In circuit and cavity quantum electrodynamics devices where control qubits are dispersively coupled to high-quality-factor cavities, characteristic functions of cavity states can be directly probed with conditional displacement (CD) gates. In this Letter, I propose a method to certify non-Gaussian entanglement between cavities using only CD gates and qubit readouts. The CD witness arises from an application of Bochner's theorem to a surprising connection between two negativities: that of the reduced Wigner function, and that of the partial transpose. Non-Gaussian entanglement of some common states, like entangled cats and photon-subtracted two-mode squeezed vacua, can be detected by measuring as few as four points of the characteristic function. Furthermore, the expectation value of the witness is a simultaneous lower bound to the Wigner negativity volume and a geometric measure of entanglement conjectured to be the partial transpose negativity. Both negativities are strong monotones of non-Gaussianity and entanglement, respectively, so the CD witness provides experimentally accessible lower bounds to quantities related to these monotones without the need for tomography on the cavity states.
In circuit and cavity quantum electrodynamics devices where control qubits are dispersively coupled to high-quality-factor cavities, characteristic functions of cavity states can be directly probed with conditional displacement (CD) gates. In this Letter, I propose a method to certify non-Gaussian entanglement between cavities using only CD gates and qubit readouts. The CD witness arises from an application of Bochner's theorem to a surprising connection between two negativities: that of the reduced Wigner function, and that of the partial transpose. Non-Gaussian entanglement of some common states, like entangled cats and photon-subtracted two-mode squeezed vacua, can be detected by measuring as few as four points of the characteristic function. Furthermore, the expectation value of the witness is a simultaneous lower bound to the Wigner negativity volume and a geometric measure of entanglement conjectured to be the partial transpose negativity. Both negativities are strong monotones of non-Gaussianity and entanglement, respectively, so the CD witness provides experimentally accessible lower bounds to quantities related to these monotones without the need for tomography on the cavity states.
Wigner negativity and genuine multipartite entanglement (GME) are key nonclassical resources that enable computational advantages and broader quantum-information tasks. In this Letter, we prove two theorems for multimode continuous-variable systems that relate these nonclassical resources. Both theorems show that sufficient Wigner negativity-either a sufficiently-large Wigner negativity volume along a suitably chosen two-dimensional slice, or a sufficiently large nonclassicality depth of the center-of-mass mode of a system-certifies the presence of GME. Moreover, violations of the latter inequality provide lower bounds of the trace distance to the set of non-GME states. Our results also provide sufficient conditions for generating GME by interfering a state with the vacuum through a multiport interferometer, complementing long-known necessary conditions. Beyond these fundamental connections, our methods have practical advantages for systems with native phase-space measurements: they require only measuring the Wigner function over a finite region, or measuring a finite number of characteristic function points. Such measurements are frequently performed with readouts common in circuit and cavity quantum electrodynamic systems, trapped ions and atoms, and circuit quantum acoustodynamic systems. As such, our GME criteria are readily implementable in these platforms.
Quantifying non-Gaussianity is essential for assessing the computational power of bosonic quantum systems. We introduce a framework to witness and quantify non-Gaussianity from displaced parity measurements, and we directly apply it to experimental data obtained with superconducting cavities. Our method estimates fidelities with target pure states from the displaced parity measurements, enabling certification of non-Gaussianity via the stellar rank. We further introduce refined witnesses computed by measuring the value of the Wigner function at a few points, providing efficient certification tools outperforming existing ones. Applying these techniques to Fock, binomial, cat, and GKP experimental data, we rigorously certify non-Gaussian resources and establish a stellar rank of 8 for a GKP state, setting a new benchmark across all quantum platforms. Our methods enable a rigorous quantification of non-Gaussian quantum resources directly applicable to superconducting devices.
Many existing genuine multipartite entanglement (GME) witnesses for continuous-variable (CV) quantum systems typically rely on quadrature measurements, which are challenging to implement in platforms where the CV degrees of freedom can be indirectly accessed only through qubit readouts. In this work, we propose methods to implement GME witnesses through phase-space measurements in state-of-the-art experimental platforms, leveraging controlled Gaussian unitaries readily available in qubit-CV architectures. Based on two theoretical results showing that sufficient Wigner negativity can certify GME, we present five concrete implementation schemes using controlled parity, displacement, and beam-splitter operations. Our witnesses can detect paradigmatic GME states like the Dicke and multipartite N00N states, which include the W states as a special case, and GHZ-type entangled cat states. We analyze the performance of these witnesses under realistic noise conditions and finite measurement resolution, showing their robustness to experimental imperfections. Crucially, our implementations require exponentially fewer measurement settings than full tomography, with one scheme requiring only a single measurement on auxiliary modes. The methods are readily applicable to circuit/cavity quantum electrodynamics, circuit quantum acoustodynamics, as well as trapped ions and atomic systems, where such dichotomic phase-space measurements are already routinely performed as native readouts.
Entanglement is central to quantum physics, yet detecting and exploiting it in non-Gaussian systems remains a major challenge. In continuous variable platforms, standard inseparability criteria based on Gaussian statistics-such as the Duan-Simon criterion-fail when quantum correlations are encoded in higher moments of the field quadratures. Here we introduce a framework for detecting non-Gaussian entanglement using higher-order quadrature cumulants. In the Gaussian limit, the lowest order condition reduces to the Duan criterion, while higher-order violations reveal entanglement inaccessible to second-order methods. We experimentally demonstrate a tomography-free certification of inseparability in photon-subtracted squeezed states of light, where Gaussian witnesses fail despite the presence of entanglement. We further show that such higher-order inseparability enables enhanced quantum teleportation of Wigner negativity as compared to Gaussian protocols. These results identify higher-order cumulants as natural observables for non-Gaussian entanglement and open new routes to harnessing non-Gaussian resources in continuous variable quantum technologies.
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.
Entanglement plays a crucial role in quantum information science and many-body physics, yet quantifying it in mixed quantum many-body systems has remained a notoriously difficult problem. Here, we introduce families of quantitative entanglement witnesses, constructed from partial transpose and realignment moments, which provide rigorous bounds on entanglement monotones as well as entanglement dimensionality. Our witnesses can be efficiently measured using SWAP tests or variants of Bell measurements, thus making them directly implementable on current hardware. Leveraging our witnesses, we present several novel results on entanglement properties of mixed states, both in quantum information and many-body physics. We develop efficient algorithms to test whether mixed states with bounded entropy have low or high entanglement, which previously was only possible for pure states. We also provide an efficient algorithm to test the Schmidt rank using only two-copy measurements, and the operator Schmidt rank using four-copy measurements. Further, our witnesses robustly certify the quantum circuit depth in the presence of noise, as well as the Schmidt rank of mixed states. Finally, we show that the entanglement phase diagram of Haar random states, quantified by the partial transpose negativity, can be fully established solely by computing our witness, a result that also applies to any state 4 -design. Our witnesses can also be efficiently computed for matrix product states, thus enabling the characterization of entanglement in extensive many-body systems. Finally, we make progress on the entanglement required for quantum cryptography, establishing rigorous limits on pseudoentanglement and pseudorandom density matrices with bounded entropy. Our work opens new avenues for quantifying entanglement in large and noisy quantum systems.