The Naimark dilated PT-symmetric brachistochrone

TL;DR

This paper demonstrates how PT-symmetric quantum systems can be embedded into Hermitian systems in higher dimensions, enabling potential experimental realization of ultra-fast quantum evolution in entangled spin systems.

Contribution

It introduces a Naimark dilation approach to PT-symmetric brachistochrone systems, linking them to Hermitian systems for experimental feasibility.

Findings

PT-symmetric brachistochrone can be embedded in Hermitian systems

Enables experimental implementation of ultra-fast quantum evolution

Provides a framework for studying PT-symmetric quantum dynamics

Abstract

The quantum mechanical brachistochrone system with PT-symmetric Hamiltonian is Naimark dilated and reinterpreted as subsystem of a Hermitian system in a higher-dimensional Hilbert space. This opens a way to a direct experimental implementation of the recently hypothesized PT-symmetric ultra-fast brachistochrone regime of [C. M. Bender et al, Phys. Rev. Lett. {\bf 98}, 040403 (2007)] in an entangled two-spin system.