Ruling Out Multi-Order Interference in Quantum Mechanics

Abstract

Quantum mechanics and gravitation are two pillars of modern physics. Despite their success in describing the physical world around us, they seem to be incompatible theories. There are suggestions that one of these theories must be generalized to achieve unification. For example, Born's rule, one of the axioms of quantum mechanics could be violated. Born's rule predicts that quantum interference, as shown by a double slit diffraction experiment, occurs from pairs of paths. A generalized version of quantum mechanics might allow multi-path, i.e. higher order interferences thus leading to a deviation from the theory. We performed a three slit experiment with photons and bounded the magnitude of three path interference to less than 10 -2 of the expected twopath interference, thus ruling out third and higher order interference and providing a bound on the accuracy of Born's rule. Our experiment is consistent with the postulate both in semi-classical and quantum regimes.Born's interpretation (1) of the wave function ( ) t r , r ! for a quantum mechanical state stipulates that the probability density to find a particle at position r r and at time t is given by:A double slit diffraction experiment is a direct consequence of this rule and the probability to detect a particle at r r after passing through an aperture with two slits A and B, is given by ( )

Measuring quantum coherence in multislit interference

“…There are no 3-slit or multiple-slit terms, which is a direct consquence of the Born rule. This aspect of interference has been used to test Born rule in 3-slit interference experiments [26]. Now, if one wants to find out which slit the particle went through, one has to have some kind of path-detecting device in place.…”

How to Measure the Quantum Measure

“…Beyond level 2, several researchers have been investigating the possibility of theories residing at level 3 or higher [2,15,14,16,22,19,21,29], but for the moment there has not been any evidence of higher-order interference from the experiments that have looked for it. See for example the three-slit experiments that have put increasingly stringent bounds on third order interference.…”

Hybrid waveguide-bulk multi-path interferometer with switchable amplitude and phase

“…[13][14][15][16]28 Here, the absence of ϵ 3 is implied by electrodynamics 21 and will be used for a consistency check of the interferometer. Note that ϵ 3 = 0 must hold also in the presence of non-vanishing reflected signals in the "off"-state of a mirror.…”

“…For many applications, however, it is also desirable to be able to switch and manipulate the interferometer. For example, multi-path interferometers with switchable transmission amplitudes are a promising platform for investigations on the foundations of quantum mechanics, [12][13][14][15][16] whereas tunable phases can be used to tailor the output state of the photons. 11 The two requirements of stability and capability for manipulation are often in conflict with each other.…”

“…We characterise this interferometer by measuring the contrast of two-path interference and by testing for undesired systematic correlations between the transmission amplitudes of the individual mirror settings of all three paths. The latter test is performed by measuring the so-called higher-order interferences, 14 which are expected to vanish in the regime of classical electrodynamics. 21 No higher-order interferences are detected, suggesting that the interferometer is free of significant systematic correlations.…”