Quantum correlations and the Bloch representation of quantum states

• Applicant: Dr. Christopher Eltschka
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2016 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 311953832

• Final Report Year: 2024

Final Report Abstract

In this project we investigated various aspects of correlations and entanglement in bipartite and multipartite systems including exact solutions for entanglement measures, entanglement of states with positive partial transpose, the existence of absolutely maximally entangled states as well as correlation properties of multipartite quantum states. The common theme of all these investigations was their close links with the technical development of the generalized Bloch representation. In particular, the Bloch representation naturally invokes a Euclidean geometry of the state space that can be visualized and is amenable to our geometric intuition from everyday life. A particularly nice example of this is the extension of the well-known qubit Bloch ball to a three-dimensional model of the qutrit that was constructed on the basis of the findings in this project.

Publications

• Quantifying Entanglement of Maximal Dimension in Bipartite Mixed States. Physical Review Letters, 117(19).
  Sentís, Gael; Eltschka, Christopher; Gühne, Otfried; Huber, Marcus & Siewert, Jens
  
• Quantitative bound entanglement in two-qutrit states. Physical Review A, 94(2).
  Sentís, Gael; Eltschka, Christopher & Siewert, Jens
  
• Absolutely Maximally Entangled States of Seven Qubits Do Not Exist. Physical Review Letters, 118(20).
  Huber, Felix; Gühne, Otfried & Siewert, Jens
  
• Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity. Journal of Physics A: Mathematical and Theoretical, 51(17), 175301.
  Huber, Felix; Eltschka, Christopher; Siewert, Jens & Gühne, Otfried
  
• Distribution of entanglement and correlations in all finite dimensions. Quantum, 2, 64.
  Eltschka, Christopher & Siewert, Jens
  
• Exponentially many entanglement and correlation constraints for multipartite quantum states. Physical Review A, 98(5).
  Eltschka, Christopher; Huber, Felix; Gühne, Otfried & Siewert, Jens
  
• Dimensionally sharp inequalities for the linear entropy. Linear Algebra and its Applications, 584, 294-325.
  Morelli, Simon; Klöckl, Claude; Eltschka, Christopher; Siewert, Jens & Huber, Marcus
  
• Maximum N-body correlations do not in general imply genuine multipartite entanglement. Quantum, 4, 229.
  Eltschka Christopher & Siewert Jens