Minimum Time for the Evolution to a Nonorthogonal Quantum State and Upper Bound of the Geometric Efficiency of Quantum Evolutions
Abstract
We present a simple proof of the fact that the minimum time TAB for quantum evolution between two arbitrary states jAi and jBi equals TAB = } cosx1F;1[jhAjBij]/DE with DE being the constant energy uncertainty of the system. This proof is performed in the absence of any geometrical arguments. Then, being in the geometric framework of quantum evolutions based upon the geometry of the projective Hilbert space, we discuss the roles played by either minimum-time or maximum energy uncertainty concepts in defining a geometric efficiency measure of quantum evolutions between two arbitrary quantum states. Finally, we provide a quantitative justification of the validity of the inequality 1 even when the system only passes through nonorthogonal quantum states.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 16, 2021
- Accession Number
- AD1196643
Entities
People
- Carlo Cafaro
- Paul M. Alsing
Organizations
- SUNY Polytechnic Institute