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Spekkens Toy Model
The Spekkens toy model is a conceptually simple toy model 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. Much of the mathematics associated with quantum theory has strong analogues inside the toy model, such as the Bloch sphere and similar forms of transformations. The model is not, however, a restriction of quantum mechanics, as there are effects in the model not present in quantum theory.
==Background==
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 generally accepted view 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. The knowledge balance principle of the model ensures that any measurement done on a system within it gives incomplete knowledge of the system, and thus the observable states of the system are epistemic. This model also implicitly assumes that there ''is'' an ontic state which the system is in at any given time, but simply that we are unable to observe it. The model can not be used to derive quantum mechanics, as there are fundamental differences between the model and quantum theory. In particular, the model is one of local and noncontextual variables, which Bell's theorem tells us cannot ever reproduce all the predictions of quantum mechanics. The toy model does, however, reproduce a number of strange quantum effects, and it does so from a strictly epistemic perspective; as such, it can be interpreted as strong evidence in favour of the epistemic view.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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