Observer effect, quasi-probabilities and generalized Specker's boxes

Quantum non-locality and contextuality can be simulated with quasi-probabilities, i.e. probabilities that take negative values. Here, we show that another quantum phenomenon, the observer effect, admits a quasi-probabilistic description too. We also investigate post-quantum observer effects based on the Specker's triangle scenario. This scenario comprises three observables, with the possibility of measuring two simultaneously. Represented as three boxes with a hidden ball, this scenario exhibits counterintuitive behaviour: regardless of the chosen pair of boxes, one box always contains the ball. Moreover, the scenario demonstrates a strong observer effect. When an observer selects and opens the first box, finding it empty, the ball is guaranteed to be in the second box, thereby allowing the observer to determine the ball's location among the remaining two boxes. We extend this scenario to include additional boxes and multiple balls. By employing negative probabilities, we demonstrate amplification of the observer effect. This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'.