ψ-Epistemic Models are Exponentially Bad at Explaining the Distinguishability of Quantum States

Abstract

The status of the quantum state is perhaps the most controversial issue in the foundations of quantum theory. Is it an epistemic state (state of knowledge) or an ontic state (state of reality)? In realist models of quantum theory, the epistemic view asserts that nonorthogonal quantum states correspond to overlapping probability measures over the true ontic states. This naturally accounts for a large number of otherwise puzzling quantum phenomena. For example, the indistinguishability of nonorthogonal states is explained by the fact that the ontic state sometimes lies in the overlap region, in which case there is nothing in reality that could distinguish the two states. For this to work, the amount of overlap of the probability measures should be comparable to the indistinguishability of the quantum states. In this letter, I exhibit a family of states for which the ratio of these two quantities must be ≤ 2de −cd in Hilbert spaces of dimension d that are divisible by 4. This implies that, for large Hilbert space dimension, the epistemic explanation of indistinguishability becomes implausible at an exponential rate as the Hilbert space dimension increases. The status of the quantum state is one of the most controversial issues in the foundations of quantum theory. Is it a state of knowledge (an epistemic state), or a state of physical reality (an ontic state)? Many realist interpretations of quantum theory employ ontic quantum states, but the rise of quantum information science has revived interest in the epistemic alternative because many of the puzzling phenomena employed in quantum information are explained quite naturally in terms of the epistemic quantum states [1]. For example, consider the fact that two nonorthogonal quantum states cannot be perfectly distinguished. On the ontic view, the two states represent distinct arrangements of physical reality, so it is puzzling that this distinctness cannot be detected. However, on the epistemic view, a quantum state is represented by a probability measure over the physical properties of a system and nonorthogonal states correspond to overlapping probability measures. Indistinguishability is thus explained by the fact that preparations of the two quantum states sometimes result in the same physical properties of the system, in which case there is nothing existing in reality that could distinguish them.Recently, several theorems have been proved aiming to show that the quantum state must be ontic [2-6]. These have been proved within the ontological models framework [7], which is a refinement of the hidden variable approach used to prove earlier no-go results, such as Bell's theorem [8] and the Kochen-Specker theorem [9]. Each of these theorems employs questionable auxiliary assumptions 1 . Without such assumptions, explicit counterexamples show that the epistemic view of quantum states can be maintained [11,12]. Within the ontological models framework, a model is ψ-ontic if the probability measures corresponding to every pair of pure quantum states have zero overlap, ...

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