# Probing quantum coherence, uncertainty, steerability of quantum coherence and quantum phase transition in the spin model

Probing quantum coherence, uncertainty, steerability of quantum coherence and quantum phase... In this paper, we study the relation among quantum coherence, uncertainty, steerability of quantum coherence based on skew information and quantum phase transition in the spin model by employing quantum renormalization-group method. Interestingly, the results show that the value of the local quantum uncertainty is equal to the local quantum coherence corresponding to local observable $$\sigma _z$$ σ z in XXZ model, and unlikely in XY model, local quantum uncertainty is minimal optimization of the local quantum coherence over local observable $$\sigma _x$$ σ x and this proposition can be generalized to a multipartite system. Therefore, one can directly achieve quantum correlation measured by local quantum uncertainty and coherence by choosing different local observables $$\sigma _x$$ σ x , $$\sigma _z$$ σ z , corresponding to the XY model and XXZ model separately. Meanwhile, steerability of quantum coherence in XY and XXZ model is investigated systematically, and our results reveal that no matter what times the QRG iterations are carried out, the quantum coherence of the state of subsystem cannot be steerable, which can also be suitable for block–block steerability of local quantum coherence in both XY and XXZ models. On the other hand, we have illustrated that the quantum coherence and uncertainty measure can efficiently detect the quantum critical points associated with quantum phase transitions after several iterations of the renormalization. Moreover, the nonanalytic and scaling behaviors of steerability of local quantum coherence have been also taken into consideration. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Probing quantum coherence, uncertainty, steerability of quantum coherence and quantum phase transition in the spin model

, Volume 16 (5) – Apr 10, 2017
15 pages

/lp/springer_journal/probing-quantum-coherence-uncertainty-steerability-of-quantum-go0LPQkHI4
Publisher
Springer Journals
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/s11128-017-1588-9
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we study the relation among quantum coherence, uncertainty, steerability of quantum coherence based on skew information and quantum phase transition in the spin model by employing quantum renormalization-group method. Interestingly, the results show that the value of the local quantum uncertainty is equal to the local quantum coherence corresponding to local observable $$\sigma _z$$ σ z in XXZ model, and unlikely in XY model, local quantum uncertainty is minimal optimization of the local quantum coherence over local observable $$\sigma _x$$ σ x and this proposition can be generalized to a multipartite system. Therefore, one can directly achieve quantum correlation measured by local quantum uncertainty and coherence by choosing different local observables $$\sigma _x$$ σ x , $$\sigma _z$$ σ z , corresponding to the XY model and XXZ model separately. Meanwhile, steerability of quantum coherence in XY and XXZ model is investigated systematically, and our results reveal that no matter what times the QRG iterations are carried out, the quantum coherence of the state of subsystem cannot be steerable, which can also be suitable for block–block steerability of local quantum coherence in both XY and XXZ models. On the other hand, we have illustrated that the quantum coherence and uncertainty measure can efficiently detect the quantum critical points associated with quantum phase transitions after several iterations of the renormalization. Moreover, the nonanalytic and scaling behaviors of steerability of local quantum coherence have been also taken into consideration.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Apr 10, 2017

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