Extreme violation of the Leggett-Garg inequality in nonunitary dynamics with complex energies

Abstract

We study the Leggett-Garg inequality (LGI) of a two-level system (TLS) undergoing coherent dynamics described by a non-Hermitian Hamiltonian and Lindblad equation with no quantum jumps. The nonlinear Bloch equation for the TLS density matrix predicts violations of LGI above the TLS Lüders bound of , approaching the extremal case of LGI parameter in the -symmetric region and the -broken region. We show that these findings are reproduced by using postselection to remove instantaneous quantum jumps from a three-level system described by the Lindblad equation with a single spontaneous emission dissipator. We trace the excesses beyond the standard quantum limit of to a nonuniform speed of evolution on the Bloch sphere. Finally, we consider the effects of competing Lindblad dissipators on the postselected non-Hermitian dynamics and the viability of observing exceeding the Lüder bound and approaching its algebraic maximum of three in current experimental setups.