Generalized Heralded Generation of Non-Gaussian States Using an Optical Parametric Amplifier

TL;DR

This work addresses the challenge of generating high-quality non-Gaussian states in continuous-variable quantum information by generalizing the heralded optical parametric amplifier (OPA) to accept arbitrary non-classical inputs. The authors demonstrate two main regimes: (i) a squeezed-vacuum input yields an integrated two-photon subtraction that produces high-fidelity, larger-amplitude squeezed Schrödinger cat states with $\alpha$ near $1.4$, and (ii) a small-amplitude Schrödinger cat input acts as a non-Gaussianity amplifier, distilling into high-purity photon-number superpositions and related resources. They provide quantitative results, including fidelities $F\approx0.998$ for the SV case and $F>0.999$ for certain small-SC scenarios, along with Wigner negativity control through gain and robust performance under practical losses. The reported per-trial success probabilities $p_s\sim10^{-4}-10^{-2}$ translate to substantial generation rates ($10^{5}-10^{7}$ states/s) with current laser and detector technologies, highlighting the approach's practicality. Overall, the generalized heralded OPA offers a single, integrated, versatile platform for generating a wide class of non-Gaussian states, with significant implications for CV quantum computation and metrology.

Abstract

The heralded optical parametric amplifier (OPA) has emerged as a promising tool for quantum state engineering. However, its potential has been limited to coherent state inputs. Here, we introduce a generalized heralded OPA protocol that unlocks a vastly expanded class of quantum phenomena by accepting arbitrary non-classical inputs. With a squeezed vacuum input, the setup functions as an integrated two-photon subtractor, deterministically generating high-fidelity, larger-amplitude squeezed Schrödinger cat states -- an operation previously requiring complex, discrete setups. Furthermore, when fed a small-amplitude SC state, the protocol acts as a non-Gaussianity amplifier, distilling it into high-purity approximations of key quantum resources like specific photon-number superpositions. This work transforms the OPA from a specialized source into a versatile and practical platform for advanced quantum state engineering, enabling the generation of a wide array of non-Gaussian states from a single, integrated setup.

Figures (8)

• Figure 1: Schematic of non-Gaussian state generation using an OPA. Specific states $\vert\phi\rangle$-- such as squeezed vacuum and small-amplitude Schrödinger cat (SC) states - are injected into the signal mode, while a single photon is input into the idler mode of the OPA. A single-photon detection at the idler output port heralds the generation of a non-Gaussian quantum state $\vert\Phi\rangle$ at the signal output. The characteristics of the output state can be controlled by adjusting the gain of the amplifier.
• Figure 2: Wigner functions of the input and output states. (a) and (c) show the Wigner functions of the input SV states with squeezing parameters $r=0.5$ and $r=1.0$, respectively. The corresponding Wigner functions of the output signal states $\vert\Psi^{\prime}\rangle$ are shown in (b) and (d). The amplitude gain is fixed at $g=2.5$.
• Figure 3: (a) Optimal fidelity between output state $\vert\Psi^{\prime}\rangle$ and the target squeezed even SC state. (b) Corresponding squeezing parameter $\gamma$ of the target squeezed SC state that maximizes the fidelity in panel (a). The squeezing parameter of the initial SV state is fixed at $r=1.0$. Other parameters are the same as in Fig. \ref{['fig:2']}.
• Figure 4: Dependence of the Wigner-negative volume $N$ on the squeezing parameter $r$ for different values of the amplitude gain $g$.
• Figure 5: (a) and (b) show the Wigner functions of the input even SC state with coherent amplitudes $\alpha=0.8$ and $\alpha=1.01$, respectively. The corresponding Wigner functions of the output signal states are shown in (b) and (d), generated with amplitude gains $g=5$ and $g=g_{0}$, respectively.