Advanced statistical methods for quantum experiments

• Applicant: Privatdozent Dr. Matthias Kleinmann
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2014 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 253338819

• Final Report Year: 2017

Final Report Abstract

The key advances achieved during the fellowship concern the statistical evaluation of data from photonic Bell-type experiments and new constraints on the structure of measurements in nature. Photonic Bell-type experiments are experimental setups, where, from a source of two entangled photons, each photon is distributed to one of two parties, Alice and Bob. Those parties then measure their photon with alternating measurement settings. John Bell showed that the correlations obtained from such a setup exceed those which are explicable by local hidden variable models, i.e., mechanistic explanations that do not allow for communication or interaction between Alice and Bob. This kind of experiments has attracted considerable attention and many such experiments have been performed. The surprising finding during the project was that almost all experiments (with the exception of the recent loophole-free Bell tests) fail, by far, to pass a statistical test of the nonsignaling conditions. These conditions ensure that the measurement outcomes of one party are independent of the choice of the measurement setting of the other party and even quantum correlations must obey this condition. This issue can be tracked down to design flaws in the experiments. Subsequently, in ongoing research, a new experiment was designed and performed which avoids these problems. A different class of results was obtained when studying in more detail the general correlations attainable in quantum theory. We proved that quantum correlations can be fundamentally nonbinary and even fundamentally not m-ary for no m. Binary or m-ary correlations are such that they can be explained by a mechanism which locally, for each party, selects from moutcome measurements. Consequently, Bell-inequalities show that quantum correlations are not fundamentally unary. We showed, that the statement that quantum correlations are not fundamentally m-ary even holds if one allows that the m-outcome measurements are not restricted to quantum measurements but can be any measurement from a generalized probabilistic theory. Generalized probabilistic theories are a broad class of theories, containing classical probability theory, quantum theory as well as hypothetical models that would have correlations exceeding those allowed according to quantum theory. Therefore, if such correlations can be verified without assuming quantum theory, then we have proof that nature implements measurements which are not fundamentally binary and this statement will persist even if one day quantum theory would be abandoned. We also succeeded to make an experimental proposal for this prediction of quantum theory which is such that it is feasible with current quantum technology. This proposal has recently been implemented successfully.

Publications

• Device-independent certification of a nonprojective qubit measurement. Phys. Rev. Lett. 117, 260401 (2016)
  E.S. Gómez, S. Gómez, P. González, G. Cañas, J.F. Barra, A. Delgado, G.B. Xavier, A. Cabello, M. Kleinmann, T. Vértesi, and G. Lima
  
• Quantum correlations are stronger than all nonsignaling correlations produced by n-outcome measurements. Phys. Rev. Lett. 117, 150401 (2016)
  M. Kleinmann and A. Cabello
  
• Optimal witnessing of the quantum Fisher information with few measurements. Phys. Rev. A 95, 032330 (2017)
  I. Apellaniz, M. Kleinmann, O. Gühne, and G. Tóth
  
• Proposed experiment to test fundamentally binary theories. Phys. Rev. A 96, 032104 (2017)
  M. Kleinmann, T. Vértesi, and A. Cabello