2020/11/02 by Timothy Qian, Jacob Bringewatt, Igor Boettcher +3
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Duality (order theory) #Field (mathematics) #Function (biology) #Mathematical physics #Mathematics #Parameterized complexity #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum field theory #Quantum mechanics #Qubit #quant-ph
paper · pdf · doi:10.1103/physreva.103.l030601
published as Phys. Rev. A 103, 030601 (2021) · 15 pages, 1 figure
arxiv created 2020/11/02 · openalex publication_date 2021/03/29 · arxiv updated 2021/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We consider a quantum sensor network of qubit sensors coupled to a field f(\mathbitx;\mathbit\ensuremathθ) analytically parameterized by the vector of parameters \mathbit\ensuremathθ. The qubit sensors are fixed at positions \mathbitx1,\ensuremath⋯,\mathbitxd. While the functional form of f(\mathbitx;\mathbit\ensuremathθ) is known, the parameters \mathbit\ensuremathθ are not. We derive saturable bounds on the precision of measuring an arbitrary analytic function q(\mathbit\ensuremathθ) of these parameters and construct the optimal protocols that achieve these bounds. Our results are obtained from a combination of techniques from quantum information theory and duality theorems for linear programming. They can be applied to many problems, including optimal placement of quantum sensors, field interpolation, and the measurement of functionals of parametrized fields.