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
p3-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
p2 and
p3 are constructed directly from randomized homodyne data and used to evaluate the
p3-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
p2 and
p3 up to additive error
ε at Fock cutoff
N from
O((N+1)14/3/ε2) 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
∼103 to
104 homodyne measurements for states with
nˉ≈2, placing non-Gaussian entanglement detection within reach of current homodyne experiments.
Homodyne measurement is a crucial tool widely used to address continuous variables for bosonic quantum systems. While an ideal homodyne detection provides a powerful analysis, e.g., to effectively measure quadrature amplitudes of light in quantum optics, it relies on the use of a strong reference field, the so-called local oscillator, typically in a coherent state. Such a strong coherent local oscillator may not be readily available, particularly for a massive quantum system like a Bose-Einstein condensate, posing a substantial challenge in dealing with continuous variables appropriately. It is necessary to establish a practical framework that includes the effects of nonideal local oscillators for a rigorous assessment of various quantum tests and applications. We here develop entanglement criteria beyond a Gaussian regime applicable for this realistic homodyne measurement that do not require assumptions on the state of local oscillators. We discuss the working conditions of homodyne detection to effectively detect non-Gaussian quantum entanglement under various states of local oscillators.