The quantification of wave-particle duality (WPD) by means of measurable features associated to it, such as fringe visibility ($\mathcal {V}$) and path distinguishability ($\mathcal {D}$), led to the establishment of the constraint $\mathcal {V}^{2}+\mathcal {D}^{2} \leq \,1$. The two involved quantities refer to so-called "quantons", physical objects that are capable of generating an interferometric pattern, while being at least partially localizable. Any quanton's internal degree of freedom (DOF) can in principle be used as a path-marker. When the quanton and its internal DOF are simultaneously engaged, new constraints can be derived and experimentally tested. Generalized constraints show how $\mathcal {V}$ and $\mathcal {D}$ relate to other quantifiers and bring to light coherences that might remain otherwise hidden in both quantum and classical light. We submitted two-qubit constraints to experimental tests, using optical light beams. This shows that, despite the rather contrived nature of the constraints, linear optics setups are appropriate to test them. Our experimental results are in very good agreement with theoretical predictions related to the tested constraints. Our results also show that quantifiers such as $\mathcal {V}$ and $\mathcal {D}$ help not only to quantify, but also to generalize the concept of WPD.
The quantification of wave-particle duality (WPD) by means of measurable features associated to it, such as fringe visibility (V) and path distinguishability (D), led to the establishment of the constraint V2+D2≤1. The two involved quantities refer to so-called "quantons", physical objects that are capable of generating an interferometric pattern, while being at least partially localizable. Any quanton's internal degree of freedom (DOF) can in principle be used as a path-marker. When the quanton and its internal DOF are simultaneously engaged, new constraints can be derived and experimentally tested. Generalized constraints show how V and D relate to other quantifiers and bring to light coherences that might remain otherwise hidden in both quantum and classical light. We submitted two-qubit constraints to experimental tests, using optical light beams. This shows that, despite the rather contrived nature of the constraints, linear optics setups are appropriate to test them. Our experimental results are in very good agreement with theoretical predictions related to the tested constraints. Our results also show that quantifiers such as V and D help not only to quantify, but also to generalize the concept of WPD.
Photons in a two-path interferometer best embody wave-particle duality (WPD), which is a core concept of quantum theory. So far, the WPD relation is commonly written as V2+D2≤1, where V is the interference fringe visibility and D is path distinguishability, i.e., the distinguishability of which path a photon passed. This inequality is saturated only when the which-way marker (WWM), which embodies which-path information (WPI) via an internal degree of freedom of photons, such as polarization, is in a pure state. For mixed-state WWM, conventionally defined distinguishability underestimates the amount of WPI and thus does not saturate the WPD relation. Here, we introduce a generalized measure of distinguishability D that properly quantifies the WPI and saturates the WPD relation for all pure- and mixed-state WWM within a purification-based framework. To this end, mixed-state WWM is treated as a result of entanglement formation between the WWM and an external degree of freedom, e.g., environment, and D is defined so that it incorporates the total WPI shared between the WWM and the environment. We show that D thus defined is experimentally quantifiable, independently of V, without access to the environment. We experimentally evaluate V and D using true single photons generated in the completely mixed (unpolarized) state, and thus verify the saturated WPD relation.
Quantum objects, sometimes called quantons, often display a characteristic feature referred to as wave-particle duality (WPD). Lately, this and other quantum traits have been subjected to intensive research, mainly motivated by the development of quantum information science. As a consequence, the scopes of some concepts have been extended, and it has been realized that they are not in the exclusive domain of quantum physics. This is particularly clear in optics, where qubits may show up as Jones vectors and WPD has its counterpart as wave-ray duality. WPD was originally addressed by focusing on a single qubit, which was afterwards supplemented with a second one playing the role of a path-marker in an interferometer setup. Fringe contrast, a sign of wave-like behavior, was proved to be diminished in connection with the effectiveness of the marker, the inducer of particle-like behavior. Going from bipartite to tripartite states is a natural and necessary step towards better understanding of WPD. This step is what we have accomplished in this work. We report some constraints ruling WPD for tripartite systems, as well as their experimental display with single photons.
According to the relevant theories on duality relation, the summation of the extractable information of a quanton’s wave and particle properties, which are characterized by interference visibility V and path distinguishability D, respectively, is limited. However, this relation is violated upon quantum superposition between the wave-state and particle-state of the quanton, which is caused by the quantum beamsplitter (QBS). Along another line, recent studies have considered quantum coherence C in the l1-norm measure as a candidate for the wave property. In this study, we propose an interferometer with a quantum which-path detector (QWPD) and examine the generalized duality relation based on C. We find that this relationship still holds under such a circumstance, but the interference between these two properties causes the full-particle property to be observed when the QWPD system is partially present. Using a pair of polarization-entangled photons, we experimentally verify our analysis in the two-path case. This study extends the duality relation between coherence and path information to the quantum case and reveals the effect of quantum superposition on the duality relation.
We present an extension of the polarization coherence theorem (PCT) for the case in which two qubits play similarly important roles. The standard version of the PCT: V2+D2=P2, involves three measures, visibility V, distinguishability D, and the degree of polarization P, all of which refer to a single qubit, regardless of its physical realization. This is also the case with the inequality that is implied by the PCT: V2+D2≤1, which was originally derived in an attempt to quantify Bohr’s complementarity principle. We show that all of these constraints hold true, no matter how the involved qubits are physically realized, either as quantum or else as classical objects.
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.
Updating the wave-particle duality Maria C. Bosca e-mail: bosca@ugr.es Departamento de Fisica Atomica, Molecular y Nuclear Universidad de Granada E-18071. Granada Spain The wave-particle-duality, the fundamental component of the new quantum formalism in Bohr’s opinion, must be reformulated by incorporating the results of some experiments accomplished in the last decades of twentieth century. The Bohr´s complementarity principle stated the mutual exclusiveness and joint full completeness of the two (classical) descriptions of quantum systems; after Einstein-Podolsky-Rosen’paper, the wave-particle duality, or wave-particle complementarity, could be expressed by stating that it is impossible to build up an experimental arrangement in which we observe at the same time both corpuscular and wave aspects. In a two-slit experiment, they would correspond, respectively, to the which-way knowledge and the observation of interference pattern. Bohr showed this mutual exclusivity in numerous examples , and linked it to the unavoidable disturbance inherent in any measurement event. In quantum mechanical formalism, the complementarity principle has a clear mathematical expression: two observables are complementary if precise knowledge of one of them implies that all possible outcomes of the other are equally probable; their extension to classical concepts (as wave and particle) is not concerned. In 1991 Scully et al published a variant of the two-slit experiment that incorporates two micromasers cavities and a laser beam to provide which-path information without net momentum transferred during the interaction ; the impossibility of know which slit an atom went through and still observe the interference fringes is preserved by the establishing of quantum correlations between the measuring apparatus and the system being observed. They claimed that complementarity, of which wave-particle duality would be to them a manifestation, is more fundamental than the uncertainty principle . In 1996 B-G. Englert, following an approach originally due to Wooters and Zurek , derived , without making use of Heisenberg’s uncertainty relation, an inequality that quantifies the mutual compatibility relation between fringe visibility and which-way information. The inequality, that they denominated as “interferometric duality”, has the expression D^2 + V^2 ≤ 1, where D stands for the distinguishability of the ways and V for the fringe visibility; both of them are mathematical expressions that can be measured to check experimentally the inequality . Today, it is clear that intermediate particle-wave behaviours exist and, in addition to that, there are single experiments in which both classical wave-like and particle-like behaviours are showed total and simultaneously on an individual system. For instance, in the Bose’s double-prism experiment , tunnelling and perfect anticoincidence were observed in single photon states. Consequently, the meaning of the wave-particle duality must incorporate the simultaneous use of the two classical descriptions in the interpretation of experiments, loosing their original mutual exclusivity , which is incorporated as an extreme case in the new interferometric duality, a continuous quantum concept . The wave-particle duality, therefore, must be formulated as an interpretative addition to quantum mechanics, to which is possible to renounce if any pretension of visualize quantum phenomena in terms of classical concepts and intuitions is abandoned.