Howψ-Epistemic Models Fail at Explaining the Indistinguishability of Quantum States

Abstract

We study the extent to which ψ-epistemic models for quantum measurement statistics-models where the quantum state does not have a real, ontic status-can explain the indistinguishability of nonorthogonal quantum states. This is done by comparing the overlap of any two quantum states with the overlap of the corresponding classical probability distributions over ontic states in a ψ-epistemic model. It is shown that in Hilbert spaces of dimension d ≥ 4, the ratio between the classical and quantum overlaps in any ψ-epistemic model must be arbitrarily small for certain nonorthogonal states, suggesting that such models are arbitrarily bad at explaining the indistinguishability of quantum states. For dimensions d = 3 and 4, we construct explicit states and measurements that can be used experimentally to put stringent bounds on the ratio of classical-to-quantum overlaps in ψ-epistemic models, allowing one in particular to rule out maximally ψ-epistemic models more efficiently than previously proposed.Despite its central role, the quantum state remains one of the most mysterious objects of quantum theory. Does it correspond to any physical reality, or does it merely represent one's information on a quantum system? These questions have triggered intense debates among physicists and philosophers since the advent of quantum theory, and are still the subject of active research in the study of quantum foundations.The general framework of ontological models [1] proposes a rigorous approach to address such questions. This framework presupposes the existence of underlying states of physical reality-ontic states-and describes the quantum state as a state of knowledge-an epistemic stateabout the actual ontic state of a given quantum system, represented by a probability distribution over the set of ontic states. A fundamental distinction is made between so-called ψ-ontic models, in which any underlying ontic state determines the quantum state uniquely, and socalled ψ-epistemic models, where the same ontic state can be compatible with different quantum states; i.e., the probability distributions corresponding to two different quantum states can overlap. In the former case, the ontic state "encodes" the quantum state, which can hence be understood as a physical property of the system, while in the latter case the quantum state cannot be given the status of a real physical property.The epistemic view of the quantum state is quite attractive, as it gives a natural explanation to many puzzling quantum phenomena [2]-including, for instance, the collapse of the wave function, or the impossibility to perfectly distinguish nonorthogonal quantum states. However, it has been shown that ψ-epistemic models must be severely constrained if they are to reproduce the statistics of quantum measurements. Notably, Pusey, Barrett, and Rudolph showed that no ψ-epistemic models satisfying some natural independence condition for composite systems can reproduce quantum predictions [3]. A number of other no-go theorems have since been proven, under various a...

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