No-Go Theorems for $\psi$-Epistemic Models Based on a Continuity Assumption

The quantum state $\psi$ is a mathematical object used to determine the probabilities of different outcomes when measuring a physical system. Its fundamental nature has been the subject of discussions since the inception of quantum theory. Is it ontic, that is, does it correspond to a real property of the physical system? Or is it epistemic, that is, does it merely represent our knowledge about the system? Assuming a natural continuity assumption and a weak separability assumption, we show here that epistemic interpretations of the quantum state are in contradiction with quantum theory. Our argument is different from the recent proof of Pusey, Barrett, and Rudolph and it already yields a nontrivial constraint on $\psi$-epistemic models using a single copy of the system in question.

Figure 1

Illustration of $\psi$-ontic and $\delta$-continuous $\psi$-epistemic models. Depicted is the space $\Lambda$ of ontic states, as well as the support of the probability distribution $P(\lambda |Q_k)$ for preparation $Q_k$ associated to distinct pure states ${\psi }_k$, $k=1,\dots ,5$. In $\psi$-ontic models (left) distinct quantum states give rise to probability distribution $P(\lambda |Q_k)$ with no overlap. In $\delta$-continuous $\psi$-epistemic models (right), states that are close to each other (such as $\{{\psi }_1,{\psi }_2,{\psi }_3\}$ and $\{{\psi }_3,{\psi }_4,{\psi }_5\}$) all share common ontic states. However states that are further from each other (such as ${\psi }_1$ and $\{{\psi }_4,{\psi }_5\}$) do not necessarily have common ontic states $\lambda$.