Characterizing multiparticle correlations with exponential families

• Applicant: Professor Dr. Otfried Gühne
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics ; Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2014 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 247058788

• Final Report Year: 2019

Final Report Abstract

The aim of this project was the theoretical study of correlation measures in classical and quantum systems. This should be used to study complex quantum and classical systems. The project achieved its main goals. Moreover, during the research unexpected methods for analysing multiparticle entanglement were found. This allowed, surprisingly, to solve the long­standing problem of the existence of absolutely maximally entangled states for seven qubits. In addition, the criteria for the phenomenon of quantum steering could be found. The result on the absolutely maximally entangled state is clearly the highlight of this project, and was very well acknowledged in the community. For instance, Felix Huber, who did his PhD thesis within the project, has been awarded the Dissertation Prize of the Section on Atomic, Molecular, Plasma Physics and Quantum Optics of the German Physical Society in 2019.

Publications

• Characterizing ground and thermal states of few­body Hamiltonians. Phys. Rev. Lett. 117, 010403 (2016)
  Felix Huber and Otfried Gühne
  (See online at https://doi.org/10.1103/PhysRevLett.117.010403)
• Absolutely maximally entangled states of seven qubits do not exist. Phys. Rev. Lett. 118, 200502 (2017)
  Felix Huber, Otfried Gühne and Jens Siewert
  (See online at https://doi.org/10.1103/PhysRevLett.118.200502)
• Almost all four­particle pure states are determined by their two­body marginals. Phys. Rev. A (Rapid Comm.) 96, 010102 (2017)
  Nikolai Wyderka, Felix Huber and Otfried Gühne
  (See online at https://doi.org/10.1103/PhysRevA.96.010102)
• Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity. J. Phys. A: Math. Theor. 51, 175301 (2018)
  Felix Huber, Christopher Eltschka, Jens Siewert and Otfried Gühne
  (See online at https://doi.org/10.1088/1751-8121/aaade5)
• Constraints on correlations in multiqubit systems. Phys. Rev. A 97, 060101 (2018)
  Nikolai Wyderka, Felix Huber and Otfried Gühne
  (See online at https://doi.org/10.1103/PhysRevA.97.060101)
• Steering criteria from general entropic uncertainty relations. Phys. Rev. A (Rapid Comm.) 98, 050104 (2018)
  Ana C. S. Costa, Roope Uola and Otfried Gühne
  (See online at https://doi.org/10.1103/PhysRevA.98.050104)