Year: 2024
Type: preprint
Abstract: We study quantum state testing where the goal is to test whether $ρ=ρ_0\in\mathbb{C}^{d\times d}$ or $\|ρ-ρ_0\|_1>\varepsilon$, given $n$ copies of $ρ$ and a known state description $ρ_0$. In practice, not all measurements can be easily applied, even using unentangled measurements where each copy is measured separately. We develop an information-theoretic framework that yields unified copy complexity lower bounds for restricted families of non-adaptive measurements through a novel measurement information channel. Using this framework, we obtain the optimal bounds for a natural family of $k$-outcome measurements with fixed and randomized schemes. We demonstrate a separation between these two schemes, showing the power of randomized measurement schemes over fixed ones. Previously, little was known for fixed schemes, and tight bounds were only known for randomized schemes with $k\ge d$ and Pauli observables, a special class of 2-outcome measurements. Our work bridges this gap in the literature.
Source: arXiv (Cornell University)
Authors: Liu, Yuhan, Acharya, Jayadev
Institution: Cornell University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4402952205