Experimental refutation of a class ofψ-epistemic models

Abstract

The quantum state ψ is a mathematical object used to determine the outcome probabilities of measurements on physical systems. Its fundamental nature has been the subject of discussions since the origin of the 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? Recent advances in the foundations of quantum theory show that epistemic models that obey a simple continuity condition are in conflict with quantum theory already at the level of a single system. Here we report an experimental test of continuous epistemic models using high-dimensional attenuated coherent states of light traveling in an optical fiber. Due to nonideal state preparation (of coherent states with imperfectly known phase) and nonideal measurements (arising from losses and inefficient detection), this experiment tests only epistemic models that satisfy additional constraints which we discuss in detail. Our experimental results are in agreement with the predictions of quantum theory and provide constraints on a class of ψ-epistemic models.

Exploring quantum foundations with single photons

“…The predictions of this theorem have been confirmed experimentally using time-bin encoding on an optical coherent state [88]. Finally, the notion of δ-continuity has been criticised for being much too strong for ψ-ontology theorems.…”

“…This narrative, however, rather complicates the paradox which applies to arbitrary two-qubit entangled states (except maximally entangled) [88]. A simplified version in terms of black-boxes has been given by Mermin [89] and, in terms of quantum cakes by Kwiat et al [90].…”

“…Hardy's original presentation [86] relied on two overlapping interferometers, one for an electron and one for a positron, which are arranged such that electron and positron would be expected to annihilate in two of the arms, similar to the Elitzur-Vaidman bomb-test [87]. This narrative, however, rather complicates the paradox which applies to arbitrary two-qubit entangled states (except maximally entangled) [88]. A simplified version in terms of black-boxes has been given by Mermin [89] and, in terms of quantum cakes by Kwiat et al [90].…”

“…The continuity assumption is meant to translate the continuous quantum state-space to the ontic space in the sense that a slight variation of ψ should only cause a slight change of µ ψ . The authors then classify the possible ψ-epistemic models by two parameters: their continuity δ and their epistemicity [88] ε. Here δ is the radius of a ball around the state ψ, such that there exists an ontic state in µ ψ that is also in µ φ for all states φ within this δ-ball.…”

“…In Ref. [88] a generalized, experimentally testable version of the theorem is presented, using a redefinition of δ and ε to contend with imperfect detection efficiency. The predictions of this theorem have been confirmed experimentally using time-bin encoding on an optical coherent state [88].…”