Quantum contextuality: From the symplectic polar space to the IBM Quantum Experience
Wednesday April 14, 2021


In any realistic hidden variables theory that reproduces the results of quantum physics, the outcome of a measurement is context dependent, i.e. depends on the compatible measurements that could have been done before or  after the experiment. This paradox, named quantum contextuality, is nowadays considered as a resource in quantum information and quantum computing. It is for instance the basic ingredient of a quantum protocol known as the quantum pseudo-telepathy game.
In this talk, I will recall the principle of the Mermin-Peres magic square that shows that there is no non-contextual hidden variables theory. Then I will introduce the geometry of the symplectic polar space over the two element field where contextual configurations, such as the Mermin-Peres square, can be described as subgeometries. Finally I will present some recent calculations on the IBM Quantum Experience where I obtained strong violations of the classical bounds of contextual inequalities due to Adan Cabello based on the configuration given by full symplectic polar space. These results show that the measurements obtained with the IBM Quantum Experience are compatible with the prediction of quantum physics. I will conclude with some remarks on how the use of noisy intermediate scale quantum computers can benefit basic research on quantum information.
Mis à jour le 6 April 2021