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- If no information gain implies no disturbance, then any discrete physical theory is classical

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PIRSA Number:

12120016

(based on http://arxiv.org/abs/1210.0194)

It has been suggested

that nature could be discrete in the sense that the underlying state space of a

physical system has only a finite number of pure states. For example, the Bloch

ball of a single qubit could be discretized into small patches and only appear

round to us due to experimental limitations. Here, we present a strong physical

argument for the quantum theoretical property that every state space (even the

smallest possible one, the qubit) has infinitely many pure states. We propose a

simple physical postulate which dictates that in fact the only possible

discrete theory is classical mechanics. More specifically, we postulate that no

information gain implies no disturbance, or read in the contrapositive, that

disturbance leads to some form of information gain. In a theory like quantum mechanics

where we already know that the converse holds, i.e. information gain does imply

disturbance, this can be understood as postulating an equivalence between

disturbance and information gain. What is more, we show that non-classical

discrete theories are still ruled out even if we relax the postulate to hold

only approximately in the sense that no information gain only causes a small

amount of disturbance. Finally, our postulate also rules out popular

generalizations such as the PR-box that allows non-local correlations beyond

the limits of quantum theory.

©2012 Perimeter Institute for Theoretical Physics