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The quantum state cannot be interpreted statistically

 Matthew F. Pusey, Jonathan Barrett, Terry Rudolph
(Submitted on 14 Nov 2011)
"Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state represents. There are at least two opposing schools of thought, each almost as old as quantum theory itself. One is that a pure state is a physical property of system, much like position and momentum in classical mechanics. Another is that even a pure state has only a statistical significance, akin to a probability distribution in statistical mechanics. Here we show that, given only very mild assumptions, the statistical interpretation of the quantum state is inconsistent with the predictions of quantum theory. This result holds even in the presence of small amounts of experimental noise, and is therefore amenable to experimental test using present or near-future technology. If the predictions of quantum theory are confirmed, such a test would show that distinct quantum states must correspond to physically distinct states of reality."

"But the new paper, by a trio of physicists led by Matthew Pusey at Imperial College London, presents a theorem showing that if a quantum wavefunction were purely a statistical tool, then even quantum states that are unconnected across space and time would be able to communicate with each other. As that seems very unlikely to be true, the researchers conclude that the wavefunction must be physically real after all."

Something screwy about the above Nature quote. It seems to say that orthodox quantum theory requires entanglement signals. This contradicts all sorts of no-signal theorems based on linearity of observables, unitarity etc., e.g. papers of Adrian Kent et-al. In Bohm's theory, the quantum potential is real, but its fragility, i.e. no direct back reaction of the hidden variable on it, gives no entanglement signaling. This is no longer the case using distinguishable non-orthogonal macro-quantum coherent Glauber states seen in lasers and also in the Higgs-Goldstone spontaneous broken symmetry of virtual quanta in vacua and real quanta in condensed matter systems with ODLRO in the Feynman propagators.