Feynman famously said that single-particle interference is ``a phenomenon which is impossible to explain in any classical way, and which has in it the heart of quantum mechanics.'' In this paper we show that some of the phenomenology of interference can be reproduced in a ``classical'' way, by reproducing the Elitzur-Vaidman Bomb Tester (including their improved version) using an extension of the quantum simulation logic (QSL) formalism. Our result improves and simplifies a previous result by Catani \emph{et al}, which relies on a much more complicated extension involving a ``toy field theory.'' We also show that not all single-particle interference can be explained by such a simple extension (including that of Catani et al), by showing that Hofmann's three-path interferometer is ``nonclassical'' in a very specific sense: it violates a Kochen-Specker-noncontextual inequality. Given that both our extension of QSL and Catani et al's extension are \emph{noncontextual} -- so do not reproduce the contextual behaviour of Hofmann's three-path interferometer -- the behaviour of that interferometer is a proper example of a phenomenon that has in it the heart of quantum mechanics, according to Feynman.
Feynman famously said that single-particle interference is a phenomenon which is impossible to explain in any classical way, and which has in it the heart of quantum mechanics.'' In this paper we show that some of the phenomenology of interference can be reproduced in a classical'' way, by reproducing the Elitzur-Vaidman Bomb Tester (including their improved version) using an extension of the quantum simulation logic (QSL) formalism. Our result improves and simplifies a previous result by Catani \emph{et al}, which relies on a much more complicated extension involving a toy field theory.'' We also show that not all single-particle interference can be explained by such a simple extension (including that of Catani et al), by showing that Hofmann's three-path interferometer is nonclassical'' in a very specific sense: it violates a Kochen-Specker-noncontextual inequality. Given that both our extension of QSL and Catani et al's extension are \emph{noncontextual} -- so do not reproduce the contextual behaviour of Hofmann's three-path interferometer -- the behaviour of that interferometer is a proper example of a phenomenon that has in it the heart of quantum mechanics, according to Feynman.
Quantum information is based on the apparent contradictions between classical logic and quantum coherence described by Kochen-Specker contextuality. Surprisingly, this contradiction can be demonstrated in a comparatively simple three-path interferometer, where it is impossible to trace the path of a single photon through five consecutive stages of the interferometer. Here, I discuss the paradoxical aspects of single photon interferences revealed by the three-path interferometer and point out the essential role of dynamics in quantum information.
Quantum interference phenomena are widely viewed as posing a challenge to the classical worldview. Feynman even went so far as to proclaim that they are the only mystery and the basic peculiarity of quantum mechanics. Many have also argued that basic interference phenomena force us to accept a number of radical interpretational conclusions, including: that a photon is neither a particle nor a wave but rather a Jekyll-and-Hyde sort of entity that toggles between the two possibilities, that reality is observer-dependent, and that systems either do not have properties prior to measurements or else have properties that are subject to nonlocal or backwards-in-time causal influences. In this work, we show that such conclusions are not, in fact, forced on us by basic interference phenomena. We do so by describing an alternative to quantum theory, a statistical theory of a classical discrete field (the `toy field theory') that reproduces the relevant phenomenology of quantum interference while rejecting these radical interpretational claims. It also reproduces a number of related interference experiments that are thought to support these interpretational claims, such as the Elitzur-Vaidman bomb tester, Wheeler's delayed-choice experiment, and the quantum eraser experiment. The systems in the toy field theory are field modes, each of which possesses, at all times, both a particle-like property (a discrete occupation number) and a wave-like property (a discrete phase). Although these two properties are jointly possessed, the theory stipulates that they cannot be jointly known . The phenomenology that is generally cited in favour of nonlocal or backwards-in-time causal influences ends up being explained in terms of inferences about distant or past systems, and all that is observer-dependent is the observer's knowledge of reality, not reality itself.
It was recently argued by Catani et al that it is possible to reproduce the phenomenology of quantum interference classically, by the double-slit experiment with a deterministic, local, and classical model (Quantum 7, 1119 (2023)). The stated aim of their argument is to falsify the claim made by Feynman (in his third book of Lectures on Physics) that quantum interference is ``impossible, absolutely impossible, to explain in any classical way'' and that it ``contains the only mystery'' of quantum mechanics. We here want to point out some problems with their argument.
Quantum contextuality can be observed in three path interferometers, suggesting a fundamental contradiction between wave propagation and particle propagation inherent in the wave-particle dualism. Here, we investigate this contradiction in a three path interferometer specifically designed to illustrate the paradoxical aspects of single particle interference. A particularly clear violation of non-contextual assumptions is obtained when interference effects suppress detection probabilities to zero in paths that seem to be necessary to explain the observation of photons in the output. This contradiction between detection probabilities in the paths and detection probabilities in the output cannot be explained by any assignment of photon paths through the interferometer, demonstrating a fundamental incompatibility of wave propagation and particle propagation.
Quantum systems show contextuality.More precisely, it is impossible to reproduce the quantum-mechanical predictions using a non-contextual realist model, i.e., a model where the outcome of one measurement is independent of the choice of compatible measurements performed in the measurement context.There has been several attempts to quantify the amount of contextuality for specific quantum systems, for example, in the number of rays needed in a KS proof, or the number of terms in certain inequalities, or in the violation, noise sensitivity, and other measures.This paper is about another approach: to use a simple contextual model that reproduces the quantum-mechanical contextual behaviour, but not necessarily all quantum predictions.The amount of contextuality can then be quantified in terms of additional resources needed as compared with a similar model without contextuality.In this case the contextual model needs to keep track of the context used, so the appropriate measure would be memory.Another way to view this is as a memory requirement to be able to reproduce quantum contextuality in a realist model.The model we will use can be viewed as an extension of Spekkens' toy model [Phys.Rev. A 75, 032110 (2007)], and the relation is studied in some detail.To reproduce the quantum predictions for the Peres-Mermin square, the memory requirement is more than one bit in addition to the memory used for the individual outcomes in the corresponding noncontextual model.
Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for by some realistic models with hidden variables. There are, however, two powerful theorems against the hidden-variable theories showing that certain quantum features cannot be reproduced based on two rationale premises of locality, Bell's theorem, and noncontextuality, due to Bell, Kochen and Specker (BKS). Noncontextuality is independent of nonlocality, and the contextuality manifests itself even in a single object. Here we report an experimental verification of quantum contextuality by a single spin-1 electron system at room temperature. Such a three-level system is indivisible and then we close the compatibility loophole which exists in the experiments performed on bipartite systems. Our results confirm the quantum contextuality to be the intrinsic property of single particles.