Quantum speed limit time in a magnetic resonance

Abstract

A visualization for dynamics of a qudit spin vector in a time-dependent magnetic field is realized by means of mapping a solution for a spin vector on the three-dimensional spherical curve (vector hodograph). The obtained results obviously display the quantum interference of precessional and nutational effects on the spin vector in the magnetic resonance. For any spin the bottom bounds of the quantum speed limit time (QSL) are found. It is shown that the bottom bound goes down when using multilevel spin systems. Under certain conditions the non-nil minimal time, which is necessary to achieve the orthogonal state from the initial one, is attained at spin S=2. An estimation of the product of two and three standard deviations of the spin components are presented. We discuss the dynamics of the mutual uncertainty, conditional uncertainty and conditional variance in terms of spin standard deviations. The study can find practical applications in the magnetic resonance, 3D visualization of computational data and in designing of optimized information processing devices for quantum computation and communication.

LaTeX; 1 figure added, 5 pages, corrected typos arXiv admin note: text overlap with arXiv:1311.2537

References in corpus (9)

• Limits on Fundamental Limits to Computation
• Stronger uncertainty relations for the sum of variances
• Generalized Clausius inequality for nonequilibrium quantum processes
• High-Speed Driving of a Two-Level System
• Experimental Demonstration of Uncertainty Relations for the Triple Components of Angular Momentum
• Minimum-Time Selective Control of Homonuclear Spins
• Rényi formulation of entanglement criteria for continuous variables
• Mutual Uncertainty, Conditional Uncertainty and Strong Sub-Additivity
• Entanglement dynamics in finite qudit chain in consistent magnetic field