Abstract A central tenet of quantum theory is that ensembles sharing the same density matrix are indistinguishable under measurements on individual systems. We show that this indistinguishability can break down when additional structure is present across multiple copies. We investigate ensembles of qubits prepared in either the computational ($Z$) or Hadamard ($X$) basis under a same-basis constraint. All qubits within a batch are prepared in the same basis, but with randomly distributed outcomes such that the reduced state of each individual qubit is maximally mixed. We introduce an experimentally realizable protocol that exploits multi-copy statistical structure to distinguish these ensembles. The graph-state protocol identifies the two basis through stabilizer measurements and higher-order statistical features. Our protocol has been implemented on the \texttt{ibm\_fez} superconducting quantum processor and demonstrates robust performance in the presence of realistic noise, achieving near-unity classification accuracy as the number of samples increases. While single-copy measurements are uninformative, aggregating outcomes across multiple instances produces a clear and scalable separation between basis families. Our result identifies a regime in which quantum information is not accessible at the level of individual systems but emerges through structured multi-copy measurements. This highlights the role of higher-order statistical correlations in quantum information processing and provides a practical route for exploiting such structure on near-term quantum devices.
Abstract A central tenet of quantum theory is that ensembles sharing the same density matrix are indistinguishable under measurements on individual systems. We show that this indistinguishability can break down when additional structure is present across multiple copies. We investigate ensembles of qubits prepared in either the computational (Z) or Hadamard (X) basis under a same-basis constraint. All qubits within a batch are prepared in the same basis, but with randomly distributed outcomes such that the reduced state of each individual qubit is maximally mixed. We introduce an experimentally realizable protocol that exploits multi-copy statistical structure to distinguish these ensembles. The graph-state protocol identifies the two basis through stabilizer measurements and higher-order statistical features. Our protocol has been implemented on the \texttt{ibm_fez} superconducting quantum processor and demonstrates robust performance in the presence of realistic noise, achieving near-unity classification accuracy as the number of samples increases. While single-copy measurements are uninformative, aggregating outcomes across multiple instances produces a clear and scalable separation between basis families. Our result identifies a regime in which quantum information is not accessible at the level of individual systems but emerges through structured multi-copy measurements. This highlights the role of higher-order statistical correlations in quantum information processing and provides a practical route for exploiting such structure on near-term quantum devices.
Mixed states of a quantum system, represented by density operators, can be decomposed as a statistical mixture of pure states in a number of ways where each decomposition can be viewed as a different preparation recipe. However the fact that the density matrix contains full information about the ensemble makes it impossible to estimate the preparation basis for the quantum system. Here we present a measurement scheme to (seemingly) improve the performance of unsharp measurements. We argue that in some situations this scheme is capable of providing statistics from a single copy of the quantum system, thus making it possible to perform state tomography from a single copy. One of the by-products of the scheme is a way to distinguish between different preparation methods used to prepare the state of the quantum system. However, our numerical simulations disagree with our intuitive predictions. We show that a counterintuitive property of a biased classical random walk is responsible for the proposed mechanism not working.
More than two decades ago, Bennett \emph{et al.} [Phys. Rev. A \textbf{59}, 1070 (1999)] asked whether perfect local discrimination of orthogonal quantum states can require more than two copies. This question was subsequently answered for adaptive protocols that process the copies separately [Phys. Rev. Lett. \textbf{126}, 210505 (2021)], but remained open when each laboratory is allowed to process its local copies collectively. Here we resolve this stronger setting and identify collective access across repeated local inputs as a distinct resource. For every fixed odd-prime local dimension, there exist complete maximal-stabilizer eigenbases whose copy complexity under individual-copy separable measurements diverges with system size. Under collective processing this behavior changes sharply: every maximal-stabilizer eigenbasis in odd-prime local dimension is perfectly decoded by one-round collective LOCC using at most three copies. Collective processing, however, does not remove multicopy hardness in general. For every fixed local dimension d≥2, we prove the existence, within an explicit phase family, of complete bases whose copy complexity remains unbounded even under collective separable measurements, with a square root of the number of subsystems as lower-bound scale. Thus sample number, spatial measurement power, and coherent access across repeated local inputs are distinct resources in distributed quantum measurement.
Nonlinear properties of quantum states are essential to quantum information and many-body physics, but assessing them experimentally is challenging, as it typically requires multi-copy operations or a large number of measurement settings. To address this challenge, we develop a universal framework, collision-based nonlinear estimation (CBNE), for efficiently measuring nonlinear quantities of a quantum state ρ, such as the higher-order expectation value tr(Oρt) for some observable O, using single-copy randomized measurements. Strikingly, our protocol requires only a single measurement setting, provided that the system dimension is sufficiently large or a few ancillary qubits are available; this contrasts with the conventional expectation that multiple measurement bases are necessary for nonlinear estimation. In addition, CBNE is observable-independent at the experimental stage, which enables simultaneous estimation of multiple nonlinear functions. It further extends to broader tasks, including the estimation of principal component properties and partial-transpose moments of quantum states. Our results provide a practical and scalable route for measuring nonlinear state properties on near-term quantum devices.
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.
Estimating nonlinear properties of quantum states is a central task in quantum information science. Multivariate traces, tr(ρ1⋯ρK), and nonlinear observables such as tr(ρK), for integer K, can be accessed through collective measurements on multiple state copies, but standard protocols based on swap tests require coherent operations on the full Hilbert space and become experimentally unfeasible for large systems. In this work, we introduce a framework for multi-copy measurements based on random projections onto lower-dimensional subspaces prior to the collective measurement, which is then performed only on the reduced Hilbert space. This procedure yields a tunable tradeoff between coherent quantum resources and statistical sampling overhead, allowing the amount of coherent processing to be matched to the capabilities of the underlying hardware. We derive explicit formulas relating the Haar-averaged projected moments to multivariate traces of the original states and analyze the sampling overhead induced by the projection procedure. Specifically, after compressing an n-qubit state to a reduced q-qubit subspace, estimating tr(ρK) requires approximately O(2(n−q)(K−1)) copies of ρ, with each qubit projected out increasing the sampling cost by a factor of 2K−1. Our results establish how coherent multi-copy operations can be traded for additional state copies, enabling multi-copy quantum protocols to be optimized for the available hardware resources.
What does measuring one qubit reveal about another? K-networks as a directed diagnostic for quantum circuits
Many-qubit circuit states are hard to inspect directly, so they are often summarized by pairwise graph weights. Common pairwise weights report symmetric correlations, while many circuit questions are directed and basis-specific: if qubit i is measured in a given basis, how strongly does the outcome reshape the conditional state of qubit j? We define Ki→j, a directed, basis-conditioned edge weight for this question. It is large when the two measurement outcomes occur with comparable probability and leave qubit j in clearly different conditional states; it is zero when the source outcome is deterministic or the target states are indistinguishable. The scalar uses standard binary-ensemble distinguishability; the paper's contribution is to turn this conditional comparison into a directed network layer for circuit states. The resulting networks are computable from two-qubit reduced density matrices. They are diagnostic (not entanglement measures): for pure two-qubit states K reduces to the tangle C2 (squared concurrence)~\cite{WoottersConcurrence,CKWTangle}, while separable mixed states can reach K=1. Examples on teleportation, Grover, QAOA, and random circuit families show the intended use: K-networks map feed-forward, phase, and interaction-graph structure that symmetric or computational-basis summaries can leave weak or absent.