Quantum ontological excess baggage

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Abstract

A theorem is presented showing that, in a certain well-defined sense, any ontological embedding of quantum theory must have infinite excess baggage beyond that required simply to make predictions about the outcomes of experiments.

Section snippets

Ontic states, epistemic states and instrumental states

What is the essential meaning behind saying something is ontic? It is, simply, that a system actually has an underlying state. That is to say there is a real state of affairs and this real state of affairs is such and such. Consider a particular system. Let us assume that there is a real state of affairs and let us denote that real state of affairs by s. We will call this the ontic state. The ontic state could be different in which case we might denote it by s′≠s. In general, it is possible

Ontic embeddings and the quantum ontological excess baggage theorem

As stated already, any empirically useful theory must enable us to predict the instrumental state, p. Call such a theory T. If we want to believe that the underlying state of affairs is ontic then there must exist an ontic theory which makes the same predictions. This will employ the epistemic state P which lists the probabilities for the different ontic states si. For consistency it must be the case that the probabilities pk in the instrumental state can be determined by the probabilities Pi

Discussion

A possible misunderstanding of the ideas in this paper might lead one to conclude that γ=∞ even in classical theories. Thus one could argue that only two parameters are required to specify the state of a particle moving in one dimension—the position and momentum—and therefore that Kinstrumental=2. Nevertheless, there are an infinite number of distinct ontic states (all the different points in the phase space) and therefore γ=∞. However this is the wrong notion of state for our purposes because

Acknowledgements

It is a great honour to dedicate this paper to the memory of Rob Clifton. He had a strong positive impact on me and my work especially in the early days when he was doing his PhD in Cambridge and I was doing mine in Durham. I have very happy memories of the hours we spent at that time (in the early 1990s) debating whether realistic interpretations of quantum theory could be consistent with Lorentz invariance. I am grateful to Chris Fuchs, Ian Gatensby, Rob Spekkens, and Antony Valentini for

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    This is because the notion of what states can carry information is now formulated in terms of available causal correlations, which depend only on the possible counterfactuals as well as the prescriptions of fundamental physical laws in a manner similar to that recommended in (Maudlin, 2007). The identity between causation and information is then used to address the problem of ‘excess baggage’ in quantum mechanics (Hardy, 2004), where states (if they are in some way ontic) must seemingly carry both finite and infinite amounts of classical information (Jennings & Leifer, 2016; Leifer, 2014a,b), in contravention of the established finite limits of the Holevo theorem (Holevo, 1973). The correspondence of information and causation is used to tease out this problem and demonstrate that only the finite information carried by the quantum state actually corresponds to causal correlations of a single qubit, the infinite component is accommodated by an ensemble of qubits only.

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