Comparison between the effects of Hamiltonian and Liouvillian exceptional points on the Leggett–Garg inequality and no-signaling-in-time conditions

Abstract In this paper, we investigate the effect of exceptional points (EPs) on the violation of Leggett–Garg inequality (LGI) and no-signaling-in-time (NSIT) conditions and compare the different effects between the Hamiltonian EP (HEP) and Liouvillian EP (LEP) on those violations. We consider an open system consisting of two coupled qubits and each qubit is contacted with a thermal bath at a different temperature. In the case of omitting quantum jumps, we find that the system exhibits a second-order HEP, which separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI and NSIT conditions can be violated in both regimes and not violated at the HEP. In the case of without omitting quantum jumps, we find that the system exhibits a third-order LEP, which also separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI can only be violated in the underdamped regime with large coupling strength between the qubits. Conversely, the NSIT conditions can be violated in both regimes, as well as at the LEP, except in the overdamped regime with small coupling strength between the qubits. Comparing the violations of the LGI and NSIT conditions with HEP and LEP, we find that the quantum jumps would reduce the generation of coherence, enhance the decoherence, and lead to narrower parameter regimes that the LGI and NSIT conditions can be violated. Furthermore, in both cases, the NSIT conditions can be violated in a wider parameter regime than the LGI.