The effects of single-quantum states and entangled states in quantum information based on fractional time Schrödinger equation
Source abstract
Abstract
Fractional time quantum mechanics is a method for the description of time evolution of quantum dynamics based on fractional derivatives. In this research, by applying fractional order quantum mechanics to quantum information, we introduced a new fractional time Schrödinger equation (FTSE) and constructed two models for the simulation of single-quantum states and entangled states under noise. We find that the results obtained from the two models are consistent with existing physical phenomena under the influence of the FTSE. We also prove that these two models are stable for fractional order α.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Quantum Information and Cryptography · Quantum Computing Algorithms and Architecture · Quantum Mechanics and Applications
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Sichuan University College of Mathematics , Chengdu,
Funding
Natural Science Foundation of Sichuan Province
References (36)
Show source-provided references
1. Sur quelques questions de géométrie et de mécanique, et sur un nouveau genre de calcul pour résoudre ces questions
2. Versuch einer allgemeinen auffassung der integration und differentiation
3. Solution de quelques problèmes á l’aide d’intégrales définies
4. Sur le calcul des dérivées à indices quelconques
5. Some properties of integrals of fractional order
6. 1977
7. Fractional quantum mechanics and Lévy path integrals10.1016/s0375-9601(00)00201-2 ↗
8. Fractional corresponding operator in quantum mechanics and applications: A uniform fractional Schrödinger equation in form and fractional quantization methods10.1016/j.aop.2014.07.007 ↗
9. Phase transitions of energy and wave functions and bound states in the continuum10.1103/physreva.93.042106 ↗
10. Stabilization of impulsive fractional-order dynamic systems involving the Caputo fractional derivative of variable-order via a linear feedback controller10.1016/j.chaos.2021.111525 ↗
11. The transition of energy and bound states in the continuum of fractional Schrödinger equation in gravitational field and the effect of the minimal length10.1016/j.cnsns.2018.05.002 ↗
12. Time dependent solutions for fractional coupled Schrödinger equations10.1016/j.amc.2018.10.074 ↗
13. Time fractional Schrödinger equation10.1063/1.1769611 ↗
14. Quantization method and Schrödinger equation of fractional time and their weak effects on Hamiltonian: Phase transitions of energy and wave functions10.1016/j.cnsns.2020.105531 ↗
15. Fractional Schrödinger equation10.1103/physreve.66.056108 ↗
16. Generalized fractional Schrödinger equation with space-time fractional derivatives10.1063/1.2716203 ↗
17. Space–time fractional Schrödinger equation with time-independent potentials10.1016/j.jmaa.2008.03.061 ↗
18. Time fractional Schrödinger equation with a limit based fractional derivative10.1016/j.chaos.2022.111941 ↗
19. The fractional Schrödinger equation for delta potentials10.1063/1.3525976 ↗
20. Fractional Feynman-Kac equation for non-Brownian functionals10.1103/physrevlett.103.190201 ↗
21. Fractional Schrödinger equation for a particle moving in a potential well10.1063/1.4777472 ↗
22. On distributions of functionals of anomalous diffusion paths10.1007/s10955-010-0086-6 ↗
23. Time fractional Schrödinger equation revisited10.1155/2013/290216 ↗
24. Fractional-time quantum dynamics10.1103/physreve.80.022103 ↗
25. Time fractional quantum mechanics10.1016/j.chaos.2017.04.010 ↗
26. Unitary evolution for a two-level quantum system in fractional-time scenario10.1103/physreve.106.054126 ↗
27. Bounded solution structure of Schrödinger equation in the presence of the minimal length and its effect: Bound states in the continuum are universal10.1016/j.cnsns.2021.105694 ↗
28. Strichartz estimates for space-time fractional Schrödinger equations10.1016/j.jmaa.2020.123999 ↗
29. Local well-posedness of semilinear space-time fractional Schrödinger equation10.1016/j.jmaa.2019.06.077 ↗
30. Accurate sets of solitary solutions for the quadratic–cubic fractional nonlinear Schrödinger equation10.1063/5.0050624 ↗
31. An algorithm for fractional Schrödinger equation in case of morse potential10.1063/1.5113593 ↗
32. 2000
33. Quantum communication10.1038/nphoton.2007.22 ↗
34. Advances in coherent magnonics10.1038/s41578-021-00332-w ↗
35. Time fractional evolution of a single quantum state and entangled state10.1016/j.chaos.2021.110930 ↗
36. Entanglement of formation of an arbitrary state of two qubits10.1103/physrevlett.80.2245 ↗