Entropic uncertainty relation of a two-qutrit Heisenberg spin model in nonuniform magnetic fields and its dynamics under intrinsic decoherence

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.

Entropic uncertainty relation of a qubit–qutrit Heisenberg spin model and its steering

“…B is approximately anti-correlated with that of the entanglement, which is in good agreement with the result obtained in [31]. Next we focus on the relationship of QMA-EUR with coupling constant J and the anisotropic intensity Δ in the XY-plane.…”

“…The Heisenberg spin chain model can explain many phenomena in magnetic systems and has been applied to the study of quantum correlations, quantum phase transitions, and so on. Some research of QMA-EUR in Heisenberg XX, XXZ and XYZ spin-1/2 or spin-1 models are carried out in [30][31][32][33][34]. But QMA-EUR is rarely analyzed in the Heisenberg XYZ hybrid-spin (1/2,1) model.…”

Nonlocal advantage of quantum coherence and entanglement of two spins under intrinsic decoherence*

“…( 4) with its RHS being expanded to different orders 070307-2 in γ. Based on this solution, decay of Bell nonlocality, [50] entanglement, [51][52][53] and entropic uncertainty, [54,55] have been extensively investigated. By further expanding the RHS of Eq.…”

Quantum‐Memory‐Assisted Entropic Uncertainty Relations

“…Yang et al [94] also studied dynamical characteristics of the entropic uncertainty in a general Heisenberg XYZ model with DM interaction. More recently, Zhang et al [95] and Shi et al [96] investigated quantum-memory-assisted EUR in the higher-dimensional Heisenberg model.…”