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

• URL: http://arxiv.org/abs/2606.28698v1
• Date: Sat, 27 Jun 2026 02:55:23 GMT
• Title: Detecting entanglement of non-Gaussian continuous-variable states from single-copy homodyne measurements
• Abstract summary: Non-Gaussian entanglement detection remains an experimental challenge.<n>$p_3$-PPT criterion detects entanglement using moments of the partial transpose of the density matrix.<n>We introduce a single-copy homodyne protocol that detects bipartite CV entanglement via the same criterion.
• Score: 0.047056701241378535
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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