: Establishing an efficient framework for non-Gaussian states engineering and optical implementation of measurements

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Quantum optical technologies (computing, sensing, communications) are fundamentally based on the generation of quantum states and the detection thereof. For example, quantum computing requires reliable generation of the so-called non-Gaussian states in order not to be simulable by a classical computer, while sensing and communications tasks require optical implementation of measurements which might have an abstract mathematical description, e.g., projection on non-Gaussian states. Therefore, non-Gaussianity is a resource which, similar to entanglement, is a cornerstone of quantum information. This project aims to develop a systematic procedure for understanding resource-efficient production of non-Gaussianity and to provide constructive ways of generating any desired non-Gaussian state useful to a plethora of quantum informational tasks. The project also aims to find systematic ways of decomposing any given quantum optical measurement into a set of quantum operations which have known optical implementations. The results that will be enabled by this project are anticipated to have a two-fold impact: advancement of quantum photonic technologies with immediate impact on defense and security systems, and the advancement of basic physics by providing novel mathematical tools for fundamental effects in quantum optics. Graduate students supported by this project will have the opportunity to gain knowledge on continuous variable quantum information systems beyond the Gaussian regime, with an emphasis on non-Gaussianity and entanglement measures. The fundamental results from this project will have far reaching impacts on communications over the future quantum internet, on discovering receiver structures for attaining quantum-limited photonic state discrimination for applications in optical communications and sensing, on the realizability of various near-term applications of photonic quantum processors to problems in optimization, and molecular simulations for evaluating vibronic spectra with applications in drug discovery, and also to special-purpose applications such as all-photonic quantum repeaters based on cluster states for entanglement distribution over long-distances.It is known that Gaussian states and operations -- realizable using squeezed states, lasers and linear optics -- complemented with a single non-Gaussian operation, is "universal", in a sense that any transformation and measurement on a set of optical modes allowed by the laws of quantum physics, can be realized using elements chosen from this aforesaid set. The single non-Gaussian operation could be a non-Gaussian unitary such as a cubic-phase gate. But it can also be a non-Gaussian measurement such as photon resolving (PNR) detection, i.e., projection on Fock states, which have been proven a reliable choice for state engineering in early and recent works. Indeed, one can produce a non-Gaussian state by projecting a subset of a Gaussian state’s modes on the multi-mode Fock basis. However, a systematic way to understand the underlying phenomena, and a neat mathematical description is missing. The broad goals of this project are twofold. First is to devise a mathematical tool, specifically a non-Gaussianity measure, tailored in a fashion that will be useful to state engineering. When the envisioned measure is equal for two different quantum states, the two states must be equal up to a unitary Gaussian operator. This will allow for conclusive results as to if a produced non-Gaussian state is indeed the desired target state (up to a Gaussian unitary operation which is in principle implementable using known photonic components) that a quantum circuit is supposed to be able to produce. Earlier works on non-Gaussianity measures do not possess said property. At the same time earlier works on state engineering focus on fidelity as the measure of closeness of quantum states. Fidelity being close to one is a necessary, but not sufficient criterion for successful state engineering. Finally, the aforesaid tools will enable us to “stitch” together, simple non-Gaussian states, e.g., Fock states, into larger, general entangled non-Gaussian target states desired in a given application. Ultimately, this project aims to devise a systematic way of constructing any desired non-Gaussian state reliably. Our results will be of fundamental interest in a deeper understanding of the mathematical structures of quantum optics, while paving the way to scalable realizations of photonic quantum technologies. Our second goal is to find recipes with which any quantum optical measurement (POVM) can be realized using easy-to-prepare Gaussian states, Gaussian operations and PNR detectors. A POVM on a part of quantum state transforms the initial state into another state from a set of possible states with some probability. Leveraging this property, we will re-write a measurement (e.g., the vacuum-or-not measurement—which has relevance to constructing quantum optimal receivers for laser communications) as an input state (consisting of the state to be measured tensored with ancillary Gaussian states), which undergoes Gaussian unitary evolution, and finally partially projected on Fock states in a manner that gives the proper set of states and probabilities prescribed by the given POVM.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.