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Quantum walks: the first detected transition time
- Source :
- Phys. Rev. Research 2, 033113 (2020)
- Publication Year :
- 2020
-
Abstract
- We consider the quantum first detection problem for a particle evolving on a graph under repeated projective measurements with fixed rate $1/\tau$. A general formula for the mean first detected transition time is obtained for a quantum walk in a finite-dimensional Hilbert space where the initial state $|\psi_{\rm in}\rangle$ of the walker is orthogonal to the detected state $|\psi_{\rm d}\rangle$. We focus on diverging mean transition times, where the total detection probability exhibits a discontinuous drop of its value, by mapping the problem onto a theory of fields of classical charges located on the unit disk. Close to the critical parameter of the model, which exhibits a blow-up of the mean transition time, we get simple expressions for the mean transition time. Using previous results on the fluctuations of the return time, corresponding to $|\psi_{\rm in}\rangle = |\psi_{\rm d}\rangle$, we find close to these critical parameters that the mean transition time is proportional to the fluctuations of the return time, an expression reminiscent of the Einstein relation.
- Subjects :
- Condensed Matter - Statistical Mechanics
Quantum Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. Research 2, 033113 (2020)
- Publication Type :
- Report
- Accession number :
- edsarx.2001.00231
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevResearch.2.033113