Exact dimension estimation of interacting qubit systems assisted by a single quantum probe
Name
PhysRevA.96.062334.pdf
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379.99 KB
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Adobe PDF
Checksum (MD5)
80275d8d71a85280c598b5dd032f8ab3
Author(s)
Sone, Akira
Cappellaro, Paola
Date Issued
December 2017
Journal
Physical Review A
Publisher
American Physical Society
Citation
Sone, Akira, and Paola Cappellaro. “Exact Dimension Estimation of Interacting Qubit Systems Assisted by a Single Quantum Probe.” Physical Review A, vol. 96, no. 6, Dec. 2017. © 2017 American Physical Society
Version
Final published version
Abstract
Estimating the dimension of an Hilbert space is an important component of quantum system identification. In quantum technologies, the dimension of a quantum system (or its corresponding accessible Hilbert space) is an important resource, as larger dimensions determine, e.g., the performance of quantum computation protocols or the sensitivity of quantum sensors. Despite being a critical task in quantum system identification, estimating the Hilbert space dimension is experimentally challenging. While there have been proposals for various dimension witnesses capable of putting a lower bound on the dimension from measuring collective observables that encode correlations, in many practical scenarios, especially for multiqubit systems, the experimental control might not be able to engineer the required initialization, dynamics, and observables. Here we propose a more practical strategy that relies not on directly measuring an unknown multiqubit target system, but on the indirect interaction with a local quantum probe under the experimenter's control. Assuming only that the interaction model is given and the evolution correlates all the qubits with the probe, we combine a graph-theoretical approach and realization theory to demonstrate that the system dimension can be exactly estimated from the model order of the system. We further analyze the robustness in the presence of background noise of the proposed estimation method based on realization theory, finding that despite stringent constrains on the allowed noise level, exact dimension estimation can still be achieved.
MIT Department
Massachusetts Institute of Technology. Department of Nuclear Science and Engineering
Massachusetts Institute of Technology. Research Laboratory of Electronics
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DOI of Published Version
https://doi.org/10.1103/PhysRevA.96.062334
