arXiv subjects

Alexander C. B. Greenwood

Publications and source records attributed to Alexander C. B. Greenwood.

6 recordsLinked to original sources

arXiv2026

Induced random mixed states are symmetric Dirichlet mixtures

We establish an exact equivalence in distribution between $D$-dimensional random mixed states induced by partial traces over $K$-dimensional environments and the Mai-Alquier distribution, a mixture of $K$ independent Haar-random pure states weighted by a symmetric Dirichlet distribution. This identification recasts a class of expectation values for induced ensembles into calculations involving Dirichlet moments and low-order Haar averages on a single-system state space. As applications, we recover exact purity moments up to fourth order, derive the mean Hilbert--Schmidt distance between independent induced ensembles with possibly different environment dimensions, and obtain exact average determinants. These results provide a unified and constructive perspective on induced random mixed states and on the evaluation of quantities such as purity moments, overlaps, and determinants.

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arXiv2026

A Universal Entanglement Witness Generator

Entanglement witnesses are essential for certifying entanglement, yet constructing ones that are both noise-robust and economical in measurement settings remains challenging - particularly beyond qubits and for non-stabilizer ("magic") states. We present a machine-learning method that, given a target state and a user-specified number of measurement settings, generates an entanglement witness optimized for noise tolerance in the neighborhood of that state, requiring only local measurements. The approach is fully general, applying to multipartite qubit and qudit systems alike, including non-stabilizer states. For N qudits of dimension d, we train on the fully-separable eigenstates of each qudit's SU(d) generators to find a prototype witness, then tune the witness's bias term via gradient descent to maximize noise tolerance. Adversarial training further strengthens the witnesses, delivering greater noise tolerance with even fewer settings; critically, under this scheme the required training-set size becomes independent of system size. We package the entire pipeline as an automated script that, in every case we tested, produces witnesses surpassing all existing methods in noise tolerance and/or number of measurement settings. We demonstrate the method on Bell, GHZ, W, and hypergraph states, along with a range of qudit states, spanning 2-6 qubits, bipartite qudits up to d=10, and tripartite qutrits. Our witnesses achieve perfect accuracy across both physical experimental test states and large numerical sets of separable mixed states-including 30 million test states for a 3-qubit W-state witness and 10 million for a 4-qubit hypergraph-state witness-and we experimentally confirm the noise tolerance of Bell- and hypergraph state witnesses on both photonic and superconducting platforms, respectively.

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arXiv2026

Re-examining the Role of State Texture in Gate Identification and Fixed-Point Resource Theories

A protocol for identifying controlled-NOT (CNOT) gates versus single-qubit-only gates in universal quantum circuits using randomized input states was recently shown to be intimately connected to the quantum resource of state texture. Here we revisit this gate identification protocol and demonstrate that a more general fidelity-based formulation succeeds for nearly all laboratory bases. We then examine a broader family of quantum resource theories, where a distinct resource theory can be defined for each choice of reference pure state, establishing core resource-theoretic requirements without the computational shortcut offered by the "grand sum" employed in the original formulation of state texture. By extending from single "resourceless" states to convex sets via a convex-roof construction, we recover single-qubit measures of known resource theories such as imaginarity and coherence. Finally, we introduce a family of "fixed-point resource theories" that includes fixed-point instances of the theories of state texture, genuine coherence, purity, and athermality. For these fixed-point resource theories we show that, under free operations, the fidelity-based lower bound is weakly monotonic, while specific violations of strong monotonicity are found for the convex-roof logarithmic measure.

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arXiv2026

Random Party Distillation on a Superconducting Processor

Random party distillation refers to the process by which Einstein-Podolsky-Rosen pairs are probabilistically extracted from a single copy of a multipartite entangled state after multiple rounds of local operations and classical communications (LOCC). In this work, we propose a qubit-based implementation of a random party distillation protocol and demonstrate it on the superconducting hardware device, ibm_aachen. We implement up to 4-rounds of the protocol, achieving a distillation rate of ~0.85 pairs/ W state, surpassing previous experimental demonstrations. Our results demonstrate the utility of multi-round LOCC protocols in an experimental regime that remains comparatively unexplored.

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arXiv2024

An Exponential Reduction in Training Data Sizes for Machine Learning Derived Entanglement Witnesses

We propose a support vector machine (SVM) based approach for generating an entanglement witness that requires exponentially less training data than previously proposed methods. SVMs generate hyperplanes represented by a weighted sum of expectation values of local observables whose coefficients are optimized to sum to a positive number for all separable states and a negative number for as many entangled states as possible near a specific target state. Previous SVM-based approaches for entanglement witness generation used large amounts of randomly generated separable states to perform training, a task with considerable computational overhead. Here, we propose a method for orienting the witness hyperplane using only the significantly smaller set of states consisting of the eigenstates of the generalized Pauli matrices and a set of entangled states near the target entangled states. With the orientation of the witness hyperplane set by the SVM, we tune the plane's placement using a differential program that ensures perfect classification accuracy on a limited test set as well as maximal noise tolerance. For $N$ qubits, the SVM portion of this approach requires only $O(6^N)$ training states, whereas an existing method needs $O(2^{4^N})$. We use this method to construct witnesses of 4 and 5 qubit GHZ states with coefficients agreeing with stabilizer formalism witnesses to within 6.5 percent and 1 percent, respectively. We also use the same training states to generate novel 4 and 5 qubit W state witnesses. Finally, we computationally verify these witnesses on small test sets and propose methods for further verification.

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arXiv2023

Machine-Learning-Derived Entanglement Witnesses

In this work, we show a correspondence between linear support vector machines (SVMs) and entanglement witnesses, and use this correspondence to generate entanglement witnesses for bipartite and tripartite qubit (and qudit) target entangled states. An SVM allows for the construction of a hyperplane that clearly delineates between separable states and the target entangled state; this hyperplane is a weighted sum of observables ('features') whose coefficients are optimized during the training of the SVM. We demonstrate with this method the ability to obtain witnesses that require only local measurements even when the target state is a non-stabilizer state. Furthermore, we show that SVMs are flexible enough to allow us to rank features, and to reduce the number of features systematically while bounding the inference error. This allows us to derive W state witnesses capable of detecting entanglement with fewer measurement terms than the fidelity method dominant in today's literature. The utility of this approach is demonstrated on quantum hardware furnished through the IBM Quantum Experience.

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