How statistical are quantum states?

Abstract

A novel no-go theorem is presented which sets a bound upon the extent to which 'Ψ-epistemic ' interpretations of quantum theory are able to explain the overlap between non-orthogonal quantum states in terms of an experimenter's ignorance of an underlying state of reality. The theorem applies to any Hilbert space of dimension greater than two. In the limit of large Hilbert spaces, no more than half of the overlap between quantum states can be accounted for. Unlike other recent no-go theorems no additional assumptions, such as forms of locality, invasiveness, or non-contextuality, are required.

Bell Nonlocality and the Reality of Quantum Wavefunction

“…Our theorem establishes a general result in this direction as it shows that a class of epistemic models satisfying the metaphysical assumption of NOR is inconsistent with the nonlocal behavior of quantum theory. Extent of our theorem is also broader than the ψ-ontology theorems in [15][16][17][18][19][20][21] as these results exclude only certain degree of epistemicity and apply to Hilbert spaces with dimension greater than two but remain silent for qubit system. Our result also opens up new research possibilities.…”

“…Interestingly, Owen Maroney came up with a new kind of ψ-ontology theorem that uses no additional assumption and rules out a class of ontological models with certain degree of epistemicity [15,16]. Subsequently, several other results were obtained excluding ψ-epistemic models with increasingly lower degree of epistemicity and consequently imposing higher degree of onticity on quantum wavefunction [17][18][19][20][21].…”

“…Degree of epistemicity:-An ontological model where the quantum overlap | ψ|φ | 2 for any two state vectors |ψ and |φ is completely accounted for by the overlap between the corresponding epistemic distributions µ(λ|ψ) and µ(λ|φ) is called maximally ψ-epistemic, i.e., in a maximally ψ-epistemic model Λ φ µ(λ|ψ)dλ = | ψ|φ | 2 for all pairs of |ψ , |φ [15]. Maroney's theorem [15] and the subsequent results [16][17][18][19][20][21] exclude maximally ψ-epistemic model and a class of ontological models with increasingly lower degree of epistemicity. Denoting Supp[ξ(ψ|λ)] := {λ ∈ Λ | ξ(ψ|λ) > 0} and Core[ξ(ψ|λ)] := {λ ∈ Λ | ξ(ψ|λ) = 1}, the following set inclusion relations are immediate:…”

How Real are Quantum States in $ψ$-ontic Models?

“…The overlap in probability distributions allowed in these ψ-epistemic models is quite small though. It was shown by Maroney (2013) that this is necessarily so: even though ψ-epistemic models can always be constructed, they cannot be "maximally ψ-epistemic". As a consequence, these models cannot do all of the explanatory work one would hope ψ-epistemic models to do.…”

Noncontextuality inequalities from antidistinguishability

“…It was shown that ψ-epistemic models exist in all finite Hilbert space dimensions [34,35]. This led to the definition of maximally ψ-epistemic models [36][37][38] [39] and the study of overlap bounds for probability distributions in ontological models [40][41][42][43][44].…”