Fundamental Limits on the Speed of Evolution of Quantum States

TL;DR

This paper explores new inequalities related to the speed of quantum state evolution, highlighting the role of energy spectrum statistics and a novel link to imaginary-time thermodynamics for understanding quantum dynamics.

Contribution

It introduces new inequalities of Margolus-Levitin-Mandelstam-Tamm type and reveals a correspondence between real-time quantum evolution and imaginary-time thermodynamics.

Findings

Energy spectrum statistics determine quantum evolution speed.

New inequalities provide bounds on quantum state evolution.

Imaginary-time thermodynamics offers insights into quantum dynamics.

Abstract

This paper reports on some new inequalities of Margolus-Levitin-Mandelstam-Tamm-type involving the speed of quantum evolution between two orthogonal pure states. The clear determinant of the qualitative behavior of this time scale is the statistics of the energy spectrum. An often-overlooked correspondence between the real-time behavior of a quantum system and the statistical mechanics of a transformed (imaginary-time) thermodynamic system appears promising as a source of qualitative insights into the quantum dynamics.