Topological insulator and quantum memory
Abstract
Measurements performed on quantum systems are too specific. Unlike their classical counterparts, quantum measurements can be invasive and destroy the state of interest. Besides, quantumness limits the accuracy of measurements performed on quantum systems. Uncertainty relations define the universal accuracy limit of the quantum measurements. Relatively recently, it was discovered that quantum correlations and quantum memory might reduce the uncertainty of quantum measurements. In this paper, we study two different types of measurements performed on the topological system. Namely, we discuss measurements performed on the spin operators and measurements performed on the canonical pair of operators: momentum and coordinate. We quantify the spin operator's measurements through the entropic measures of uncertainty and exploit the concept of quantum memory. In contrast, for the momentum and coordinate operators, we exploit the improved uncertainty relations. We discover that quantum memory reduces the uncertainties of spin measurements. On the other hand, we prove that the uncertainties in the measurements of the coordinate and momentum operators depend on the value of the momentum and are substantially enhanced at small distances between itinerant and localized electrons (the large-momentum limit). We note that the topological nature of the system leads to the spin-momentum locking. The momentum of the electron depends on the spin, and vice versa. Therefore we suggest an indirect measurement scheme for the momentum and coordinate operators through the spin operator. Due to the factor of quantum memory, such indirect measurements in topological insulators have smaller uncertainties than direct measurements.
- Publication:
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Physical Review B
- Pub Date:
- October 2023
- DOI:
- 10.1103/PhysRevB.108.134411
- arXiv:
- arXiv:2306.11691
- Bibcode:
- 2023PhRvB.108m4411K
- Keywords:
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- Quantum Physics