Abstract Spectro-temporal modes of light can be exploited for the generation of high-dimensional Gaussian quantum states. Such states are at the basis of continuous variable quantum information protocols where they have to support mode-selective non-Gaussian operations. We develop a general framework for single-photon addition on multimode states of light via parametric down conversion (PDC) processes. We identify the analytical conditions for single-mode and mode-selective photon addition. We show that spectral mode selectivity can be achieved in the type-II collinear down conversion, while single-mode condition are retrieved for noncollinear type-I and type-II processes. Numerical results are shown for photon addition in PDC process at near-infrared and telecommunications wavelengths.
Abstract Spectro-temporal modes of light can be exploited for the generation of high-dimensional Gaussian quantum states. Such states are at the basis of continuous variable quantum information protocols where they have to support mode-selective non-Gaussian operations. We develop a general framework for single-photon addition on multimode states of light via parametric down conversion (PDC) processes. We identify the analytical conditions for single-mode and mode-selective photon addition. We show that spectral mode selectivity can be achieved in the type-II collinear down conversion, while single-mode condition are retrieved for noncollinear type-I and type-II processes. Numerical results are shown for photon addition in PDC process at near-infrared and telecommunications wavelengths.
Multimode spectro-temporal non-Gaussian quantum states of light play a crucial role in continuous-variable quantum information processing. In particular, the non-Gaussian quantum states generated through a single-photon addition (SPA) to multimode quantum fields at telecommunication wavelengths constitute a useful resource for quantum technologies. We present a detailed theoretical analysis and numerical simulations of single-photon addition (SPA) and mode-selective single-photon addition (MSSPA) to a multimode quantum field at telecommunication wavelengths. The analysis is performed for congruently grown lithium niobate (LN), 5% MgO-doped lithium niobate (MgO:LN) and various concentrations of ZnO-doped lithium niobate (ZnO:LN) bulk crystals. We investigate MSSPA using type-II parametric down-conversion (PDC) and SPA using the type-I PDC processes. We further present spectro-temporal mode-selective SPA at the telecom wavelength using 5% MgO:LN for temperatures ranging from 0∘C to 15∘C. In addition, we perform simulations to investigate SPA based on the noncollinear type-I PDC configuration. These theoretical results identify optimal experimental conditions and phase-matching parameters to achieve SPA and mode-selective SPA for LN-based crystals, providing a potential platform for non-Gaussian quantum state engineering at telecommunication wavelengths, mainly at 1550 nm.
Parametric down-conversion (PDC) forms one of the basic building blocks for quantum optical experiments. However, the intrinsic multimode spectral-temporal structure of pulsed PDC often poses a severe hindrance for the direct implementation of the heralding of pure single photon states or, for example, continuous-variable entanglement distillation experiments. To get rid of multimode effects narrowband frequency filtering is frequently applied to achieve a single-mode behaviour. To date, the theoretical models of filtered PDC, however, only account for filtering in the low gain regime, where only a few photon-pairs are emitted at any single point in time. In this paper we extend these theoretical descriptions and present a rigorous theoretical model for filtered type-II PDC. Our theoretical investigations reveal that filtering a multimode type-II PDC state, followed by a careful optimization of the measurement basis, effectively achieves a single-mode behaviour and further enables the generation of single-mode EPR-entanglement. Considering the ever increasing brightness of PDC sources our developed theoretical framework, enables the accurate description of filtered PDC in quantum optical experiments.
Advancements in photonic platforms have enabled the precise control of light’s spectral and temporal degrees of freedom, a capability crucial for the development of scalable quantum information systems. In this work, we address the challenge of implementing spectro-temporal mode-selective non-Gaussian quantum operations, specifically single-photon subtraction (SPS) and addition (SPA), in the telecom wavelength regime. Building on prior experimental demonstrations of mode-selective near-infrared SPS, we present the first design framework for achieving mode-selective SPA and SPS using thin-film lithium niobate nonlinear waveguide platforms. We introduce an inverse-design optimization scheme by modeling the quantum-optical response via the joint spectral amplitude (JSA) and transfer function (TF), in order to identify optimal waveguide and pump parameters that maximize mode selectivity and state purity. This approach is first tested on a metallic waveguide design. We then exploit the dispersion engineering capabilities of thin-film waveguides, which offer enhanced nonlinear interactions through tighter light confinement. Our findings demonstrate that tailored nonlinear processes, particularly parametric down-conversion and frequency up-conversion, can support high-fidelity non-Gaussian operations essential for next-generation quantum photonic networks.
Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after the subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyze the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.
Non-Gaussian quantum states of light are important resources for implementing quantum information tasks, ranging from fault-tolerant optical quantum information processing to long distance quantum communication. These states can be generated by applying non-Gaussian operations, such as photon addition and subtraction, to an input Gaussian quantum state. Also, the use of Gaussian operations (like homodyne measurement) allows the transformation of non-Gaussian input quantum states while maintaining their non-Gaussianity. It has been shown that in such context, iterative tailoring of arbitrary quantum states is possible, by cascading elementary operation blocks. This invitably comes at the cost of increasing the protocol complexity. Spectral modes, on the other hand, can be used to handily carry multiple quantum states in a single spatial mode. Moreover, multimode states populating such modes are readily available in commonly exploited processes such as spontaneous parametric down conversion.In this work, we propose a protocol to generate non-Gaussian quantum states using spectral multiplexing of input states and Gaussian operations. We give the analytical expression of the output non-Gaussian state as a function of the number of input state, the Gaussian operation and the properties of spectral modes carrying the input quantum states. Taking as an example the cat breeding operation, we show that with a single mixing and measurement operation, we can obtain an amplified output cat state comparable to the one obtained using iterative breeding scheme with multiple mixing operations and measurements with the same number of input states. We show also that the generation of approximated GKP states is possible with this protocol. We believe that the proposed protocol will have a major impact on the field of non-Gaussian quantum states generation, and can be used to extend the study beyond the cases considered in our work.
Parametric down-conversion (PDC) forms one of the basic building blocks for quantum optical experiments. However, the intrinsic multimode spectral-temporal structure of pulsed PDC often poses a severe hindrance for the direct implementation of the heralding of pure single-photon states or, for example, continuous-variable entanglement distillation experiments. To get rid of multimode effects narrowband frequency filtering is frequently applied to achieve a single-mode behavior. A rigorous theoretical description to accurately describe the effects of filtering on PDC, however, is still missing. To date, the theoretical models of filtered PDC are rooted in the discrete-variable domain and only account for filtering in the low-gain regime, where only a few photon pairs are emitted at any single point in time. In this paper we extend these theoretical descriptions and put forward a simple model, which is able to accurately describe the effects of filtering on PDC in the continuous-variable domain. This developed straightforward theoretical framework enables us to accurately quantify the tradeoff between suppression of higher-order modes, reduced purity, and lowered Einstein--Podolsky--Rosen entanglement, when narrowband filters are applied to multimode type-II PDC.