{"title":"Limitations on the maximal level of entanglement of two singlet–triplet qubits in GaAs quantum dots","authors":"Igor Bragar, Łukasz Cywiński","doi":"10.1007/s11128-024-04407-9","DOIUrl":null,"url":null,"abstract":"<div><p>We analyze in detail a procedure of entangling of two singlet–triplet (<i>S</i>–<span>\\(T_{0}\\)</span>) qubits operated in a regime when energy associated with the magnetic field gradient, <span>\\(\\Delta B_{z}\\)</span>, is an order of magnitude smaller than the exchange energy, <i>J</i>, between singlet and triplet states (Shulman et al. in Science 336:202, 2012). We have studied theoretically a single <i>S</i>–<span>\\(T_{0}\\)</span> qubit in free induction decay and spin echo experiments. We have obtained analytical expressions for the time dependence of components of its Bloch vector for quasistatic fluctuations of <span>\\(\\Delta B_{z}\\)</span> and quasistatic or dynamical <span>\\(1/f^{\\beta }\\)</span>-type fluctuations of <i>J</i>. We have then considered the impact of fluctuations of these parameters on the efficiency of the entangling procedure which uses an Ising-type coupling between two <i>S</i>–<span>\\(T_{0}\\)</span> qubits. In particular, we have obtained an analytical expression for evolution of two qubits affected by <span>\\(1/f^{\\beta }\\)</span>-type fluctuations of <i>J</i>. This expression indicates the maximal level of entanglement that can be generated by performing the entangling procedure. Our results deliver also an evidence that in the above-mentioned experiment <i>S</i>–<span>\\(T_{0}\\)</span> qubits were affected by uncorrelated <span>\\(1/f^{\\beta }\\)</span> charge noises.</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11128-024-04407-9.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Information Processing","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11128-024-04407-9","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We analyze in detail a procedure of entangling of two singlet–triplet (S–\(T_{0}\)) qubits operated in a regime when energy associated with the magnetic field gradient, \(\Delta B_{z}\), is an order of magnitude smaller than the exchange energy, J, between singlet and triplet states (Shulman et al. in Science 336:202, 2012). We have studied theoretically a single S–\(T_{0}\) qubit in free induction decay and spin echo experiments. We have obtained analytical expressions for the time dependence of components of its Bloch vector for quasistatic fluctuations of \(\Delta B_{z}\) and quasistatic or dynamical \(1/f^{\beta }\)-type fluctuations of J. We have then considered the impact of fluctuations of these parameters on the efficiency of the entangling procedure which uses an Ising-type coupling between two S–\(T_{0}\) qubits. In particular, we have obtained an analytical expression for evolution of two qubits affected by \(1/f^{\beta }\)-type fluctuations of J. This expression indicates the maximal level of entanglement that can be generated by performing the entangling procedure. Our results deliver also an evidence that in the above-mentioned experiment S–\(T_{0}\) qubits were affected by uncorrelated \(1/f^{\beta }\) charge noises.
期刊介绍:
Quantum Information Processing is a high-impact, international journal publishing cutting-edge experimental and theoretical research in all areas of Quantum Information Science. Topics of interest include quantum cryptography and communications, entanglement and discord, quantum algorithms, quantum error correction and fault tolerance, quantum computer science, quantum imaging and sensing, and experimental platforms for quantum information. Quantum Information Processing supports and inspires research by providing a comprehensive peer review process, and broadcasting high quality results in a range of formats. These include original papers, letters, broadly focused perspectives, comprehensive review articles, book reviews, and special topical issues. The journal is particularly interested in papers detailing and demonstrating quantum information protocols for cryptography, communications, computation, and sensing.