Limitations of Quantum Measurements and Operations of Scattering Type under the Energy Conservation Law
Year: 2022
Type: preprint
Abstract: It is important to improve the accuracy of quantum measurements and operations both in engineering and fundamental physics. It is known, however, that the achievable accuracy of measurements and unitary operations are generally limited by conservation laws according to the Wigner-Araki-Yanase theorem (WAY theorem) and its generalizations. Although many researches have extended the WAY theorem quantitatively, most of them, as well as the original WAY theorem, concern only additive conservation laws like the angular momentum conservation law. In this paper, we explore the limitation incurred by the energy conservation law, which is universal but is one of the non-additive conservation laws. We present a lower bound for the error of a quantum measurement using a scattering process satisfying the energy conservation law. We obtain conditions that a control system Hamiltonian must fulfill in order to implement a controlled unitary gate with zero error when a scattering process is considered. We also show the quantitative relationship between the upper bound of the gate fidelity of a controlled unitary gate and the energy fluctuation of systems when a target system and a control system are both one qubit.
Source: arXiv (Cornell University)
Authors: Katsube, Ryota, Ozawa, Masanao, Hotta, Masahiro
Institution: Tohoku University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: New Developments in Interactive Proofs - From Classical to Quantum, G1496355786, G3143016988, Machine Learning using Quantum-Classical Hybrid Algorithms, New Developments in the Theory of Quantum Instruments, G6520859003, G6593834203, G7568984604, Research of spacetime quantum information and quantum measurement
OpenAlex ID: W4310269638