Common sense suggests that a particle must have a definite origin if its full path information is available. In quantum mechanics, the knowledge of path information is captured through the well-established duality relation between path distinguishability and interference visibility. If visibility is zero, high path distinguishability can be achieved, which enables one to determine with high predictive power where the particle originates. We investigate the complementarity between path information and interference visibility through an experiment involving three sources emitting into identical modes. Our findings challenge the classical intuition that a particle can be traced back to its origin through its trajectory when full path information is available. By grouping the crystals in different ways, we demonstrate that it is impossible to ascribe a definite physical origin to the photon pair, even if the emission probability of one individual source is zero and full path information is available. Our results shed new light on the physical interpretation of probability assignment and path information beyond its mathematical meaning and show that the interpretation of path information in quantum mechanics is subjective.
Common sense suggests that a particle must have a definite origin if its full path information is available. In quantum mechanics, the knowledge of path information is captured through the well-established duality relation between path distinguishability and interference visibility. If visibility is zero, high path distinguishability can be achieved, which enables one to determine with high predictive power where the particle originates. We investigate the complementarity between path information and interference visibility through an experiment involving three sources emitting into identical modes. Our findings challenge the classical intuition that a particle can be traced back to its origin through its trajectory when full path information is available. By grouping the crystals in different ways, we demonstrate that it is impossible to ascribe a definite physical origin to the photon pair, even if the emission probability of one individual source is zero and full path information is available. Our results shed new light on the physical interpretation of probability assignment and path information beyond its mathematical meaning and show that the interpretation of path information in quantum mechanics is subjective.
We derive a generalized wave-particle duality relation for arbitrary multipath quantum interference phenomena. Beyond the conventional notion of the wave nature of a quantum system, i.e., the interference fringe visibility, we introduce a quantifier as the normalized quantum coherence, recently defined in the framework of quantum information theory. To witness the particle nature, we quantify the path distinguishability or the which-path information based on unambiguous quantum state discrimination. Then, the Bohr complementarity principle for multipath quantum interference can be stated as a duality relation between the quantum coherence and the path distinguishability. For two-path interference, the quantum coherence is identical to the interference fringe visibility, and the relation reduces to the well-known complementarity relation. The duality relation continues to hold in the case where mixedness is introduced due to possible decoherence effects.
Wave-particle duality in multipath interference is fraught with issues despite substantial progress in recent years. It was experimentally shown that in certain specific conditions, getting path information in a multipath experiment can actually increase the visibility of interference. As a result, it was argued that in multipath interference experiments, visibility of interference and which-path information are not always complementary observables. In the present paper, an alternative wave-particle duality relation is presented, based on a sum of visibilities of interference from individual pairs of paths. This relation is always respected, even in the kinds of specific situations mentioned above. This sum of visibilities turns out to be related to a recently introduced measure of coherence. As one of the consequences, it provides an alternative way of experimentally measuring coherence in a multipath interference experiment. As another consequence, this relation suggests a simple way of measuring path-distinguishability in multipath interference. In addition, it resolves several outstanding issues concerning wave-particle duality in multipath interference.
Abstract Quantum coherence stemming from the superposition behaviour of a particle beyond the classical realm, serves as one of the most fundamental features in quantum mechanics. The wave-particle duality phenomenon, which shares the same origin, has a strong relationship with quantum coherence. Recently, an elegant relation between quantum coherence and path information has been theoretically derived. Here, we experimentally test such new duality by l1-norm measure and the minimum-error state discrimination. We prepare three classes of two-photon states encoded in polarisation degree of freedom, with one photon serving as the target and the other photon as the detector. We observe that wave-particle-like complementarity and Bagan’s equality, defined by the duality relation between coherence and path information, is well satisfied. Our results may shed new light on the original nature of wave-particle duality and on the applications of quantum coherence as a fundamental resource in quantum technologies.
One of the most puzzling consequences of interpreting quantum mechanics in terms of concepts borrowed from classical physics, is the so-called wave-particle duality. Usually, wave-particle duality is illustrated in terms of complementarity between path distinguishability and fringe visibility in interference experiments. In this work, we instead propose a new type of complementarity, that between the continuous nature of waves and the discrete character of particles. Using the probabilistic methods of quantum field theory, we show that the simultaneous measurement of the wave amplitude and the number of photons in the same beam of light is, under certain circumstances, prohibited by the laws of quantum mechanics. Our results suggest that the concept of “interferometric duality'' could be eventually replaced by the more general one of “continuous-discrete duality''.
This article develops an expanded critical-propositional analysis of S. Dürr, T. Nonn, and G. Rempe’s 1998 experiment, “Origin of Quantum-Mechanical Complementarity Probed by a ‘Which-Way’ Experiment in an Atom Interferometer,” published in Nature, in systematic dialogue with the Theory of Objectivity (TO) developed by Vidamor Cabannas and Denivaldo Silva. The Dürr–Nonn–Rempe experiment constitutes an especially significant empirical case because it addresses a foundational question of quantum mechanics: whether the disappearance of interference following the acquisition of which-way information must be explained through mechanical momentum disturbance, as elementary presentations of the uncertainty principle sometimes suggest, or whether complementarity emerges more fundamentally from correlations between distinguishable degrees of freedom. Using an atom interferometer based on rubidium atoms, optical Bragg diffraction, microwave manipulation of hyperfine states, and path marking through internal atomic degrees of freedom, Dürr, Nonn, and Rempe showed that interference can disappear even when the mechanical back action associated with path detection is too small to account for the observed loss of visibility (Dürr, Nonn, and Rempe 1998b). The phenomenon is instead explained through correlations between atomic motion and the internal which-way marker. Their companion quantitative experiment further examined the relation between path distinguishability D and interference visibility V , providing empirical support for the duality relation associated with Englert’s formulation, D 2 + V 2 ≤ 1. The present article examines these results under the modal and methodological discipline proposed by the Theory of Objectivity. It distinguishes three epistemological levels: (1) empirical confirmation of a physical phenomenon; (2) structural compatibility between that phenomenon and categories of the TO; and (3) specific empirical confir- mation of propositions uniquely derived from the TO. This distinction prevents the mistaken inference that an experiment compatible with an axiom thereby demonstrates the axiom’s claimed modal necessity. Particular attention is given to VA4, concerning boundary and distinction; VA5, concerning observation and relational structure; VA6, concerning composition from prior elements and relations; and VA7, concerning the transcendent element understood within the TO as knowledge or information generated in atomic relations and considered equivalent, within the theory, to atomic radiation. The experiment provides a strong empirical demonstration that physically instantiated information can be generated, stored in atomic internal states, correlated with motional alternatives, and associated with measurable changes in interference. This constitutes a potentially important indirect empirical bridge toward the informational dimensions of VA7. Nevertheless, the experiment does not by itself establish the stronger TO proposition that information is ontologically equivalent to atomic radiation, nor does it prove the necessary truth of VA1–VA7. The analysis also considers the phenomenic elements of light, electromagnetic radiation, atomic transitions, information, boundary formation, and observation; the TO concepts of Expansive and Reductive Inducing Effects (EIE/EIR); the cosmogonic theorem; and the theory’s cosmological eras. It argues that the most productive contribution of the Dürr–Nonn–Rempe experiment to the TO is not cosmological but microphysical and methodological. It suggests a possible operational program in which TO concepts of boundary, observation, and informational differentiation are mapped onto measurable quantities such as path distinguishability, coherence, visibility, mutual information, entropy, and state overlap. The resulting assessment is that the Dürr–Nonn–Rempe experiment has a high degree of dialogue with the Theory of Objectivity, particularly through VA4–VA7, while simultaneously exposing an important burden on the TO: to transform philosophical and modal correspondences into mathematically defined, quantitatively testable, and potentially discriminating empirical propositions. Keywords: Theory of Objectivity; quantum complementarity; which-way information; atom interferometry; distinguishability; interference visibility; physical information; quantum correlations; modal ontology; VA4; VA5; VA6; VA7; information and radiation; operational bridges.
A recent experiment performed by Afshar et al (2007 Found. Phys. 37 295–305) has been interpreted as a violation of Bohr's complementarity principle between interference visibility and which-path information (WPI) in a two-path interferometer. We have reproduced this experiment, using true single-photon pulses propagating in a two-path wavefront-splitting interferometer realized with a Fresnel's biprism, and followed by a grating with adjustable transmitting slits. The measured values of interference visibility V and WPI, characterized by the distinguishability parameter D , are found to obey the complementarity relation V 2 + D 2 ⩽1. This result demonstrates that the experiment can be perfectly explained by the standard interpretation of quantum mechanics.