Quantum-memory-assisted entropic uncertainty relation in a HeisenbergXYZchain with an inhomogeneous magnetic field

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 XYZ 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.

Entropic Uncertainty in Spin XY Model with Long-Range Interactions

“…It is worth mentioning that the close relation between mixedness and uncertainty has been discussed widely as a concerned topic [ 33 , 34 , 35 , 36 , 37 ]. The dynamics of entropic uncertainty relation in a Heisenberg spin chain, under an inhomogeneous magnetic field, has been explored [ 38 , 39 , 40 ]. Thermal quantum correlations and the entropic uncertainty relation in the presence of quantum memory under two kinds of two-qubit spin squeezing models have been investigated [ 41 ].…”

Dynamical Measurement's Uncertainty in the Curved Space‐Time

“…[39] Canonically, a quantum system cannot escape from its surrounding environment and inevitably couples with the environmental noises, which will result in decoherence or dissipation effects. [49] Up to now, the dynamical features of correlation and entanglement have been explored in the curved space-time. To date, there have been some authors to explore the QMA-EUR under the various types of environment noises.…”

Effects of Hawking Radiation on the Entropic Uncertainty in a Schwarzschild Space‐Time

“…In practice, a physical system is remarkably susceptible to ambient environments, which may unavoidably inject decoherence effects. In this regard, it is of fundamental importance to pursue an understanding of the influence of various decoherence effects on QMA‐EUR; these effects have been shown to be nontrivial in the domain of quantum information science . Recently, Fan et al., and Jing et al have explored the dynamic characteristics of the QMA‐EUR while the particle to be measured is taken to be curved space‐time (e.g., Schwarzschild and de Sitter spaces); Huang et al .…”