Hierarchy, factorization law of two measurement-induced nonlocalities and their performances in quantum phase transition

Hierarchy, factorization law of two measurement-induced nonlocalities and their performances in... There are two measurement-induced nonlocalities, which are, respectively, defined via the trace norm (MIN-1) and Hilbert–Schmidt norm (MIN-2). We investigate the hierarchy relation and factorization law of them. Their performances in quantum phase transition have also been explored. For X-shape states, a rigorous hierarchy relation is established between two MINs. When two qubits, which are initially prepared in an X-shape state, interact independently with the corresponding multimode vacuum reservoirs, the evolutions of two MINs satisfy the factorization law. With quantum renormalization group method, it is found that two MINs can signify the criticality of the spin system while the position where the derivative of MIN-1 takes the minimum value is always larger than that where the derivative of MIN-2 takes the minimum value. Therefore, MIN-1 is more suitable to identify the critical point of quantum phase transition. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Hierarchy, factorization law of two measurement-induced nonlocalities and their performances in quantum phase transition

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Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer Science+Business Media New York
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/s11128-016-1256-5
Publisher site
See Article on Publisher Site

Abstract

There are two measurement-induced nonlocalities, which are, respectively, defined via the trace norm (MIN-1) and Hilbert–Schmidt norm (MIN-2). We investigate the hierarchy relation and factorization law of them. Their performances in quantum phase transition have also been explored. For X-shape states, a rigorous hierarchy relation is established between two MINs. When two qubits, which are initially prepared in an X-shape state, interact independently with the corresponding multimode vacuum reservoirs, the evolutions of two MINs satisfy the factorization law. With quantum renormalization group method, it is found that two MINs can signify the criticality of the spin system while the position where the derivative of MIN-1 takes the minimum value is always larger than that where the derivative of MIN-2 takes the minimum value. Therefore, MIN-1 is more suitable to identify the critical point of quantum phase transition.

Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 9, 2016

References

  • Einselection and decoherence from an information theory perspective
    Zurek, WH
  • Geometric quantum discord through the Schatten 1-norm
    Paula, FM; Oliveira, TR; Sarandy, MS
  • Negativity of quantumness and its interpretations
    Nakano, T; Piani, M; Adesso, G
  • Uncertainty-induced quantum nonlocality
    Wu, SX; Zhang, J; Yu, CS; Song, HS
  • Non-Markovian dynamics of a qubit
    Maniscalco, S; Petruccione, F

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