Identifying the entanglement structure of a many-body quantum state, namely how its constituents partition into unentangled blocks, is a central task in quantum information science, yet conventional tomography scales exponentially with system size. Here we introduce a scalable framework that recognizes large-scale entanglement structures directly from local correlation fingerprints. By choosing a representative local Pauli basis that satisfies a boundary-matching condition p_1 = p_R, the entire chain is read out in a single measurement configuration, keeping the measurement effort independent of system size. In noisy simulations, this single-basis protocol classifies GHZ-, W-, and cluster-type structures among 30 candidate partitions with a mean accuracy exceeding 95% for systems of up to 100 qubits. We further validate the protocol on a superconducting quantum processor, where it reliably classifies block structures for systems of up to 13 qubits before noise- and depth-induced degradation sets in at larger sizes. By mapping these failure modes explicitly, our results delineate the boundary of hardware-level scalability and point to a concrete strategy for characterizing entanglement structure on near-term quantum devices.
Extracting total correlations from a quantum system usually requires reconstructing its state, whereas many experiments access only a few measurement settings. A possible shortcut is to add the mutual informations obtained from complementary measurements; in dimensions above two, however, this procedure can count the same classical correlation twice. We establish that qubits are protected from such overcounting. For every two-qubit state, the correlations observed in two complementary local bases are bounded by the premeasurement quantum mutual information. The proof traces this protection to binary-entropy curvature on the Bloch ball and combines a qubit information-exclusion tradeoff with data processing under local dephasing. Consequently, two correlation tables give a tomography-free lower bound on total correlation. A score above one bit also certifies a quantitative one-way entanglement-distillation rate; when applied to the Choi state of a qubit channel, the same data lower bound its quantum capacity. The theorem therefore identifies both an operational use of complementarity and the trusted two-dimensional setting in which its correlation accounting is valid.
Can a classical network not only encode a quantum-like state, but also read out its measurement statistics through its own collective dynamics? Here we introduce a network-native readout scheme for a structured classical network whose community modes form an effective two-qubit state space. Network connectivity selects a dominant collective mode that encodes the state, while a fixed set of ten elementary connectivity perturbations probes its collective response. The resulting shifts of the dominant growth rate form a complete basis of expectation values for the real two-qubit sector, from which joint-outcome probabilities associated with arbitrary real projectors are reconstructed by linear combination. Once these ten spectral responses are measured, the same data generate correlations over a continuous family of measurement settings. As a benchmark, for an encoded Bell state four selected correlations give $|S|=\chsh>2$, whereas a separable product-state reference remains within the Clauser--Horne--Shimony--Holt (CHSH) bound $|S| \leq 2 $. These results establish an informationally complete dynamical readout of effective two-qubit states directly from the spectral response of a classical network.
Song-Bo Xie, Ethan Dickey, Syed Ahmed Taimoor et al.· 0 citations
The standard benchmark for high-dimensional entanglement is the number of dimensions in which entanglement must be present in order to generate the state. This is called the Schmidt number and its detection is usually based on implementing an appropriate set of local basis measurements. However, as quantum technology brings increasingly large physical dimensions within reach, the implementation of such measurements typically becomes more costly. Here, we develop a scheme for detecting Schmidt numbers based only on sequences of single-qubit observables. These measurements are simpler to implement as they require only low-depth quantum circuits. Using up to sixteen-dimensional photonic spatial mode entanglement and multi-plane light conversion technology, we demonstrate how it simplifies setup complexity and successfully detects the maximal (or close-to-maximal) Schmidt number. Our results reveal that simple and more scalable measurements are sufficient to detect high-dimensional entanglement properties.
Suraj Goel, Alexander Bernal, G. Cobucci et al.· 0 citations
We provide an explicit geometric classification of single-qubit projective measurements on one-dimensional (1D) linear cluster states (LCS) within a topological framework. By establishing an explicit geometrical correspondence between local measurements and topological surgery operations on an associated link model i.e. a measurement-surgery correspondence, we represent the cluster state as a linear Hopf chain. Within this model, measurements in the computational ( Z) basis act as topological severance in case of bulk measurements while boundary pruning happens for end measurements of qubits. In contrast, transverse ( X) basis measurements remove the measured qubit and, rather than fusing its neighbours into a single splice, induce a geometric stratification of the residual state into a superposition of two disjoint, correlated segments joined only through real-valued classical correlations. We show that lateral ( Y) basis measurements instead preserve a single continuous spliced chain while generating intrinsically complex phase factors that are not captured by unframed link models. The unframed linking pattern already distinguishes the X- and Y-basis outcomes from one another by shape; what it cannot resolve is which of the two possible outcomes occurred within a fixed basis, since both members of either outcome pair share an identical unframed diagram. To resolve this residual ambiguity, we introduce a framed ribbon representation in which quantum phases are encoded as geometric twists, with chiral ±90∘ twists corresponding to the phases ±i. This framing yields a phase-sensitive, outcome-resolved geometric description of single-shot Pauli measurements on LCS. We stress that the twist angles introduced here are not topological invariants: they are geometric labels fixed operationally by the measurement outcome and by the resulting by-product operator, whereas the linking pattern of the underlying unframed link is a genuine topological datum. The present work is deliberately restricted to single-shot single-qubit Pauli measurements on 1D LCS; composition rules for sequential measurements and for classical feedforward are not established here and are identified as the principal open problem.
Quantum state tomography provides complete information about a quantum state, but its measurement cost generally grows exponentially with system size. In many-particle quantum simulators, this challenge is further compounded by the limited accessibility of local measurements and controls. Here we develop a tomography protocol for permutation-invariant fermionic many-body states with U(1) particle-number symmetry. We show that any such state is completely determined by the distribution of the total particle number and the occupation of a single collective mode within each particle-number sector, both of which are accessible in current ultracold-atom experiments. The number of required observables scales only linearly with the system size. More generally, the protocol reconstructs the permutation-symmetrized component of arbitrary U(1)-symmetric fermionic states, which can still encode nontrivial many-body and state-level structure beyond conventional few-body observables. We demonstrate this protocol in interacting non-Gaussian states of the complex Sachdev-Ye-Kitaev model and in free-fermion chains across a Lifshitz transition. This framework opens a route toward information-theoretic characterization of strongly correlated itinerant quantum matter in experimentally realistic fermionic quantum simulators.
Bell-state measurements are essential ingredients in many protocols for quantum information processing, ranging from quantum teleportation and dense coding to entanglement distribution in quantum networks. Their power relies on the fact that they are measurements in an entangled basis of a two-particle system and that the used Bell-state basis can be generated from a single Bell state by local unitary transformations. How can these measurements be generalized to more particles? We develop a general framework for this state-to-measurement problem: We introduce a hierarchy of classes of measurement bases, distinguished by the local transformations the parties may use for their generation from a single state. This leads to a generalization of the concept of maximally entangleable (or weighted hypergraph) states and the identification of a novel maximally entangled basis of four qubits, being a candidate for data-hiding tasks or distillation protocols. Finally, we prove that not all forms of entanglement can be encoded in an entire measurement basis.
Jef Pauwels, O. Gühne· 0 citations
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