The quantum pigeonhole principle and the nature of quantum correlations

Aharonov, Yakir; Colombo, Fabrizio; Popescu, Sandu; Sabadini, Irene; Struppa, Daniele C.; Tollaksen, Jeff

doi:10.48550/arxiv.1407.3194

Cited by 10 publications

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“…These projectors do not specify which hole pigeons a and b are in, only that it is the same for both. Using the definitions above it is easily verified that +i +i +i|Π ab |+ ++ = 0, (8) which is the central equation in [1] and leads to the vanishing of…”

Section: States and Operatorsmentioning

confidence: 99%

“…The authors of [1] propose an experiment to test the QPC using a Mach-Zehnder interferometer for electrons. In this experiment, three electrons travel along one of two possible paths (see Fig.…”

Section: Experiments a Electron Mach-zehnder Interferometer Experimentsmentioning

confidence: 99%

“…In this experiment, three electrons travel along one of two possible paths (see Fig. 1 in [1]) toward one of two possible detectors. The post-selected state |+i +i +i is analogous to all three electrons arriving at the same detector.…”

Section: Experiments a Electron Mach-zehnder Interferometer Experimentsmentioning

confidence: 99%

“…claim the dynamics of the experiment is governed by the following interaction Hamiltonian (see Eq. ( 23) in [1]):…”

Section: Experiments a Electron Mach-zehnder Interferometer Experimentsmentioning

confidence: 99%

“…al. [1] argued that a seemingly fundamental principal of Nature known as the pigeonhole counting principle (PCP) is violated in quantum mechanics. The classical PCP is the intuitive statement that if one puts three pigeons in two boxes, then there must be at least two pigeons in one of the boxes.…”

mentioning

confidence: 99%

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Escape from the Quantum Pigeon Conundrum

Kunstatter,

Ziprick,

McNab

et al. 2020

Preprint

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It has recently been argued in that quantum mechanics violates the Pigeon Counting Principle (PCP): if one distributes three pigeons among two boxes there must be at least two pigeons in one of the boxes. The article describes how this Quantum Pigeon Conundrum (QPC) can be observed in an experiment using a Mach-Zehnder interferometer with three weakly coupled electrons. We provide a detailed theoretical analysis of the QPC and new experimental results obtained with the IBM Yorktown quantum processor. Although these results and previous experiments confirm certain predicted amplitudes, we argue that the PCP is not violated in quantum mechanics unless one makes untenable hidden variable assumptions. Simply put, the physical Hilbert space is spanned by states each having at least two particles in the same box. This leads to the quantum version of the PCP, an operator identity that forbids assigning values of zero to all three two-particle projection operators. The statement "there are no two particles in the same box" prior to the projection onto the final state is therefore no more viable than the contention that each particle in the Einstein-Podolsky-Rosen state has specific values for both position and momentum prior to any measurement. Our conclusion is that PCP and QPC provide a novel and elegant pedagogical framework for understanding the (non-)viability of local hidden variables but do not constitute a radically new quantum effect as suggested by Aharonov et al.

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Section: States and Operatorsmentioning

confidence: 99%

Section: Experiments a Electron Mach-zehnder Interferometer Experimentsmentioning

confidence: 99%

Section: Experiments a Electron Mach-zehnder Interferometer Experimentsmentioning

confidence: 99%

“…claim the dynamics of the experiment is governed by the following interaction Hamiltonian (see Eq. ( 23) in [1]):…”

Section: Experiments a Electron Mach-zehnder Interferometer Experimentsmentioning

confidence: 99%

mentioning

confidence: 99%

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Escape from the Quantum Pigeon Conundrum

Kunstatter,

Ziprick,

McNab

et al. 2020

Preprint

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Quantum Mechanics: Knocking at the Gates of Mathematical Foundations

Ionicioiu

2015

Boston Studies in the Philosophy and History of Science

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The Weltanschauung emerging from quantum theory clashes profoundly with our classical concepts. Quantum characteristics like superposition, entanglement, wave-particle duality, nonlocality, contextuality are difficult to reconcile with our everyday intuition. In this article I survey some aspects of quantum foundations and discuss intriguing connections with the foundations of mathematics. I. WHAT IS THE PROBLEM? (IS THERE A PROBLEM?)From its very inception quantum mechanics generated a fierce debate regarding the meaning of the mathematical formalism and the world view it provides [1][2][3][4]. The new quantum Weltanschauung is characterized, on the one hand, by novel concepts like wave-particle duality, complementarity, superposition and entanglement, and on the other by the rejection of classical ideas such as realism, locality, causality and non-contextuality. For instance, quantum correlations with no causal order [5] challenge Reichenbach's principle of common cause [6].The disquieting feeling one has at the contact with quantum theory was echoed by several physicists, including the founding fathers: "Anyone who is not shocked by quantum mechanics has not understood it" (Bohr); "I think I can safely say that nobody understands quantum mechanics" (Feynman). Consequently, there is an unsolved tension between what we predict and what we understand [7,8]. Although the predictions of quantum mechanics are by far and away unmatched (in terms of precision) by any other theory, understanding "what-allthis-means" is lacking. Briefly, we would like to have a story behind the data, to understand the meaning of the formalism.There is a wide spectrum of positions concerning the problem of quantum foundations [9], with attitudes ranging from "there is no problem, don't waste my time" to "we do have a problem and we don't know how to solve it":Actually quantum mechanics provides a complete and adequate description of the observed physical phenomena on the atomic scale. What else can one wish? [10] Quantum theory is based on a clear mathematical apparatus, has enormous significance for the natural sciences, enjoys phenomenal predictive success, and plays a critical role in modern technological developments. Yet, nearly 90 years after the theory's development, there is still no consensus in the scientific community regarding the interpretation of the theory's foundational building blocks.[11]The confusion around the meaning of the formalism and the lack of an adequate solution to the measurement problem (among others) resulted in a plethora of interpretations. Apart from the (once) dominant Copenhagen interpretationinformally known as "shut-up-and-calculate" -there are numerous others: pilot wave (de Broglie-Bohm), many-worlds Historically, the tone of the discussion was set by the BohrEinstein debate on the foundations of quantum theory [2][3][4]. Einstein lost the conceptual battle due to his persistence to understand quantum phenomena in classical terms like realism, locality and causality. In this respect Einstein was ...

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Contextuality, Pigeonholes, Cheshire Cats, Mean Kings, and Weak Values

Waegell

Tollaksen

2017

Quantum Stud.: Math. Found.

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The structural connections between the Kochen-Specker (KS) theorem, pre-and post-selection (PPS) paradoxes, and anomalous weak values are explored in detail. All PPS paradoxes, such as the 3-box paradox, the Quantum Cheshire Cat, and the Quantum Pigeonhole principle, construct a particular type of ontological model that assigns an eigenvalue to each observable (independent of context) of a system such that these assignments are consistent with the PPS. It is shown that such an ontological model must be explicitly contextual in the sense of the KS theorem, or otherwise implies either a restriction on free random choice or explicitly retrocausal behavior. We call such models PPS-contextual. The structure of each paradox is always such that there are particular contexts of mutually commuting observables that violate the product rule or sum rule, when the ontological model is extended to include observables that are not measured during the experiment. These paradoxes are counterfactual, in the sense that they are not directly observed, and also because the product and sum rules are always obeyed by projective measurements in actual experiments. It is shown that by adopting an alternate ontological model, where all hidden variables are weak values (which are not always eigenvalues, but obey the sum rule by definition), the same contexts that presented the original paradox must also contain observables with anomalous weak values. These anomalous weak values are not counterfactual because they can be probed through weak measurements on an ensemble of identically pre-and post-selected states, allowing this localized signature of KS contextuality to be experimentally observed. The weak values of all observables of a system can in principle be measured during an experiment, making this model a promising candidate for describing PPS-contextual ontological 'elements of reality.' As a related issue, we show using the mathematical properties of weak values, that any KS set can be used to ensure that the Mean King always wins his game against the stranded physicist. *

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The quantum pigeonhole principle and the nature of quantum correlations

Cited by 10 publications

References 0 publications

Escape from the Quantum Pigeon Conundrum

Escape from the Quantum Pigeon Conundrum

Quantum Mechanics: Knocking at the Gates of Mathematical Foundations

Contextuality, Pigeonholes, Cheshire Cats, Mean Kings, and Weak Values

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