Spekkens toy model

The Spekkens toy model is a conceptually simple toy hidden-variable theory introduced by Robert Spekkens in 2004, to argue in favour of the epistemic view of quantum mechanics. The model is based on a foundational principle: "If one has maximal knowledge, then for every system, at every time, the amount of knowledge one possesses about the ontic state of the system at that time must equal the amount of knowledge one lacks." This is called the "knowledge balance principle". Within the bounds of this model, many phenomena typically associated with strictly quantum-mechanical effects are present. These include (but are not limited to) entanglement, noncommutativity of measurements, teleportation, interference, the no-cloning and no-broadcasting theorems, and unsharp measurements. The toy model cannot, however, reproduce quantum nonlocality and quantum contextuality, as it is a local and non-contextual hidden-variable theory. For nearly a century, physicists and philosophers have been attempting to explain the physical meaning of quantum states. The argument is typically one between two fundamentally opposed views: the ontic view, which describes quantum states as states of physical reality, and the epistemic view, which describes quantum states as states of our incomplete knowledge about a system. Both views have had strong support over the years; notably, the ontic view was supported by Heisenberg and Schrödinger, and the epistemic view by Einstein. The majority of 20th-century quantum physics was dominated by the ontic view, and it remains the view generally accepted by physicists today. There is, however, a substantial subset of physicists who take the epistemic view. Both views have issues associated with them, as both contradict physical intuition in many cases, and neither has been conclusively proven to be the superior viewpoint. The Spekkens toy model is designed to argue in favour of the epistemic viewpoint. It is, by construction, an epistemic model.