Quartic quantum theory: an extension of the standard quantum mechanics

Understand

We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states.

• As the simplex of classical N-point probability distributions can be embedded inside a higher dimensional convex body of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states.
• The embedding proposed corresponds to an assumption that the physical system described in N dimensional Hilbert space is coupled with an auxiliary subsystem of the same dimensionality.
• The extended theory works for simple quantum systems and is shown to be a non-trivial generalisation of the standard quantum theory for which K=N^2.