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Quantum Information Processing

Dynamical characteristic of entropic uncertainty relation in the long-range Ising model with an arbitrary magnetic field

R. A. Abdelghany, A.‐B. A. Mohamed, Mahmoud Tammam, A.‐S. F. Obada

Published Nov 1, 2020• 15 citations
Publisher
DOI
10.1007/s11128-020-02897-x

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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.
Dynamics of Quantum Correlation and Entropic Uncertainty in Spin‐1212\frac{1}{2}21​ Alternating Transverse Ising Model
Abstract By implementing the quantum renormalization group method, the effective Hamiltonian of the spin‐ Ising model with regularly altering strengths of both the magnetic fields and the exchange couplings are first derived analytically. Then, tripartite quantum discord (QD) and entropic uncertainty (EU) of the Ising model and their quantum phase transitions are investigated. Moreover, the quantum critical points and correlation length exponents of the model are analyzed, and both the block–block EU and the site–site EU are discussed through numerical calculations. It is found that under the system size increasing, the first derivatives of both tripartite QD and block–block EU show nonanalytic and scaling behaviors near the critical point. Furthermore, the strong quantum correlations among multi‐particles do not necessarily lead to the decrease of EU, as the site–site EU in the vicinity of the critical point increases due to competitions among quantum correlations. The findings may offer new insights into utilizing EU as an observable of the quantum phase transitions.