Relating relative Renyi entropies and Wigner-Yanase-Dyson skew information to generalized multiple quantum coherences

Year: 2020

Authors: Pires DP., Smerzi A., Macri T.

Autors Affiliation: Univ Fed Rio Grande do Norte, Dept Fis Teor & Expt, BR-59072970 Natal, RN, Brazil; CNR INO, QSTAR, Largo Enrico Fermi 2, I-50125 Florence, Italy; LENS, Largo Enrico Fermi 2, I-50125 Florence, Italy; Univ Fed Rio Grande do Norte, Int Inst Phys, Campus Univ, BR-59078970 Natal, RN, Brazil.

Abstract: Quantum coherence is a crucial resource for quantum information processing. By employing the language of coherence orders largely applied in NMR systems, quantum coherence has been currently addressed in terms of multiple quantum coherences (MQCs). Here we investigate alpha-MQCs, a class of multiple quantum coherences which is based on alpha-relative purity, an information-theoretic quantifier analogous to quantum fidelity and closely related to Renyi relative entropy of order alpha. Our framework enables linking alpha-MQCs to Wigner-Yanase-Dyson skew information, an asymmetry monotone-finding application in quantum thermodynamics and quantum metrology. Furthermore, we derive a family of bounds on alpha-MQCs, particularly showing that alpha-MQCs define a lower bound to quantum Fisher information. We illustrate these ideas for quantum systems described by single-qubit states, two-qubit Bell-diagonal states, and a wide class of multiparticle mixed states. Finally, we investigate the time evolution of the alpha-MQC spectrum and the overall signal of relative purity by simulating the time-reversal dynamics of a many-body all-to-all Ising Hamiltonian and comment on applications to physical platforms such as NMR systems, trapped ions, and ultracold atoms.

Journal/Review: PHYSICAL REVIEW A

Volume: 102 (1)      Pages from: 012429-1  to: 012429-17

More Information: We thank T. Roscilde for fruitful discussions. D.P.P. and T.M. acknowledge the financial support from the Brazilian ministries MEC and MCTIC, funding agencies CAPES and CNPq. T.M. acknowledges CNPq for support through Bolsa de produtividade em Pesquisa No. 311079/20156. This work was supported by the Serrapilheira Institute (Grant No. Serra-1812-27802), CAPES-NUFFIC Project No. 88887.156521/2017-00. This study was financed by the Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior-Brasil (CAPES)-Finance Code 001. This work was also supported by the QuantERA ERA-NET Cofund in Quantum Technologies projects CEBBEC.
KeyWords: ENTANGLEMENT ENTROPY; INEQUALITIES; DIVERGENCE; CAPACITY
DOI: 10.1103/PhysRevA.102.012429

ImpactFactor: 3.140
Citations: 6
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