Quantum theory of simple alternatives

Millard Baublitz

The mean energy of tunneling electrons at low temperatures may provide a very simple fundamental test between quantum mechanics and a class of alternative theories, the classical stochastic theories, since quantum theory and the stochastic alternatives differ in their descriptions of tunneling.

Berthold‐Georg Englert

Thomas D. Galley, Lluís Masanes

Using the existing classification of all alternatives to the Measurement Postulates of Quantum Mechanics we study the properties of multi-partite systems in these alternative theories. We prove that in all these theories the Purification Principle is violated, meaning that some mixed states are not the reduction of a pure state in a larger system. This implies that simple operational processes, like mixing two states, cannot be described in an agent-free universe. This appears like a crucial clue for the problem of deriving the Born Rule within unitary quantum mechanics or the many-worlds interpretation. We also prove that in all such modifications the task of state tomography with local measurements is impossible, and present a simple toy theory displaying all these exotic non-quantum phenomena. This toy model shows that, contrarily to previous claims, it is possible to modify the Born rule without violating the No-Signalling Principle. Finally, we argue that the quantum measurement postulates are the most non-classical amongst all alternatives.

Adán Cabello

The author presents a simple proof of a theorem which places constraints on hidden-variables theories alternative to quantum mechanics.

Carl Friedrich von Weizsäcker, Thomas Görnitz, Holger Lyre