Naimark-Dilated $\mathcal{P}\mathcal{T}$-Symmetric Brachistochrone

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