arXiv subjects

Jacob Beckey

Publications and source records attributed to Jacob Beckey.

4 recordsLinked to original sources

arXiv2026

Tight Bounds for Purity and Product Testing from Partial Transposition

Coherent measurements across multiple copies of an unknown quantum state can substantially reduce the number of samples required to learn its properties, but remain experimentally challenging. Current experiments typically prepare and measure one copy at a time, potentially adapting later measurements to earlier outcomes. A central challenge is adaptivity, which makes the space of possible measurement strategies difficult to characterize. The positive-partial-transpose (PPT) relaxation bypasses this complexity by considering a larger, mathematically tractable class of measurements, at the risk of weakening the resulting bounds. Here we show, surprisingly, that the relaxation loses nothing at the level of asymptotic sample complexity for two fundamental tasks: purity testing and product testing. In both cases, lower bounds against the full class of PPT measurements are matched by nonadaptive single-copy protocols. Moreover, our proof requires only basic symmetric subspace identities, providing a simple route to sharp lower bounds for adaptive single-copy measurements.

quant-ph↗

arXiv2026

An Optimal Analysis of the Product Test

Product testing, i.e., deciding whether a pure multipartite quantum state is fully unentangled across a specified tensor decomposition, serves as a bridge between quantum property testing, unentangled quantum proof systems, and tensor optimization. Despite being a fundamental property testing task and having many applications, the product test's exact (worst-case) acceptance probability curve has yet to be fully determined. In this work, we determine this curve exactly. Let $\omega$ be the maximum squared overlap of the input with a product state, and let $\mathrm{PT}_n(\omega)$ be the largest possible acceptance probability of the product test over all $n$-partite pure states with product overlap $\omega$, allowing arbitrary finite local dimensions. We prove that, for every $n\ge 2 $ and every $\omega\in(0,1] $, $$ \mathrm{PT}_n(\omega)=\frac12\left(1+m\omega^2+(1-m\omega)^2\right), $$ where $m=\lfloor1/\omega\rfloor $. The formula recovers the previously known tight section of the curve for $\omega\ge 1/2 $, resolves all low-overlap regimes $\omega<1/2 $, and implies $\mathrm{PT}_n(\omega)\to 1/2 $ as $\omega\to 0$ answering an open problem in [Soleimanifar and Wright, SODA 2022]. As a complexity-theoretic application, our results improve the one-shot soundness parameter in the Harrow-Montanaro reduction from $\mathsf{QMA}(k)$ to $\mathsf{QMA}(2)$. Our techniques, built upon those of Soleimanifar and Wright, allow us to resolve these open questions while remaining surprisingly elementary.

quant-ph↗

arXiv2025

Product testing with single-copy measurements

In this work, we study the sample complexity of two variants of product testing when restricted to single-copy measurements. In particular, we consider both bipartite product testing (i.e., does there exist at least one non-trivial cut across which the state is product) and multipartite product testing (i.e., is the state fully product across every cut). For the first variant, we prove an exponential lower bound on the sample complexity of any algorithm for this task which utilizes only single-copy measurements. When comparing this with known efficient algorithms that utilize multi-copy measurements, this establishes an exponential separation for this and several related entanglement learning tasks. For the second variant, we prove another sample lower bound that establishes a separation between single- and multi-copy strategies. To obtain our results, we prove a crucial technical lemma that gives a lower bound on the overlap between tensor products of permutation operators acting on subsystems of states that themselves carry a tensor structure. Finally, we provide an algorithm for multipartite product testing using only single-copy, local measurements, and we highlight several interesting open questions arising from this work.

quant-ph↗

arXiv2023

Quantum measurements in fundamental physics: a user's manual

We give a systematic theoretical treatment of linear quantum detectors used in modern high energy physics experiments, including dark matter cavity haloscopes, gravitational wave detectors, and impulsive mechanical sensors. We show how to derive the coupling of signals of interest to these devices, and how to calculate noise spectra, signal-to-noise ratios, and detection sensitivities. We emphasize the role of quantum vacuum and thermal noise in these systems. Finally, we review ways in which advanced quantum techniques -- squeezing, non-demolition measurements, and entanglement -- can be or currently are used to enhance these searches.

hep-ph↗