We establish an exact identity among four dimensionless invariants accessible by standard polarimetric and interferometric measurements in a polarized double-slit experiment: the in-phase and quadrature components V_A and V_N of fringe visibility, the path predictability P, and the mixedness I of the path-reduced state satisfy V_A^2 + V_N^2 + P^2 + I^2 = 1. The identity is a universal algebraic consequence of the positivity of the reduced state and holds for every normalized path-polarization density matrix. It unifies the Englert-Greenberger-Yasin and Jakob-Bergou relations, separates the two operationally distinct components of visibility measurable by phase-shifted interferometry, and admits a natural interpretation within the Jaynes maximum-entropy framework: the three path invariants parametrize the minimal exponential family on the accessible algebra, while I^2 emerges as the residual mixedness that saturates the positivity bound. The separation V^2 = V_A^2 + V_N^2 identifies the antisymmetric sector of the coherence matrix rho = A + iN as the specific substrate of phase-sensitive information and permits a sector-resolved diagnosis of environmental coupling.
We establish an exact identity among four dimensionless invariants accessible by standard polarimetric and interferometric measurements in a polarized double-slit experiment: the in-phase and quadrature components V_A and V_N of fringe visibility, the path predictability P, and the mixedness I of the path-reduced state satisfy V_A^2 + V_N^2 + P^2 + I^2 = 1. The identity is a universal algebraic consequence of the positivity of the reduced state and holds for every normalized path-polarization density matrix. It unifies the Englert-Greenberger-Yasin and Jakob-Bergou relations, separates the two operationally distinct components of visibility measurable by phase-shifted interferometry, and admits a natural interpretation within the Jaynes maximum-entropy framework: the three path invariants parametrize the minimal exponential family on the accessible algebra, while I^2 emerges as the residual mixedness that saturates the positivity bound. The separation V^2 = V_A^2 + V_N^2 identifies the antisymmetric sector of the coherence matrix rho = A + iN as the specific substrate of phase-sensitive information and permits a sector-resolved diagnosis of environmental coupling.
The dual wave–particle nature of light and the degree of polarization are fundamental concepts in quantum physics and optical science, but their exact relation has not been explored within a full vector-light quantum framework that accounts for interferometric polarization modulation. Here, we consider vector-light quantum complementarity in double-pinhole photon interference and derive a general link between the degree of polarization and wave–particle duality of light. The relation leads to an interpretation for the degree of polarization as a measure describing the complementarity strength between photon path predictability and so-called Stokes visibility, the latter taking into account both intensity and polarization variations in the observation plane. It also unifies results advanced in classical studies by showing that the degree of polarization can be viewed as the ability of a light beam to exhibit intensity and polarization-state fringes. The framework we establish thus provides novel aspects and deeper insights into the role of the degree of polarization in quantum-light complementarity and photon interference.
Bohr’s principle of complementarity, after gaining contributions from several researchers, moved from a qualitative analysis to a quantitative analysis through what we call today complementarity relations (CR). This change made it possible to quantify aspects of path superposition and distinguishability (predictability and entanglement) in a single experimental apparatus, for example, the Mach-Zehnder interferometer (MZI), gaining historical appeal in the quantification of path superposition through interferometric visibility. Furthermore, CR of quantum coherence, predictability and entanglement functions that are dependent on the quantum state, have also gained relevance in this area of research. In this dissertation, based on other research, we were directed to carry out two works involving the IMZ and analysis through CR. In the first work, we build a version of the MZI and show that interferometric visibility is not always able to correctly quantify the path superposition within the MZI for two-path systems. We found that CR involving quantum coherence end up reflecting the expected behavior for the photon in this same experimental apparatus. In the second work, we performed an integral analysis, through the complete CR, of the entangled quantum eraser (EQE). In this experimental apparatus, we consider a variable partially-polarizing beam splitter (VPPBS) that can produce path superposition of the horizontal and vertical polarizations entering the MZI. Due to the inclusion of the VPPBS, part of the experimental apparatus of the standard quantum eraser was modified, so that we need to perform Bell’s basis measurements of the degree of freedom of the polarizations of the two entangled photons. Therefore, the analysis of the EQE, through the CR, ends up being much richer, producing situations where there are even partial erasures of the information available before the erasure process. In both papers, we verified our theoretical findings by implementing experiments on IBM’s quantum computers.
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.
The analogs of optical elements in light-pulse atom interferometers are generated from the interaction of matter waves with light fields. As such, these fields possess quantum properties, which fundamentally lead to a reduced visibility in the observed interference. This loss is a consequence of the encoded information about the atom's path. However, the quantum nature of the atom-optical elements also gives an additional degree of freedom to reduce such effects: We demonstrate that entanglement between all light fields can be used to erase information about the atom's path and by that to partially recover the visibility. Thus, our work highlights the role of complementarity on atom-interferometric experiments.
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.