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.
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.
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.
Abstract The uncertainty principle configures a low bound to the measuring precision for a pair of non-commuting observables, and hence is considerably nontrivial to quantum precision measurement in the field of quantum information theory. In this letter, we consider the entropic uncertainty relation (EUR) in the context of quantum memory in a two-qubit isotropic Heisenberg spin chain. Specifically, we explore the dynamics of EUR in a practical scenario, where two associated nodes of a one-dimensional XXX -spin chain, under an inhomogeneous magnetic field, are connected to a thermal entanglement. We show that the temperature and magnetic field effect can lead to the inflation of the measuring uncertainty, stemming from the reduction of systematic quantum correlation. Notably, we reveal that, firstly, the uncertainty is not fully dependent on the observed quantum correlation of the system; secondly, the dynamical behaviors of the measuring uncertainty are relatively distinct with respect to ferromagnetism and antiferromagnetism chains. Meanwhile, we deduce that the measuring uncertainty is dramatically correlated with the mixedness of the system, implying that smaller mixedness tends to reduce the uncertainty. Furthermore, we propose an effective strategy to control the uncertainty of interest by means of quantum weak measurement reversal. Therefore, our work may shed light on the dynamics of the measuring uncertainty in the Heisenberg spin chain, and thus be important to quantum precision measurement in various solid-state systems.
Abstract In this study, the quantum-memory assisted entropic uncertainty (QM-EU) and entanglement dynamics of the two-qubit Heisenberg XXX chain have been explored in the presence of intrinsic decoherence. The effect of the x-component of Dzyaloshinskii-Moriya (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions has been considered. The generation and preservation of quantum memory and entanglement have been examined for various values of the DM, KSEA, spin-spin, and spin coupling strengths. The uncertainty negatively affects the entanglement and both have anti-correlation. The absence and presence of intrinsic decoherence prevail in differing impacts on the dynamics of the system. In the first case, prolonged entanglement preservation, uncertainty suppression, and oscillatory dynamics have been observed. Moreover, in order to achieve the best-prolonged entanglement preservation and relative reduction of the entropic uncertainty, we have analyzed several parameter settings. We find that the effects of raising the DM, KSEA, and spin-spin interaction individually and simultaneously are different. The individual and simultaneous increase of the DM, KSEA, and spin-spin interaction parameters control the degree of entanglement, entropic uncertainty, and primarily the dynamics of the system.
Abstract We investigate the quantum-memory-assisted entropic uncertainty relation (QMA-EUR) in a Heisenberg XYZ mixed-spin (1/2, 1) model. Coupling strength, Dzyaloshinskii–Moriya (DM) interaction and inhomogeneous magnetic field, respectively, contributing to QMA-EUR by a thermal entanglement in the hybrid-spin model are studied in detail. Furthermore, we compare the uncertainty of the bipartite hybrid model with those of qubit–qubit and qutrit–qutrit systems. Meanwhile, the effects of local PT-symmetric operation and weak measurement on the steering of entropic uncertainty are analyzed. We find that the local PT-symmetric operation can reduce the entropic uncertainty, and the entropic uncertainty can also be decreased by weak measurement reversal.
Abstract By assuming a general pure state and a mixed Werner state as two initial states, we investigate the time evolution of entropic uncertainty bound in the presence of quantum memory for a two-qubit system interacting with an XY spin chain regarded as an environment constrained to carry the energy current. We obtain an explicit relationship between the entropic uncertainty bound and decoherence factor, and analytically study the dynamical process of entropic uncertainty bound for both weak and strong-coupling cases in two initial states. Our results reveal that the evolution of entropic uncertainty bound depends not only on the energy current, the system-environment couplings and the anisotropy parameter but also on the size of the environmental XY spin chain. Interestingly, we find that the entropic uncertainty bound can be suppressed by reducing the energy current on the environmental spin chain in a weak-coupling region, however, it has no sensitivity to the energy current in a strong-coupling region.
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.