Measurement uncertainty and entanglement in the hybrid-spin Heisenberg model

Abstract In this work, we study the dynamics of entropy-based uncertainty under a hybrid-spin (1, 1/2) Heisenberg XXZ model with an inhomogeneous magnetic field. Specifically, we examine the effect of the magnetic field strength B and coupling strength J of the two spins on the measurement uncertainty and the entanglement of the considered system, and nontrivially reveal that the magnetic field and coupling strength are responsible for the uncertainty dynamics associated with incompatible measurements. Interestingly, the entropic uncertainty eventually reaches a stable value with growing B , and the entanglement quantified by negativity eventually reduces to zero. Contrarily, a larger coupling constant J effectively reduces uncertainty. In addition, the effects of temperature T also are evaluated in the current framework. Furthermore, the relationship between uncertainty and entanglement is discussed; we claim that negativity and entropic uncertainty are approximately inversely correlated. Therefore, our observations are expected to be helpful in illustrating the dynamical entropy-based uncertainty in a hybrid Heisenberg spin-chain model and thus would be useful for realistic quantum information processing.