Light is neither wave nor particle, but both, according to Bohr’s complementarity principle, which was first devised to qualitatively characterize quantum phenomena. Later, quantification was achieved through inequalities such as V2+D2≤1, which engage visibility V and distinguishability D. Recently, equality V2+D2=P2—the polarization coherence theorem (PCT)—was established, incorporating polarization P and addressing both quantum and classical coherences. This shows that Bohr’s complementarity is not restricted to quantum phenomena. We derive an extension of the PCT that also applies to quantum and classical light fields carrying intertwined, dichotomic observables, such as polarization and two-path alternative. We discuss how constraints critically depend on the chosen measurement strategy. This may prompt various experiments to exhibit complementary features that possibly lurk behind hidden coherences.
Light is neither wave nor particle, but both, according to Bohr’s complementarity principle, which was first devised to qualitatively characterize quantum phenomena. Later, quantification was achieved through inequalities such as V2+D2≤1, which engage visibility V and distinguishability D. Recently, equality V2+D2=P2—the polarization coherence theorem (PCT)—was established, incorporating polarization P and addressing both quantum and classical coherences. This shows that Bohr’s complementarity is not restricted to quantum phenomena. We derive an extension of the PCT that also applies to quantum and classical light fields carrying intertwined, dichotomic observables, such as polarization and two-path alternative. We discuss how constraints critically depend on the chosen measurement strategy. This may prompt various experiments to exhibit complementary features that possibly lurk behind hidden coherences.
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.
For light fields, the manifestation of correlations between fluctuating electric field components at different space–time points is referred to as coherence, whereas these correlations appearing between orthogonal electric field components at a single space–time point are referred to as polarization. In this context, a natural question is as follows: how are coherence and polarization interconnected? Very recently, a tight equality P2=V2+D2, namely, the “polarization coherence theorem” (PCT) connecting polarization P with interference visibility V (measure of coherence) and distinguishability D (measure of which-path information) has been proposed [Optica4, 1113 (2017)OPTIC82334-253610.1364/OPTICA.4.001113]. We here report a direct observation of the PCT for classical light fields using a Mach–Zehnder interferometer along with a synthesized source producing a complete gamut of degrees of polarizations. Our experimental demonstration could motivate ongoing experimental efforts toward probing the hidden coherences and complementarity features.
We report experimental results that show the interplay between visibility, distinguishability, and the degree of polarization, as ruled by a recent extension of the polarization coherence theorem (PCT). Theorems of this kind address duality in both quantum and classical scenarios. We particularly focus on the inherent vector nature of the polarization degree of freedom and display various effects that lie beyond the scope of the original PCT. Our results exhibit features that can be shared by quantum and classical phenomena, whenever these phenomena reflect some hidden or exposed coherence.
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.
The principle of complementarity relationship introduced by Niels Bohr in 1927 states that particle and wave behavior are two mutually exclusive properties for a quantum system.This relationship has taken the attention of researchers for decades due to its conceptual importance.This thesis contains a theoretical research work conducted on quantum complementarity of vectorial light fields and in the doublepinhole interference.Here we have adopted the classical Stokes parameters within a quantum framework and calculated the Stokes parameters in the observation plane in double-pinhole interference.Based on these calculations, we further evaluated visibility and distinguishability parameters for an arbitrary pure single-photon state and for a specific single-photon pure state, where the photon is x polarized at the first pinhole and y polarized at the second pinhole.We have then examined and interpreted the wave-particle duality for the mentioned two states.Finally, we performed mixed state calculation where fully unpolarized photon is incident on the two pinholes, but with the photon at one pinhole rotated by an angle of π/2.From the obtained results we concluded that a priori which path information (WPI) regarding the complementarity relations for the single photon pure vectorial quantum state couples not to the intensity visibility but to the total visibility.We further found that the vectorial quantum state gives rise to polarization modulation.From the results obtained for the mixed state calculations, we discovered that the last Stokes parameter has a non-zero value and it contributes to the polarization modulation.Thereby we further recommended to repeat the calculation for different mixed states other than what we have considered here to extend the exploration about the nature of polarization modulation.
Complementarity, or more specifically, the wave-particle duality, and quantum coherence are two fundamental concepts in quantum mechanics. Recently, motivated by the progress of the quantification of quantum coherence, the complementary relation between coherence and path information is investigated by many authors, and various duality relations between them are established. Such relations not only provide insights into fundamental problems of quantum mechanics, such as the understanding of quantum coherence and wave-particle duality; but also are important in applications of quantum technologies. In this paper, based on the Bures distance and unambiguous quantum state discrimination, systematic analysis of the complementarity between the quantum coherence and path information in two path interferometers is carried out. Similarly as other related works, the wave aspect, or the visibility of the interferometer, is quantified by the l1-norm measure of quantum coherence, and the path information is considered via unambiguous quantum state discrimination. In this way, a novel duality relation in two path interferometers is obtained. Compared with known results, our work considers mixed states as well as pure states; considers the path predictability resulting from the intrinsic path asymmetry of the quantum state, as well as the path distinguishability resulting from the use of a which-path detector. Therefore, our work systematically generalizes known results in two path interferometers by removing all the unnecessary restrictions. Specifically, the most general form of quantum states in two path interferometers is considered and the duality relation between quantum coherence and path information is proved based on the positivity property of density matrices. The cases of path predictability and path distinguishability are considered separately. For path predictability, the proof is straightforward; whereas some advanced mathematical techniques, such as the Schur-Weyl inequality, properties of the fidelity and properties of positive matrices, are required in order to give a rigorous proof of the duality relation between coherence and path distinguishability. Concrete examples are provided to illustrate the abstract method and results. Our work concerns about two path interferometers exclusively and depends heavily that the dimensionality is two, therefore it would be an interesting task to generalize the results in this paper to n-path interferometers.