Lindbladian-Induced Alignment in Quantum Measurements
arXiv:2301.02664 · doi:10.1007/s10701-022-00659-6
Abstract
An expression of the Lindbladian form is proposed that ensures an unambiguous time-continuous reduction of the initial system-pointer wave-packet to one in which the readings and the observable's values are aligned, formalized as the transition from an outer product to an inner product of the system's and apparatus' density matrices. The jump operators are in the basis of the observables, with uniquely determined parameters derived from the measurement set-up (thereby differing from S. Weinberg's Lindbladian resolution of wave-packet formalism) and conforming to Born's probability rules. The novelty lies in formalising the adaptability of the surroundings (including the measuring device) to the mode of observation. Accordingly, the transition is of finite duration (in contrast to its instantaneousness in the von Neumann's formulation). This duration is estimated for a simple half-spin-like model.
arXiv comment13 pages, 2 figures
References in corpus (10)
- The maximum speed of dynamical evolution
- A short introduction to the Lindblad Master Equation
- Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
- A Straightforward Introduction to Continuous Quantum Measurement
- Fundamentals of Quantum Information Theory
- Underground test of gravity-related wave function collapse
- Speed limit for open quantum systems
- On the mathematical Structure of Quantum Measurement Theory
- What Happens in a Measurement?
- Optimizing thermalizations