Rigorous characterization of continuous-variable quantum states via optical parametric amplifiers

Research Approach

This paper addresses the challenge of characterizing non-Gaussian quantum states, which are essential for continuous-variable quantum information processing (CVQIP) but difficult to measure due to optical loss, detector inefficiency, and limited bandwidth in conventional homodyne detection. The authors propose a novel, loss-tolerant measurement scheme that replaces standard field quadrature measurements with sign-free quadrature measurements. By utilizing a high-gain phase-sensitive optical parametric amplifier (OPA) to amplify signals to macroscopic levels, the system measures the squared quadrature, effectively bypassing the need to resolve the sign of the field.

Methodology

To reconstruct the quantum states, the authors developed a computationally efficient semidefinite programming (SDP) approach. This method leverages the parity symmetry of target states—such as single-photon, Schrödinger cat, and Gottesman-Kitaev-Preskill (GKP) states—to invert the measured probability distributions back to the density matrix. The framework also includes a certification protocol that uses the same quadrature-power measurements to quantify non-classical properties like Wigner negativity and stellar rank, providing a robust alternative to full state tomography when only specific quantum features are of interest.

Findings and Significance

The researchers validated their framework using both experimental data from previous homodyne studies and numerical simulations. The results demonstrate that the OPA-based approach achieves near-unity fidelity compared to conventional homodyne tomography while significantly reducing computational runtime, particularly for complex states with larger Hilbert space dimensions. By unifying loss-tolerant measurements, state tomography, and non-classicality certification into a single, experimentally accessible pipeline, this work provides a practical pathway for verifying complex quantum states in real-world nanophotonic platforms where coupling losses and detector limitations are prevalent.