Genuine Continuous Quantumness

TL;DR

The paper addresses the challenge of identifying genuine quantum non-Gaussianity in continuous-variable systems by introducing generalized nonlinear squeezing as a universal framework to describe and verify non-Gaussian noise. It defines a nonlinear squeezing metric as a ratio of state variances to the Gaussian-baseline minimum and uses optimization over Gaussian unitaries to witness non-Gaussianity across noise shapes. The authors demonstrate the approach experimentally by preparing single- and two-photon-added coherent states, achieving high fidelity and observing cubic and quintic nonlinear squeezing, thereby certifying quantum non-Gaussianity beyond Wigner negativity. This framework provides a practical tool for diagnosing and leveraging non-Gaussian quantum resources in photonic platforms, with potential implications for quantum computing and information processing using continuous variables.

Abstract

Randomness is a key feature of quantum physics. Heisenberg's uncertainty principle reveals the existence of an intrinsic noise, usually explored through Gaussian squeezed states. Due to their insufficiency for quantum advantage, the focus is currently shifting towards genuinely quantum non-Gaussian states. However, while genuine quantum behavior comes naturally to discrete variable systems, its preparation and verification are difficult in continuous ones. Simultaneously, a unifying theoretical framework based on the continuous nature is missing. Here, we introduce nonlinear squeezing as a general framework to describe and verify genuine quantumness in the noise of continuous quantum states. Using this approach, we certify the non-Gaussianity of experimentally prepared multi-photon-added coherent states of light for the first time. Chiefly, we demonstrated the nonlinear squeezing corresponding to third- and fifth-order quantum nonlinearities, going significantly beyond the current state-of-the-art in quantum technology. This framework enables uncovering intricate quantum properties in cutting-edge experiments and provides an efficient tool for further development of quantum technologies.

Figures (6)

• Figure 1: a, Cost function $f(x,p)^2 = x^2$ for the Gaussian squeezing. It forms a narrow valley that follows a straight line. b, Cost function for the nonlinear cubic squeezing with $f(x,p)^2=(p+zx^2)^2$. Its valley follows a parabola curve. c, Cost function for the nonlinear GKP squeezing. Its minima lies on a grid and the function resembles an egg carton.
• Figure 2: Schematic of the preparation of $n$-photon-added coherent states. A coherent state $|\alpha\rangle$ from a fundamental laser is seeded into the signal mode of an optical parametric amplifier (OPA). The OPA is pumped using a second-harmonic-generated light (SHG). Detection of $n$ photons at the photon-number resolving detector (PNRD) in the auxiliary mode projects the signal mode to the desired $n$-photon-added coherent state. The resulting state is completely characterized by homodyne detection using a local oscillator (LO) and a balanced pair of photodetectors.
• Figure 3: Density plots of the Wigner function of the experimentally generated states: a, single-photon-added coherent state; b, two-photon-added coherent state. Both have the coherent drive with an amplitude $|\alpha|$ of approximately 1.0.
• Figure 4: Nonlinear cubic squeezing of photon-added coherent states. The theoretical prediction of cubic squeezing of single-photon-added coherent states, and two-photon-added coherent states are plotted as red solid, and blue dashed lines, respectively. Red dots, and blue triangles represent values of cubic squeezing experimentally determined from measured data for single-, and two-photon-added coherent states, respectively. The area below the black line contains the states with the nonlinear cubic squeezing. The error bars represent one standard deviation.
• Figure 5: Comparison of cubic (red solid lines) and quintic (blue dashed lines) nonlinear squeezing of single-photon (a) and two-photon (b) added coherent states. Red dots, and blue triangles represent values of cubic, and quintic squeezing, respectively, experimentally determined from measured states. All states manifest equal or higher quintic nonlinear squeezing compared to the cubic squeezing due to better matching between the cost function and distribution of quantum noise in measured states.