Interference effects are known to have a dependence upon indistinguishability of path. For this reason, it is accepted that different sources of a system cannot interfere if they have distinguishable states. We present an analysis of interference that predicts the allowance of interference between distinguishable states under the strict condition that the preparation has no distinguishability of path that results from the distinguishability of the states of the possible sources. This leads us to a new analysis of the quantum eraser experiment. In Principle Indistinguishability of paths In the history of interference effects in quantum mechanics it is dogmatically accepted in the literature that interference will only occur if there is no distinguishing information of path. For the classic double slit interference effect it is often argued that the knowledge of the system’s passage through one of the slits will lead to the result of non-interference, and only in the preparation where there is no such knowledge will the interference be measured. The reason for which interference effects require that the preparation be one where there is no implied knowledge of path is because any knowledge of path would imply a different state description. Knowledge of path could only be possible if the state of the system was not the superposition of states which allows for both paths. This can be loosely stated by
Interference effects are known to have a dependence upon indistinguishability of path. For this reason, it is accepted that different sources of a system cannot interfere if they have distinguishable states. We present an analysis of interference that predicts the allowance of interference between distinguishable states under the strict condition that the preparation has no distinguishability of path that results from the distinguishability of the states of the possible sources. This leads us to a new analysis of the quantum eraser experiment. In Principle Indistinguishability of paths In the history of interference effects in quantum mechanics it is dogmatically accepted in the literature that interference will only occur if there is no distinguishing information of path. For the classic double slit interference effect it is often argued that the knowledge of the system’s passage through one of the slits will lead to the result of non-interference, and only in the preparation where there is no such knowledge will the interference be measured. The reason for which interference effects require that the preparation be one where there is no implied knowledge of path is because any knowledge of path would imply a different state description. Knowledge of path could only be possible if the state of the system was not the superposition of states which allows for both paths. This can be loosely stated by
One of the central principles of quantum mechanics is that if there are multiple paths that lead to the same event and there is no way to distinguish between them, interference occurs. It is often assumed that distinguishing information in the preparation, evolution, or measurement of a system is sufficient to destroy interference. However, it is still possible for photons in distinguishable, separable states to interfere due to the indistinguishability of paths corresponding to possible exchange processes. Here we experimentally measure an interference signal that depends only on the multiparticle interference of four photons in a four-port interferometer despite pairs of them occupying distinguishable states.
Quantum interference constitutes one of the sharpest divides between our classical intuition and the weirdness of the quantum world. Whenever there are multiple paths leading to the same outcome, it is the interplay of associated probability amplitudes that determines measurement results. In the double slit experiment, wave-like interference governs the distribution of particles on a detection screen. Extending to multiple particles allows behaviour that cannot be described by a classical wave, such as the bunching of photon pairs in Hong-Ou-Mandel interference. In both these examples, the ability to distinguish the interfering paths leads to degradation of interference and a return to behaviour described by probabilities. Understanding how this transition evolves for larger multiparticle quantum systems is of fundamental interest and also vital for developing photonic quantum technologies that rely on many-photon interference. In this thesis we investigate the role of distinguishability in the interference of three and four independent photons by using polarisation and time delays. For three photons, a new type of collective distinguishing phase appears that goes beyond a pairwise description of the similarity of quantum states. We use nonlinear photon sources and a fibre interferometer to experimentally demonstrate the ability to tune and isolate this phase in interference statistics. Extending to four photons we show that, contrary to intuition from two-photon experiments, the interference of photons prepared in distinguishable states is possible due to a four-particle phase. This is confirmed experimentally using a bulk four-mode interferometer. We then extend our study to include the effects of state impurity in the interference of three photons. New properties of this interference enable diagnosis of realistic experimental imperfections and characterisation tasks impossible using only two photons. Finally, we link discussions of state distinguishability to the group representations underpinning the exchange symmetry of multiparticle wavefunctions.
In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well-known text books in quantum mechanics implicitly and/or explicitly use this assumption that is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from nonclassical paths in quantum interference experiments that provide a measurable deviation from a naive application of the superposition principle. A direct experimental demonstration for the existence of these nonclassical paths is difficult to present. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.
The issue of interference and which-way information is addressed in the context of three-slit interference experiments. A new path distinguishability |DQ| is introduced, based on unambiguous quantum state discrimination. An inequality connecting the interference visibility and path distinguishability, |V+3−DQ2DQ≤1|, is derived which puts a bound on how much fringe visibility and which-way information can be simultaneously obtained. It is argued that this bound is tight. For two-slit interference, we derive a new duality relation which reduces to Englert's duality relation and the Greenberger–Yasin duality relation, in different limits.
Recent times have seen a spurt of research activity focused on "completing" certain wave-particle duality relations using entanglement or polarization. These studies use a duality relation involving path-predictability, and not path-distinguishability. Quantum origins of these results are explored here, in the more general framework of multipath quantum interference. Multipath interference with a path-detector is theoretically analyzed to find the connection between predictability and distinguishability. It is shown that entanglement is what quantitatively connects distinguishability with predictability. Thus, a duality relation between distinguishability and coherence can also be viewed as a triality between predictability, entanglement, and coherence. There exist two different kinds of duality relations in the literature, which pertain to two different kinds of interference experiments, with or without a path-detector. Results of this study show that the two duality relations are quantitatively connected via entanglement. The roots of the new, to the best of our knowledge, results in the classical optical domain, including the polarization coherence theorem, can be understood in the light of this work.
This thesis is a dissemination of the work I have done in the last four years, under supervision of Prof. Tabish Qureshi. The central theme is towards the understanding of entanglement as a physical resource and looking for its possible applications. This thesis contains six chapters.The Chapter 1 provides the background knowledge for the thesis work, which includes the mathematical formalism of quantum mechanics and the conceptual understanding of entanglement.The Chapter 2 unfolds the idea of fundamental concepts such as Bohr’s complementarity principle, quantum interference, which-path information, their trade-off relation, quantum eraser and also discuss how these issues play their role in building the foundations of quantum theory.The Chapter 3 is devoted to three slit interference experiments. The interference experiment is one of the most prominent concept of quantum theory. The two slit interference set-up is broadly studied and clearly understood, the synopsis for more than two slits are still not clear, recently a focussed research has been shifted towards three slit set-ups. We study the trade-off relation for three slit experiment in terms of visibility and the path distinguishability based on unambiguous quantum state discrimination (UQSD) method.The Chapter 4 discusses the wave-particle duality for multi-slit interference. Several attempts have been made in the past two decades to procure the trade-off relation for multi-slit experiments, yet a satisfactory answer was lacking. We obtain an analogous wave particle duality relation in terms of coherence and path-distinguishability based on UQSD. The role of coherence in building the interference pattern is largely admitted and their amount is readily stated by fringe visibility. Recently coherence has been understood as an information theoretical resource. We explore the measure of coherence as a wave quantifier rather than well known fringe visibility. We also analyze a recently proposed multi-path relation of Bagan et al. which claims to be in Englert’s form. We show that the proposed relation does not hold the essence of complementarity. We also derive a relation similar to Englert’s one to fill the exigency and to explicate its equivalence with our earlier proposed relation.The Chapter 5 discuss the scenario when the source is considered to be entangled. The entangled photon exhibits an interesting phenomenon known as ghost interference. The trade-off relation for two and three slit ghost experiment has been formulated, and also a doable quantum eraser has been proposed.The Chapter 6 aims to use the entanglement as a resource and develop the quantum information technologies, with Quantum Key Distribution (QKD). We propose a QKD protocol using entangled qubits which is shown to add an additional security over the well known BB84 protocol.