Exploring entropic uncertainty relation in the Heisenberg XX model with inhomogeneous magnetic field

Exploring entropic uncertainty relation in the Heisenberg XX model with inhomogeneous magnetic field 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Exploring entropic uncertainty relation in the Heisenberg XX model with inhomogeneous magnetic field

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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-017-1657-0
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jul 12, 2017

References

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