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Physical Review A

Null test of quantum mechanics using two-photon down-conversion

Mark S. Hillery

Published May 1, 1998• 1 citation
Publisher

Abstract

A null test of quantum mechanics is proposed. It is based on an arrangement in which a source sends two signals to two detectors. At each detector one of two different quantities can be measured. If the source satisfies three conditions, all of which can be verified experimentally, then, according to quantum mechanics, a particular outcome is forbidden. This result follows only from the way in which quantum mechanics constructs probabilities, and does not involve any dynamics. Looking for this outcome is a test of quantum mechanics. It is shown how this test can be realized using two-photon down-conversion.

DOI
10.1103/physreva.57.3285

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•Jul 22, 2026•0 citations
A null test of quantum mechanics is proposed. It is based on an arrangement in which a source sends two signals to two detectors. At each detector one of two different quantities can be measured. If the source satisfies three conditions, all of which can be verified experimentally, then, according to quantum mechanics, a particular outcome is forbidden. This result follows only from the way in which quantum mechanics constructs probabilities, and does not involve any dynamics. Looking for this outcome is a test of quantum mechanics. It is shown how this test can be realized using two-photon down-conversion.
A number of optical experiments in which quantum mechanics is tested and the laws of classical probability are violated will be described. These all make use of the phenomenon in non-linear optics known as parametric down-conversion, in which an incident pump photon effectively splits into two correlated, lower frequency signal and idler photons in an entangled quantum state. We show that two-photon coincidence measurements of signal and idler photons violate classical probability by at least 600 standard deviations. Other measurements involving two down-converters lead to the realization of a ″quantum eraser″ and suggest a reinterpretation of the usual quantum wave function.
We comment on the so-called negative result experiments (also known as null measurements, interaction-free measurements, and so on) in quantum mechanics (QM), in the light of the new general understanding of the quantum-measurement processes, proposed recently. All experiments of this kind (null measurements) can be understood as improper measurements with an intentionally biased detector set up, which introduces exclusion or selection of certain events. The prediction on the state of a microscopic system under study based on a null measurement is sometimes dramatically described as "wave-function collapse without any microsystem-detector interactions". Though certainly correct, such a prediction is just a consequence of the standard QM laws, not different from the situation in the so-called state-preparation procedure. Another closely related concept is the (first-class or) repeatable measurements. The verification of the prediction made by a null measurement requires eventually a standard unbiased measurement involving the microsystem-macroscopic detector interactions, which are nonadiabatic, irreversible processes of signal amplification.
An experiment has been carried out to test a prediction of the deBroglie guided wave theory for photons. According to this theory, there exist electromagnetic waves as well as photons, with the former acting as guide for the latter. The wave not only determines the probability for the detection of a photon, but it also has an independent physical reality which can result in photodetection, As a result the guided wave theory predicts an interference effect when two photons pass through an interferometer with a particular geometry and one measures the rate of simultaneous detections by two photodetectors in coincidence as a function of optical path difference, By contrast, quantum mechanics predicts no interference under the same conditions. The experimental results clearly violate the prediction of the guided wave theory, but are in agreement with quantum mechanics.
It has been suggested by Sorkin that a three-slit Young experiment could reveal the validity a fundamental ingredient in the foundations of one of the cornerstones in modern physics namely quantum mechanics. In terms of a certain parameter κSκ_SκS​, it was argued that a non-zero value could imply a breakdown of the fundamental Born's rule as well as the superposition principle. Here we argue that a physical realization of such arguments could lead to an erroneous conclusion and contradict the basic rules of quantum mechanics. In fact, we argue that a proper interpretation of the procedures involved in a physical determination of κSκ_SκS​ does not necessarily lead to κS=0κ_S=0κS​=0. In order to show this we consider a mono-chromatic source of photons prepared in an {\it arbitrary} quantum state and a simple version of the well-established photon detection theory of Glauber which, by construction, obeys all the rules of quantum mechanics. It is, however, also argued that after a proper identification of the relevant quantum-mechanical probability amplitudes one can be reach κS=0κ_S=0κS​=0. As long as one only consider a single photon detector, it is verified that, in this context, there is no fundamental difference between quantum-mechanical interference and interference as expressed in terms of classical electro-magnetic waves.
It has been suggested by Sorkin that a three-slit Young experiment could reveal the validity a fundamental ingredient in the foundations of one of the cornerstones in modern physics namely quantum mechanics. In terms of a certain parameter κ S , it was argued that a non-zero value could imply a breakdown of the fundamental Born's rule as well as the superposition principle. Here we argue that a physical realization of such arguments could lead to an erroneous conclusion and contradict the basic rules of quantum mechanics. In fact, we argue that a straightforward interpretation of the procedures involved in a physical determination of κ S does not necessarily lead to κ S = 0. In order to show this we consider a mono-chromatic source of photons prepared in an arbitrary quantum state and a simple version of the well-established photon detection theory of Glauber which, by construction, obeys all the rules of quantum mechanics. It is, however, also argued that after a proper identification of the relevant quantum-mechanical probability amplitudes one can be reach κ S = 0. As long as one only consider a single photon detector, it is verified that, in this context, there is no fundamental difference between quantum-mechanical interference and interference as expressed in terms of classical electro-magnetic waves.
Whether Nature is deterministic or probabilistic has stood outside the reach of experiment since 1926: Bohmian mechanics reproduces the predictions of quantum mechanics without residue, so the choice between chance and determinism has been one of interpretation, not of measurement. This paper constructs a nilpotent steering theory --- definite corpuscles guided by physically real waves, under a global conservation constraint --- that is empirically equivalent to quantum mechanics save in one experimental arrangement, stated here. The theory treats the conservation laws as primitive ontological constraints --- a zero-totality principle called the nilpotent condition --- under which every photon pair is entangled at its creation event, carrying its conserved content as a single ledger entry. What the celebrated source arrangements of the Bell literature manufacture is not entanglement but the condition for its expression: a circularly structured pilot wave, supplied natively by the atomic-cascade source of the first Bell test and constructed after creation by the beam-splitter, crossed-crystal, and cone-intersection arrangements of the down-conversion era. This reading admits a configuration the record leaves untested: a single-pass Type-I source whose pair, separable on the orthodox account, is converted to circular guidance by a quarter-wave plate in each arm. There quantum mechanics, under any interpretation, predicts a vanishing correlation and no Bell--CHSH violation, EQM(a,b)=0E_{\mathrm{QM}}(a,b)=0EQM​(a,b)=0 and S=0S=0S=0, while the nilpotent steering postulate predicts the maximal violation, E=±cos⁡2(a−b)E=\pm\cos2(a-b)E=±cos2(a−b) and S=22S=2\sqrt2S=22​. A violation would point to globally constrained dynamics (interpreted here as deterministic); a null result rejects the theory proposed here while leaving orthodox de~Broglie--Bohm mechanics untouched. The ledger accounting offered here is bookkeeping, not yet dynamics; its completion --- a formalism in which the bookkeeping becomes the evolution of physical fields --- is stated as the theory's principal debt. Either outcome of the experiment is informative, and the enabling conditions are stated in advance.