Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0410160 · Physical Review Letters

Realization of Hardy’s Thought Experiment with Photons

William T. M. Irvine, Juan F. Hodelin, Christoph Simon, Dirk Bouwmeester

Published Jul 11, 2005• 35 citations
arXivHTMLPDF

Abstract

We present an experimental realization of Hardy's thought experiment [Phys. Rev. Lett. 68, 2981 (1992)], using photons. The experiment consists of a pair of Mach-Zehnder interferometers that interact through photon bunching at a beam splitter. A striking contradiction is created between the predictions of quantum mechanics and local hidden variables. The contradiction relies on nonmaximally entangled position states of two particles. A Clauser-Horne-type inequality is derived and violated.

DOI
10.1103/physrevlett.95.030401

Related papers

Experimental test of the violation of local realism in quantum mechanics without Bell inequalities

Giovanni Di Giuseppe, F. De Martini, D. Boschi

We report the results of an experiment in which postselected polarization-entangled photons were used to test the recent nonlocality proof by L. Hardy [Phys. Rev. Lett. 71, 1665 (1993)]. The particular source of entangled photons used in the experiment has the advantage that it is very easy to prepare a pair of photons in a state with any degree of entanglement. Hardy's theorem, which only works for nonmaximally entangled states, was tested for a range of states.

Physical Review A•Jul 1, 1997•67 citations

Bell-inequality violations with single photons entangled in momentum and polarization

Bryce Gadway, Enrique J. Galvez, F. De Zela

We present a violation of the Clauser–Horne–Shimony–Holt and the Clauser–Horne inequalities using heralded single photons entangled in momentum and polarization modes. A Mach–Zehnder interferometer and polarization optics are used to rotate the spatial and polarization bases, respectively. With this setup we were able to test quantum mechanics with the original formulation of the Clauser–Horne inequality. The results rule out a wide class of realistic non-contextual hidden-variable theories.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 16, 2008•43 citations

Quantum entanglement—introduction

Vlatko Vedral

Abstract The Mach–Zehnder interferometer experiment described earlier shows why and how quantum mechanics is different from classical mechanics. A photon sent through a beam splitter behaves like a particle when it is observed by only one of the two detectors. When two beam splitters are used, the photon “interferes with itself” and behaves like a wave. This is the so-called wave-particle duality of quantum mechanics which leads to quantum entanglement. This chapter discusses quantum superpositions when two or more particles are present. Understanding and analysing entanglement is one of the most interesting directions in the field of quantum information. First, a historical background of quantum entanglement is given, followed by a discussion on Bell's inequalities, separable states that do not violate Bell's inequalities, pure states that violate Bell's inequalities, mixed states that do not violate Bell's inequalities, and entanglement in second quantisation.

•Sep 28, 2006•0 citations

HARDY’S PHOTONIC PARADOX AND THE MODAL DISCIPLINE OF OBJECTIVITY

Vidamor Cabannas

This article develops an expanded critical–propositional analysis of William T. M. Irvine, Juan F. Hodelin, Christoph Simon, and Dirk Bouwmeester’s 2005 experiment, “Realization of Hardy’s Thought Experiment with Photons,” published in Physical Review Letters, in systematic dialogue with the Theory of Objectivity (TO) formulated by Vidamor Cabannas and Denivaldo Silva. Irvine et al. experimentally implemented a photonic version of Lucien Hardy’s two-particle argument against local hidden-variable descriptions by employing two coupled Mach–Zehnder interferometers, nonmaximally entangled path states, photon bunching at a shared beam splitter, and coincidence detection. The experiment derived a Clauser–Horne-type inequality appropriate to its nonideal optical implementation and reported a violation of the local-hidden-variable bound by twelve standard deviations. Its photonic configuration relied crucially upon high two-photon indistinguishability; the measured distinguishability probability was approximately 7.8 percent, below the 12.5 percent threshold identified by the authors for observing the relevant violation. These results provide an experimentally controlled demonstration that the class of local hidden-variable models addressed by the inequality cannot reproduce the observed path correlations (Irvine et al. 2005). The present study asks a different question: whether, and in what restricted sense, Irvine et al.’s results can enter into empirical dialogue with the modal axioms and physical proposals of TO. Particular attention is devoted to the First Absolute Truth, according to which the pre-universal “Nothing” is not absolute nonbeing but an eternal logical-mathematical essence; the Second Absolute Truth, according to which every existing element possesses its own exclusive individualizing magnetic field; the Fourth Absolute Truth concerning boundaries or interfaces; the Fifth Absolute Truth, according to which logical existence requires an element to be observed by, or to lie within the frequency of, at least two other elements, where observation is physical and non-anthropocentric; and the Seventh Absolute Truth, in which the transcendent element is interpreted as knowledge or information produced in atomic relations and regarded by TO as equivalent to atomic radiation. The analysis distinguishes modal necessity from empirical confirmation. If an axiom is claimed to possess necessary status, no finite collection of observations can establish that necessity inductively. Experiments can nevertheless test operational bridge principles linking a modal ontology to measurable consequences. Under this distinction, Irvine et al. exhibit significant compatibility with TO’s emphasis on relationality, physically efficacious boundaries, non-anthropocentric registration, and objectively instantiated correlations. At the same time, the experiment generates a particularly important tension for the Second Absolute Truth: quantum interference requires photons to be operationally indistinguishable, whereas a strongly measurable individualizing field would constitute distinguishing information and could therefore degrade two-photon bunching. The article consequently proposes a distinction between ontological individuality and experimentally accessible distinguishability and formulates potential experimental bridges through which the individualizing-field thesis could become testable. The analysis further examines TO’s phenomenic elements, Inducing Effects, Cosmogonic Theorem, and Cosmological Eras, while refusing to infer cosmological confirmation from a laboratory-scale quantum-optical experiment. The conclusion is that Irvine et al. provide meaningful indirect corroborative contact with several relational and informational motifs of TO, but neither confirm TO uniquely nor establish the modal necessity of its axioms. The most scientifically productive consequence of the comparison is therefore not retrospective assimilation of quantum mechanics into TO, but the formulation of novel, risk-bearing, quantitative predictions capable of distinguishing TO from standard quantum theory. Keywords: Theory of Objectivity; Hardy paradox; quantum nonlocality; local hidden variables; photon bunching; quantum indistinguishability; physical information; non- anthropocentric observation; modal ontology; boundaries; empirical testability.

•Sep 12, 2026•0 citations

Controlling wave-particle duality with entanglement between single-photon and Bell states

Kai Wang, Daniel R. Terno, Časlav Brukner +2 more

Wave-particle duality and entanglement are two fundamental characteristics of quantum mechanics. All previous works on experimental investigations in wave-particle properties of single photons (or single particles in general) showed that a well-defined interferometer setting determines a well-defined property of single photons. Here we take a conceptual step forward and control the wave-particle property of single photons with a Bell state. By doing so, we experimentally test the complementarity principle in a scenario in which the setting of the interferometer is not defined at any instance of the experiment, not even in principle. To achieve this goal, we establish the three-photon entangled state, i.e., the entanglement between a single photon and a two-photon Bell state, send the photon of interest $S$ into a quantum Mach-Zehnder interferometer (MZI), in which the output beam splitter of the MZI is controlled by the quantum state of the second photon $C$, which is entangled with a third photon $A$. Therefore, the individual quantum state of photon $C$ is undefined, which implements the undefined settings of the MZI for photon $S$. This is realized by using three cascaded phase-stable interferometers for three photons. There is typically no well-defined setting of the MZI and thus the very formulation of the wave-particle objectivity from local hidden variable models becomes internally inconsistent.

arXiv:2112.11659•Physical Review A•Nov 28, 2022•5 citations

Experimental Violation of a Spin-1 Bell Inequality Using Maximally Entangled Four-Photon States

John C. Howell, Antı́a Lamas-Linares, Dik Bouwmeester

We demonstrate the experimental violation of a spin-1 Bell inequality. The spin-1 inequality is based on the Clauser, Horne, Shimony, and Holt formalism. For entangled spin-1 particles, the maximum quantum-mechanical prediction is 2.55 as opposed to a maximum of 2, predicted using local hidden variables. We obtained an experimental value of 2.27+/-0.02 using the four-photon state generated by pulsed, type-II, stimulated parametric down-conversion. This is a violation of the spin-1 Bell inequality by more than 13 standard deviations.

arXiv:quant-ph/0105132•Physical Review Letters•Jan 3, 2002•203 citations
We present an experimental realization of Hardy's thought experiment [Phys. Rev. Lett. 68, 2981 (1992)], using photons. The experiment consists of a pair of Mach-Zehnder interferometers that interact through photon bunching at a beam splitter. A striking contradiction is created between the predictions of quantum mechanics and local hidden variables. The contradiction relies on nonmaximally entangled position states of two particles. A Clauser-Horne-type inequality is derived and violated.
We present a violation of the Clauser–Horne–Shimony–Holt and the Clauser–Horne inequalities using heralded single photons entangled in momentum and polarization modes. A Mach–Zehnder interferometer and polarization optics are used to rotate the spatial and polarization bases, respectively. With this setup we were able to test quantum mechanics with the original formulation of the Clauser–Horne inequality. The results rule out a wide class of realistic non-contextual hidden-variable theories.
Abstract The Mach–Zehnder interferometer experiment described earlier shows why and how quantum mechanics is different from classical mechanics. A photon sent through a beam splitter behaves like a particle when it is observed by only one of the two detectors. When two beam splitters are used, the photon “interferes with itself” and behaves like a wave. This is the so-called wave-particle duality of quantum mechanics which leads to quantum entanglement. This chapter discusses quantum superpositions when two or more particles are present. Understanding and analysing entanglement is one of the most interesting directions in the field of quantum information. First, a historical background of quantum entanglement is given, followed by a discussion on Bell's inequalities, separable states that do not violate Bell's inequalities, pure states that violate Bell's inequalities, mixed states that do not violate Bell's inequalities, and entanglement in second quantisation.
This article develops an expanded critical–propositional analysis of William T. M. Irvine, Juan F. Hodelin, Christoph Simon, and Dirk Bouwmeester’s 2005 experiment, “Realization of Hardy’s Thought Experiment with Photons,” published in Physical Review Letters, in systematic dialogue with the Theory of Objectivity (TO) formulated by Vidamor Cabannas and Denivaldo Silva. Irvine et al. experimentally implemented a photonic version of Lucien Hardy’s two-particle argument against local hidden-variable descriptions by employing two coupled Mach–Zehnder interferometers, nonmaximally entangled path states, photon bunching at a shared beam splitter, and coincidence detection. The experiment derived a Clauser–Horne-type inequality appropriate to its nonideal optical implementation and reported a violation of the local-hidden-variable bound by twelve standard deviations. Its photonic configuration relied crucially upon high two-photon indistinguishability; the measured distinguishability probability was approximately 7.8 percent, below the 12.5 percent threshold identified by the authors for observing the relevant violation. These results provide an experimentally controlled demonstration that the class of local hidden-variable models addressed by the inequality cannot reproduce the observed path correlations (Irvine et al. 2005). The present study asks a different question: whether, and in what restricted sense, Irvine et al.’s results can enter into empirical dialogue with the modal axioms and physical proposals of TO. Particular attention is devoted to the First Absolute Truth, according to which the pre-universal “Nothing” is not absolute nonbeing but an eternal logical-mathematical essence; the Second Absolute Truth, according to which every existing element possesses its own exclusive individualizing magnetic field; the Fourth Absolute Truth concerning boundaries or interfaces; the Fifth Absolute Truth, according to which logical existence requires an element to be observed by, or to lie within the frequency of, at least two other elements, where observation is physical and non-anthropocentric; and the Seventh Absolute Truth, in which the transcendent element is interpreted as knowledge or information produced in atomic relations and regarded by TO as equivalent to atomic radiation. The analysis distinguishes modal necessity from empirical confirmation. If an axiom is claimed to possess necessary status, no finite collection of observations can establish that necessity inductively. Experiments can nevertheless test operational bridge principles linking a modal ontology to measurable consequences. Under this distinction, Irvine et al. exhibit significant compatibility with TO’s emphasis on relationality, physically efficacious boundaries, non-anthropocentric registration, and objectively instantiated correlations. At the same time, the experiment generates a particularly important tension for the Second Absolute Truth: quantum interference requires photons to be operationally indistinguishable, whereas a strongly measurable individualizing field would constitute distinguishing information and could therefore degrade two-photon bunching. The article consequently proposes a distinction between ontological individuality and experimentally accessible distinguishability and formulates potential experimental bridges through which the individualizing-field thesis could become testable. The analysis further examines TO’s phenomenic elements, Inducing Effects, Cosmogonic Theorem, and Cosmological Eras, while refusing to infer cosmological confirmation from a laboratory-scale quantum-optical experiment. The conclusion is that Irvine et al. provide meaningful indirect corroborative contact with several relational and informational motifs of TO, but neither confirm TO uniquely nor establish the modal necessity of its axioms. The most scientifically productive consequence of the comparison is therefore not retrospective assimilation of quantum mechanics into TO, but the formulation of novel, risk-bearing, quantitative predictions capable of distinguishing TO from standard quantum theory. Keywords: Theory of Objectivity; Hardy paradox; quantum nonlocality; local hidden variables; photon bunching; quantum indistinguishability; physical information; non- anthropocentric observation; modal ontology; boundaries; empirical testability.
Wave-particle duality and entanglement are two fundamental characteristics of quantum mechanics. All previous works on experimental investigations in wave-particle properties of single photons (or single particles in general) showed that a well-defined interferometer setting determines a well-defined property of single photons. Here we take a conceptual step forward and control the wave-particle property of single photons with a Bell state. By doing so, we experimentally test the complementarity principle in a scenario in which the setting of the interferometer is not defined at any instance of the experiment, not even in principle. To achieve this goal, we establish the three-photon entangled state, i.e., the entanglement between a single photon and a two-photon Bell state, send the photon of interest SSS into a quantum Mach-Zehnder interferometer (MZI), in which the output beam splitter of the MZI is controlled by the quantum state of the second photon CCC, which is entangled with a third photon AAA. Therefore, the individual quantum state of photon CCC is undefined, which implements the undefined settings of the MZI for photon SSS. This is realized by using three cascaded phase-stable interferometers for three photons. There is typically no well-defined setting of the MZI and thus the very formulation of the wave-particle objectivity from local hidden variable models becomes internally inconsistent.
We demonstrate the experimental violation of a spin-1 Bell inequality. The spin-1 inequality is based on the Clauser, Horne, Shimony, and Holt formalism. For entangled spin-1 particles, the maximum quantum-mechanical prediction is 2.55 as opposed to a maximum of 2, predicted using local hidden variables. We obtained an experimental value of 2.27+/-0.02 using the four-photon state generated by pulsed, type-II, stimulated parametric down-conversion. This is a violation of the spin-1 Bell inequality by more than 13 standard deviations.