In this work, we investigate the quantum-memory-assisted entropic uncertainty relation in a two-qubit Heisenberg XX model with inhomogeneous magnetic field. It has been found that larger coupling strength J between the two spin-chain qubits can effectively reduce the entropic uncertainty. Besides, we observe the mechanics of how the inhomogeneous field influences the uncertainty, and find out that when the inhomogeneous field parameter $$b<1$$ b < 1 , the uncertainty will decrease with the decrease of the inhomogeneous field parameter b, conversely, the uncertainty will increase with decreasing b under the condition that $$b>1$$ b > 1 . Intriguingly, the entropic uncertainty can shrink to zero when the coupling coefficients are relatively large, while the entropic uncertainty only reduces to 1 with the increase of the homogeneous magnetic field. Additionally, we observe the purity of the state and Bell non-locality and obtain that the entropic uncertainty is anticorrelated with both the purity and Bell non-locality of the evolution state.
Quantum Information Processing – Springer Journals
Published: Jul 12, 2017
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