By assuming the effect of dissipative environment and the Hamiltonian XY-model and external magnetic field, the time evolution of the entropic uncertainty relation (EUR) in the presence of quantum-memory and the dynamics of quantum correlations (QC) are investigated. It is shown that EUR and QC may evolve in different ways during the time. However, they can behave similarly when the time tends to infinity. The effects of external magnetic field and anisotropic parameter are different on the dynamics of EUR and QC.
By assuming the effect of dissipative environment and the Hamiltonian XY-model and external magnetic field, the time evolution of the entropic uncertainty relation (EUR) in the presence of quantum-memory and the dynamics of quantum correlations (QC) are investigated. It is shown that EUR and QC may evolve in different ways during the time. However, they can behave similarly when the time tends to infinity. The effects of external magnetic field and anisotropic parameter are different on the dynamics of EUR and QC.
Abstract The precision of measurements for two incompatible observables in a physical system can be improved with the assistance of quantum memory. In this paper, we investigate the quantum-memory-assisted entropic uncertainty relation for a spin-1 Heisenberg model in the presence of external magnetic fields, the systemic quantum entanglement (characterized by the negativity) is analyzed as contrast. Our results show that for the XY spin chain in thermal equilibrium, the entropic uncertainty can be reduced by reinforcing the coupling between the two particles or decreasing the temperature of the environment. At zero-temperature, the strong magnetic field can result in the growth of the entropic uncertainty. Moreover, in the Ising case, the variation trends of the uncertainty are relied on the choices of anisotropic parameters. Taking the influence of intrinsic decoherence into account, we find that the strong coupling accelerates the inflation of the uncertainty over time, whereas the high magnetic field contributes to its reduction during the temporal evolution. Furthermore, we also verify that the evolution behavior of the entropic uncertainty is roughly anti-correlated with that of the entanglement in the whole dynamical process. Our results could offer new insights into quantum precision measurement for the high spin solid-state systems.
In this paper, we study the thermal dynamics of quantum correlations and uncertainty relation in a three-qubit spin chain under the effect of Hamiltonian XY model, Dzyaloshinskii–Moriya (DM) interaction and external magnetic field. The results show that quantum correlations behave contrary to uncertainty under the effect of thermal dynamics and external magnetic field. However, they evolve in the same way under effect of DM interaction and spin coupling. DM interaction, magnetic field and spin coupling enhance quantum correlations.
Abstract In this work, we investigate the dynamics of quantum-memory-assisted entropic uncertainty relation (EUR) and quantum correlation quantified by entropic discord and geometric discord within the Markovian reservoir and non-Markovian reservoir. Particularly, when the initial state is a pure sate or mixed state the EUR gradually increases during the evolution at first, but subsequently tends to stable in the long-time limit. On other hand, for the separable state the EUR almost keeps constant. In contrast, quantum discord decay asymptotically to zero for all types of initial states. As an application, we prove that both two quantum discords witnessed by the EUR are determined by the version of discord chosen, which regardless of the reservoir.
Abstract One of the fundamental arguments in quantum information theory is the uncertainty principle. According to this principle, two incompatible observables cannot be measured with high precision at the same time. In this work, we will use the entropic uncertainty relation in the presence of quantum memory. Considering a dissipative environment, the effects of the detuning between the transition frequency of a quantum memory and the center frequency of a cavity on entropic uncertainty bound and the quantum correlation between quantum memory and measured particle will be studied. It is shown that by increasing the detuning, quantum correlation is maintained. As a result, due to the inverse relationship between the uncertainty bound and quantum correlations, the measurement results are guessed more accurately.
One of the fundamental arguments in quantum information theory is the uncertainty principle. In accordance with this principle, two incompatible observables cannot be measured with high precision at the same time. In this work, we will use the entropic uncertainty relation in the presence of quantum memory. Considering a dissipative environment, the effects of the detuning between the transition frequency of a quantum memory and the center frequency of a cavity on entrpic uncertainty bound and quantum correlation between quantum memory and measured particle will be studied. It is shown that by increasing the detuning, quantum correlation is maintained. As a result, due to the inverse relationship between the uncertainty bound and quantum correlation, the measurement results is guessed more accurately.
Abstract The uncertainty principle provides a nontrivial bound to expose the precision for the outcome of the measurement on a pair of incompatible observables in a quantum system. Therefore, it is of essential importance for quantum precision measurement in the area of quantum information processing. Herein, we investigate quantum-memory-assisted entropic uncertainty relation (QMA-EUR) in a two-qubit Heisenberg X Y Z spin chain. Specifically, we observe the dynamics of QMA-EUR in a realistic model there are two correlated sites linked by a thermal entanglement in the spin chain with an inhomogeneous magnetic field. It turns out that the temperature, the external inhomogeneous magnetic field and the field inhomogeneity can lift the uncertainty of the measurement due to the reduction of the thermal entanglement, and explicitly higher temperature, stronger magnetic field or larger inhomogeneity of the field can result in inflation of the uncertainty. Besides, it is found that there exists distinct dynamical behaviors of the uncertainty for ferromagnetism ( J < 0 ) and antiferromagnetism ( J > 0 ) chains. Moreover, we also verify that the measuring uncertainty is dramatically anti-correlated with the purity of the bipartite spin system, the greater purity can result in the reduction of the measuring uncertainty, vice versa. Therefore, our observations might provide a better understanding of the dynamics of the entropic uncertainty in the Heisenberg spin chain, and thus shed light on quantum precision measurement in the framework of versatile systems, particularly solid states.