Generalized measure of quantum synchronization

We present a generalized information-theoretic measure of synchronization in quantum systems. This measure is applicable to dynamics of anharmonic oscillators, few-level atoms, and coupled oscillator networks. Furthermore, the new measure allows us to discuss synchronization of disparate physical systems such as coupled hybrid quantum systems and coupled systems undergoing mutual synchronization that are also driven locally. In many cases of interest, we find a closed-form expression for the proposed measure.

[1]  Marc Timme,et al.  Classical synchronization indicates persistent entanglement in isolated quantum systems , 2017, Nature Communications.

[2]  C. Bruder,et al.  Quantum Synchronization and Entanglement Generation. , 2018, Physical review letters.

[3]  Franziska Abend,et al.  Sync The Emerging Science Of Spontaneous Order , 2016 .

[4]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[5]  M. Plenio,et al.  Quantifying Entanglement , 1997, quant-ph/9702027.

[6]  V. Giovannetti,et al.  Mutual information as an order parameter for quantum synchronization , 2014, 1412.2585.

[7]  E Schöll,et al.  Quantum signatures of chimera states. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Franco Nori,et al.  QuTiP: An open-source Python framework for the dynamics of open quantum systems , 2011, Comput. Phys. Commun..

[9]  Franco Nori,et al.  QuTiP 2: A Python framework for the dynamics of open quantum systems , 2012, Comput. Phys. Commun..

[10]  Florian Marquardt,et al.  Noise-induced transitions in optomechanical synchronization , 2015, 1507.06190.

[11]  Chris Arney.  Sync: The Emerging Science of Spontaneous Order , 2007 .

[12]  Emilio Hernández-García,et al.  Synchronization, quantum correlations and entanglement in oscillator networks , 2013, Scientific Reports.

[13]  V. Vedral,et al.  Squeezing Enhances Quantum Synchronization. , 2018, Physical review letters.

[14]  C. Bruder,et al.  Synchronizing the Smallest Possible System. , 2018, Physical review letters.

[15]  M. Plenio,et al.  Quantifying coherence. , 2013, Physical review letters.

[16]  Christoph Bruder,et al.  Quantum synchronization of a driven self-sustained oscillator. , 2013, Physical review letters.

[17]  M. Murao,et al.  Direct evaluation of pure graph state entanglement , 2012, 1207.5877.

[18]  A. Roulet,et al.  Optimal synchronization deep in the quantum regime: Resource and fundamental limit , 2018, Physical Review A.

[19]  T. Paterek,et al.  The classical-quantum boundary for correlations: Discord and related measures , 2011, 1112.6238.

[20]  Christoph Bruder,et al.  Quantum synchronization of two Van der Pol oscillators , 2014, 1406.7134.

[21]  Tony E. Lee,et al.  Quantum synchronization of quantum van der Pol oscillators with trapped ions. , 2013, Physical review letters.

[22]  A. Pikovsky,et al.  Synchronization: Theory and Application , 2003 .

[23]  V. Vedral,et al.  Entanglement in pure and thermal cluster states , 2009, 0902.4343.

[24]  A Mari,et al.  Measures of quantum synchronization in continuous variable systems. , 2013, Physical review letters.

[25]  Tony E. Lee,et al.  Entanglement tongue and quantum synchronization of disordered oscillators. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  T. Paterek,et al.  Unified view of quantum and classical correlations. , 2009, Physical review letters.

[27]  V. Vedral,et al.  Quantum synchronization in nanoscale heat engines. , 2018, Physical review. E.

[28]  Christoph Bruder,et al.  Quantum Synchronization on the IBM Q System , 2019 .

[30]  Sai Vinjanampathy,et al.  Observation of Quantum Phase Synchronization in Spin-1 Atoms. , 2019, Physical review letters.