Gravitational redshift can cause the distortion of photon wave packets; thus, the non-Markovian speedup evolution of a photon system must be controlled by considering gravitational redshift. We analyze the non-Markovian speedup dynamics of a photon system in the amplitude-damping channel or pure-dephasing channel under the effect of gravitational redshift, which is modelled as a beam-splitter operation. We show that the gravitational redshift weakens the non-Markovian dynamical behavior in both channels. For the amplitude-damping channel, the gravitational redshift promotes further speedup evolution of a photon system when the initial coherence of the system is nonzero. A stronger gravitational redshift and larger initial coherence make improving the evolution speed of the photon system easier. For the pure-dephasing channel, the non-Markovian dynamical behavior decreases owing to the gravitational redshift; however, the evolution speed of the photon is not influenced by the gravitational redshift.
Gravitational redshift can cause the distortion of photon wave packets; thus, the non-Markovian speedup evolution of a photon system must be controlled by considering gravitational redshift. We analyze the non-Markovian speedup dynamics of a photon system in the amplitude-damping channel or pure-dephasing channel under the effect of gravitational redshift, which is modelled as a beam-splitter operation. We show that the gravitational redshift weakens the non-Markovian dynamical behavior in both channels. For the amplitude-damping channel, the gravitational redshift promotes further speedup evolution of a photon system when the initial coherence of the system is nonzero. A stronger gravitational redshift and larger initial coherence make improving the evolution speed of the photon system easier. For the pure-dephasing channel, the non-Markovian dynamical behavior decreases owing to the gravitational redshift; however, the evolution speed of the photon is not influenced by the gravitational redshift.
As photons propagate through curved spacetime, gravitational effects become unavoidable. In particular, gravitational redshift can induce significant distortion in photon wave packets, making it es?sential to investigate parameter estimation within this context. While previous research has focused on single-parameter estimation using the quantum Cramer-Rao bound, the multiparameter scenario remains largely unexplored. In this work, we investigate multiparameter quantum estimation for a photon system subject to gravitational redshift under both amplitude-damping and Ohmic-like dephasing channels. Our analysis reveals that the quantum Cramer-Rao bound fails to provide a tight error bound for the two-parameter estimation involving the initial phase and weight parameters inboth types of noisy channels. To overcome this limitation, we numerically compute two tighter error bounds, i.e., the Holevo Cramer-Rao bound and the Nagaoka bound, when utilizing a semidefinite program. We demonstrate that the Nagaoka bound yields the tightest error bound among all considered bounds, consistent with the general hierarchy of multiparameter quantum estimation. Furthermore, for the three-parameter estimation, including the initial weight parameter, the phase parameter, and the strength of gravitational redshift, we observe significantly enhanced estimation precision in the strong-coupling regime compared to the weak-coupling regime under the amplitude-damping channel. Similarly, in the Ohmic-like dephasing channel, the sub-Ohmic regime consistently affords higher precision than the Ohmic and super-Ohmic regimes.
Abstract We illustrate two linear configurations (one-side model and two-side model) for implementing a non-Markovian speedup evolution of a massive particle gravitationally coupled with a controllable environment: multiple massive particles. By controlling the environment, for instance by choosing a judicious the mass of the environmental particles or by changing the separation distance of each massive particle, two dynamical crossover behaviors from Markovian to non-Markovian and from no-speedup to speedup are achieved due to the gravitational interactions between the system particle and each environmental particle. Numerical calculation also shows that the critical mass of the environmental particles or the critical separation distance for these two dynamical crossover behaviors restrict each other directly. The larger the value of the mass of the environmental particles is, the smaller the value of the critical separation distance should be requested. In this work, the non-Markovian dynamics is the principal physical reason for the speedup evolution of a quantum system. Particularly, the non-Markovianity of the system mass particle in the two-side model has better correspondence with the quantum speed limit time than that in the one-side model.
Gravitational effects are inevitable as photons propagate in curved spacetime, and especially gravitational redshift can cause the distortion of photon wave packets, so it is very meaningful and necessary to study the controllable parameter estimation under the gravitational-redshift effect. Here, in correlated noisy channels under the effect of gravitational redshift, we analyze the precision of phase estimation of two-qubit system states which is introduced by a symplectic matrix for two-mode entangled states (two types of Werner-like states). We find that the gravitational redshift could decrease the precision of phase estimation of these two-qubit system states. Interestingly, by adjusting the correlation parameter of the channels and the initial entanglement, the precision of phase estimation in noisy channels under the influence of gravitational redshift could be enhanced. The larger the initial entanglement and the stronger the correlation of the channels, the higher the precision of phase estimation obtained. Particularly, for two types of Werner-like initial states, the phase estimation of the system is more robust for the Werner-like initial state $\mathrm{cos}(\frac{\ensuremath{\alpha}}{2})|01⟩+{e}^{i\ensuremath{\phi}}\mathrm{sin}(\frac{\ensuremath{\alpha}}{2})|10⟩$ as the strong enough gravitational-redshift effect.
In this work, we investigate the dynamical process of an open quantum system under the action of quantum cyclic n-switch in generalized amplitude-damping channels and depolarizing channels. The quantum cyclic n-switch operation is introduced by an external control system. Our results show that the quantum switch can regulate the dynamical behavior of the system dynamics and achieve non-Markovian speedup dynamics. Increasing the dimension of the control system can significantly enhance the evolution speed of the system's non-Markovian dynamics. For the generalized amplitude-damping channels, when the influence of thermal noise is intense, the greater the quantum cyclic n-switch is, the lower the initial coherence is, and the more conducive it is to the acceleration of the quantum state evolution speed. In the depolarizing channels, under the action of quantum cyclic n-switch, the evolution speed of the system dynamics is directly related to the non-Markovianity and is independent of the initial coherence of the system.
As is well known, the quantum evolution speed of quantum state can never be accelerated in the Markovian regime without any operators on the system. The Hamiltonian corrections induced by the action of coherent driving forces are often used to fight dissipative and decoherence mechanisms in experiments. For this reason, considering three noisy channels (the phase-flip channel, the amplitude damping channel and the depolarizing channel), we propose a scheme of speedup evolution of an open system by controlling an external unitary coherent driving operator on the system. It is shown that, in the presence of the coherent driving, no-speedup evolution can be transformed into quantum speedup evolution in the Markovian dynamics process. Additionally, under the fixed coherent driving strength in the above three noisy channels, the best way to achieve the most degree of quantum speedup for the system has been acquired by rotating the system with appropriate driving direction angles, respectively. Finally, we conclude that the reason for this acceleration is not the non-Markovian dynamical behavior of the system but due to the oscillation of geometric distance between the initial state and the target final state.
In this paper, the non-Markovian dissipative dynamics of the phase-damped Jaynes-Cummings model in the presence of a classical homogeneous gravitational field will be analyzed. The model consists of a moving two-level atom simultaneously exposed to the gravitational field and a single-mode traveling radiation field in the presence of a non-Markovian phase damping mechanism. First, the non-Markovian master equation for the reduced density operator of the system in terms of a Hamiltonian describing the atom-field interaction in the presence of a homogeneous gravitational field will be presented. Then, the superoperator technique will be generalized and an exact solution of the non-Markovian master equation will be obtained. Assuming that initially the radiation field is prepared in a Glauber coherent state and the two-level atom is in the excited state, the influence of gravity on the temporal evolution of collapses and revivals of the atomic population inversion, atomic dipole squeezing, and photon counting statistics of the radiation field in the presence of the non-Markovian phase damped will be investigated.