Quantum State Certification via Effective Parent Hamiltonians from Local Measurement Data
Guy-Philippe Nadon, Guanyi Heng, Pacôme Gasnier, Antoine Lemelin, Camille Coti, Zeljko Zilic, Mikko Möttönen, Ville Kotovirta, Toni Annala, Ernesto Campos, Jacob Biamonte
quant-phSubmitted Mar 4, 2026• Announced Mar 6, 2026• 0 citations
The preparation and certification of quantum states is a fundamental challenge across quantum information technology. We introduce a tomography-free state certification method that lower-bounds the fidelity by estimating expectation values of engineered parent-Hamiltonian terms from local measurement data. We apply this framework to construct a parent Hamiltonian that enables certification and variational optimization across the Dicke-state family, which includes the single-excitation $W_n$ state. We experimentally validate the framework on IBM quantum hardware, certifying genuine multipartite entanglement for $W_n$ states up to six qubits and establishing positive lower bounds on the state fidelity up to thirteen qubits. For Dicke states with two- and three-excitations, we certify genuine multipartite entanglement up to seven qubits. Within this stringent certification framework, these results constitute among the largest witness-certified demonstrations of such states on a programmable quantum processor.
The preparation and certification of quantum states is a fundamental challenge across quantum information technology. We introduce a tomography-free state certification method that lower-bounds the fidelity by estimating expectation values of engineered parent-Hamiltonian terms from local measurement data. We apply this framework to construct a parent Hamiltonian that enables certification and variational optimization across the Dicke-state family, which includes the single-excitation Wn state. We experimentally validate the framework on IBM quantum hardware, certifying genuine multipartite entanglement for Wn states up to six qubits and establishing positive lower bounds on the state fidelity up to thirteen qubits. For Dicke states with two- and three-excitations, we certify genuine multipartite entanglement up to seven qubits. Within this stringent certification framework, these results constitute among the largest witness-certified demonstrations of such states on a programmable quantum processor.
Entanglement depth quantifies how many qubits share genuine multipartite entanglement, but certification typically relies on tailored witnesses or full tomography, both of which scale poorly with system size. We recast entanglement-depth and non-k-separability certification as likelihood-based model selection among neural quantum states whose architecture enforces a chosen entanglement constraint. A hierarchy of separable neural quantum states is trained on finite-shot local Pauli outcomes and compared against an unconstrained reference model trained on the same data. When all constrained models are statistically disfavored, the data certify entanglement beyond the imposed limit directly from measurement statistics, without reconstructing the density matrix. We validate the method on simulated six- and ten-qubit datasets targeting GHZ, Dicke, and Bell-pair states, and demonstrate robustness for mixed states under local noise. Finally, we discuss lightweight interpretability diagnostics derived from trained parameters that expose coarse entanglement patterns and qubit groupings directly from bitstring statistics.
Standard quantum verification and certification protocols often assume that experimental sources emit independent and identically distributed (i.i.d.) states. In realistic scenarios, however, temporal drift, memory effects, feedback, and correlated noise can violate this assumption, causing standard analyses to underestimate uncertainty and overestimate device performance. Here, we introduce a general framework for quantum verification and certification in which the state produced in each round may depend arbitrarily on the preceding experimental history. Our method provides rigorous confidence intervals for observable expectation values averaged over the experimental trajectory. The framework covers both full verification, in which every state is measured, and spot-checking certification, in which a randomly selected subset is tested to certify the average observable value of the complementary, remaining systems. We apply the framework to importance-sampled Pauli measurements for direct fidelity estimation, energy estimation, and entanglement witnessing, and to classical shadows, allowing multiple observables to be certified simultaneously from the same test data. We illustrate the framework numerically and demonstrate it experimentally through Bell-state certification on a quantum processor.
Multipartite entanglement is a key resource for quantum technologies, yet its certification typically relies on correlations from measurements involving all particles, making it increasingly vulnerable to imperfections as the system size grows. Here we report the first experimental demonstration of genuine multipartite entanglement detection from correlations with the minimum possible nontrivial support, known as the entanglement detection length (EDL). Using a photonic platform, we certify W, Dicke, and cluster states with entanglement witnesses constructed from correlations at the EDL. In particular, we verify genuine multipartite entanglement of three- and four-qubit W states and a four-qubit Dicke state using two-body correlations, and of a four-qubit cluster state using three-body correlations. For the four-photon Dicke state, we further show that this minimal-correlation strategy is more robust than the compared global witness under the analyzed local-basis-misalignment model. We also find that, within the witness families considered here, increasing the number of measured subsets enhances the tolerance to noise. These results establish entanglement detection at the EDL limit as a measurement-efficient route to multipartite entanglement certification.
Certifying multipartite entanglement is a fundamental task. Since n-qubit state is parameterized by 4n- 1 real numbers, it is interesting to design a measurement setup that detects multipartite entanglement with as little effort as possible, and at a minimum without fully revealing the whole information of the state, the so-called “tomography”. In this paper, we study the relationship between multipartite entanglement certification and tomography, with the constraint that only single-copy measurements are allowed. We show that by using nonadaptive single-copy measurements, universal entanglement detection, among all states, can not be accomplished without full state tomography. Moreover, we show that almost all multipartite correlations, including the genuine entanglement and the entanglement depth, require full state tomography to detect in this measurement setting. We also observe that universal entanglement detection, among pure states, can be accomplished using much fewer measurements than full state tomography even using only local measurements.
Quantum networks form the backbone of long-distance quantum information processing. Genuine multipartite entanglement (GME) serves as a key indicator of network performance and overall state quality. However, the widely used methods for certifying GME suffer from a major drawback that they either detect only a limited range of states or are applicable only to systems with a small number of parties. To overcome these limitations, we propose a family of sub-symmetric witnesses (SSWs), which are tractable both theoretically and experimentally. Analytically, we establish a connection between SSWs and the cut space of graph theory, enabling several powerful detection criteria tailored to practical quantum networks. Numerically, we show that the optimal detection can be formulated as a linear program, offering a significant efficiency advantage over the semidefinite programs commonly employed in quantum certification. Experimentally, SSWs can be evaluated via local measurements, with resource requirements independent of the local dimension in general, and even independent of the overall network size in many practical networks.
Characterizing increasingly complex quantum systems is a central task in quantum information science, yet experimental costs often scale prohibitively with system size. Certifying key properties using simple local measurements is highly desirable but challenging. In this work, we introduce a highly general certification framework based on a physical phenomenon that we call localizable quantumness: for generic many-body states, essential quantum properties are robustly preserved within the projected ensembles on small subsystems after performing local projective measurements on the rest of the system. Leveraging this insight, we develop protocols to certify global properties—including multipartite entanglement, circuit complexity, and quantum magic—by witnessing them on a small, accessible subsystem. Remarkably, randomizing the local measurement bases extends this capability to certify state fidelity. Relying solely on local Pauli measurements, these protocols achieve constant sample complexity and robustness for almost all quantum states, including a wide range of physically relevant states. For certifying the fidelity of n -qubit states, this O ( 1 ) scaling dramatically improves upon state-of-the-art protocols requiring O ( n 4 ) samples. Our unified framework provides both a practical toolkit for large-scale quantum certification and a novel lens into complex many-body systems.