Moritz Straeter | Searcharxiv

arXiv2026

Continuous-variable state moments from randomized homodyne and heterodyne measurements

Continuous-variable (CV) quantum states are naturally characterized by their moments, defined as expectation values of products of single- or multimode ladder operators. Many CV Hamiltonians and quantum algorithms are formulated directly in terms of these moments, and therefore an efficient procedure to estimate moments with limited state measurements is necessary. In this paper, we present a protocol for shadow tomography of moment-generating functions (MGFs) of CV states based on randomized homodyne and heterodyne measurements. The resulting shadows enable an efficient and concurrent estimation of many multimode moments. Our complexity analysis shows that the number of measurements required to estimate a certain moment to a given precision grows exponentially in the order of the moments. Finally, we assess the precision of these moment estimators by applying them to two tasks: detecting entanglement in both Gaussian and non-Gaussian states via the Shchukin-Vogel protocol, and characterizing optical loss in a photonic chip. We demonstrate that both tasks can be accomplished with only a few thousand randomized measurements. The small number of required measurements, combined with efficient sample processing, makes our protocol applicable to a wide range of CV simulation tasks.

quant-ph↗

arXiv2026

Detecting entanglement of non-Gaussian continuous-variable states from single-copy homodyne measurements

The entanglement of Gaussian continuous-variable (CV) states is fully determined by the state's second moments. In contrast, some entangled non-Gaussian states evade every second-moment criterion, and non-Gaussian entanglement detection remains an experimental challenge. The $p_3$-PPT criterion detects entanglement using moments of the partial transpose of the density matrix. This criterion was recently extended to CV systems using photon-number-resolving detectors and multi-copy interferometry; here we introduce a single-copy homodyne protocol that detects bipartite CV entanglement via the same criterion. Unbiased U-statistic estimators for the partial-transpose moments $p_2$ and $p_3$ are constructed directly from randomized homodyne data and used to evaluate the $p_3$-PPT entanglement witnesses: a linear one for detection, and a quadratic one whose violation yields a dimension-free lower bound on the entanglement negativity. The protocol estimates $p_2$ and $p_3$ up to additive error $\varepsilon$ at Fock cutoff $N$ from $O((N+1)^{14/3}/\varepsilon^2)$ measurements at fixed confidence. We demonstrate the protocol on six families of Gaussian and non-Gaussian states, reaching $95\%$ empirical one-sided detection probability from $\sim 10^3$ to $10^4$ homodyne measurements for states with $\bar{n} \approx 2$, placing non-Gaussian entanglement detection within reach of current homodyne experiments.

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