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International Journal of Theoretical Physics

Controlling Entropic Uncertainty and Quantum Correlation of a Bath of Spins

Yinghua Ji, Juju Hu

Published Feb 8, 2021• 0 citations
Publisher
DOI
10.1007/s10773-021-04711-5

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Abstract The uncertainty principle configures a low bound to the measuring precision for a pair of non-commuting observables, and hence is considerably nontrivial to quantum precision measurement in the field of quantum information theory. In this letter, we consider the entropic uncertainty relation (EUR) in the context of quantum memory in a two-qubit isotropic Heisenberg spin chain. Specifically, we explore the dynamics of EUR in a practical scenario, where two associated nodes of a one-dimensional XXX -spin chain, under an inhomogeneous magnetic field, are connected to a thermal entanglement. We show that the temperature and magnetic field effect can lead to the inflation of the measuring uncertainty, stemming from the reduction of systematic quantum correlation. Notably, we reveal that, firstly, the uncertainty is not fully dependent on the observed quantum correlation of the system; secondly, the dynamical behaviors of the measuring uncertainty are relatively distinct with respect to ferromagnetism and antiferromagnetism chains. Meanwhile, we deduce that the measuring uncertainty is dramatically correlated with the mixedness of the system, implying that smaller mixedness tends to reduce the uncertainty. Furthermore, we propose an effective strategy to control the uncertainty of interest by means of quantum weak measurement reversal. Therefore, our work may shed light on the dynamics of the measuring uncertainty in the Heisenberg spin chain, and thus be important to quantum precision measurement in various solid-state systems.
Abstract We investigate thermal quantum correlations and the entropic uncertainty relation in the presence of quantum memory under two kinds of two-qubit spin squeezing models, namely the one-axis twisting model and two-axis countertwisting model. We provide the analytical expressions of quantum correlations and the entropic uncertainty relation in the ground state for these two models and we find a simple relationship between quantum discord and entropic uncertainty. It is found that there is a fully anti-correlated relationship between quantum correlations and entropic uncertainty. Also, the maximal quantum correlation and minimal uncertainty can be achieved when the spin squeezing parameters are large enough. Accordingly, these results may be significant in practical goals in which the maximum quantum correlation and minimum uncertainty are required such as in quantum key distribution and quantum computing.