Recently, the basic concept of quantum coherence (or superposition) has gained a lot of renewed attention, after Baumgratz et al. ( Phys. Rev. Lett. 113 , 140401. (doi:10.1103/PhysRevLett.113.140401)), following Åberg ( http://arxiv.org/abs/quant-ph/0612146 ), have proposed a resource theoretic approach to quantify it. This has resulted in a large number of papers and preprints exploring various coherence monotones, and debating possible forms for the resource theory. Here, we take the view that the operational foundation of coherence in a state, be it quantum or otherwise wave mechanical, lies in the observation of interference effects. Our approach here is to consider an idealized multi-path interferometer, with a suitable detector, in such a way that the visibility of the interference pattern provides a quantitative expression of the amount of coherence in a given probe state. We present a general framework of deriving coherence measures from visibility, and demonstrate it by analysing several concrete visibility parameters, recovering some known coherence measures and obtaining some new ones.
Recently, the basic concept of quantum coherence (or superposition) has gained a lot of renewed attention, after Baumgratz et al. ( Phys. Rev. Lett. 113 , 140401. (doi:10.1103/PhysRevLett.113.140401)), following Åberg ( http://arxiv.org/abs/quant-ph/0612146 ), have proposed a resource theoretic approach to quantify it. This has resulted in a large number of papers and preprints exploring various coherence monotones, and debating possible forms for the resource theory. Here, we take the view that the operational foundation of coherence in a state, be it quantum or otherwise wave mechanical, lies in the observation of interference effects. Our approach here is to consider an idealized multi-path interferometer, with a suitable detector, in such a way that the visibility of the interference pattern provides a quantitative expression of the amount of coherence in a given probe state. We present a general framework of deriving coherence measures from visibility, and demonstrate it by analysing several concrete visibility parameters, recovering some known coherence measures and obtaining some new ones.
Abstract Interference, which has its origin in the superposition principle, is one of the hallmarks of wave mechanics and constitutes a versatile resource for many information processing tasks. As such, it is actually a manifestation of coherence. Despite its long history in the development of physics, quantitative studies of interference are still an important topic. Traditionally, interference is often characterized via the fringe visibility from an operational perspective. This is experimentally convenient. However, from a theoretic perspective, it is desirable to reveal information‐theoretic aspects of interference. In this work, coherence of a state (with respect to a unitary operator parameterized by the interfering paths and phase shifts in multi‐path interference) is first quantified in terms of a generalized version of the Wigner‐Yanase skew information, two natural quantifiers of interference are then introduced via this coherence measure. Basic properties of these quantifiers of interference are further revealed, and the concepts are illustrated through several examples.
The interference observed for a quanton, traversing more than one path, is believed to characterize its wave nature. Conventionally, the sharpness of interference has been quantified by its visibility or contrast, as defined in optics. Based on this visibility, wave-particle duality relations have been formulated for two-path interference. However, as one generalizes the situation to multi-path interference, it is found that conventional interference visibility is not a good quantifier. A recently introduced measure of quantum coherence has been shown to be a good quantifier of the wave nature. The subject of quantum coherence, in relation to the wave nature of quantons and to interference visibility, is reviewed here. It is argued that coherence can be construed as a more general form of interference visibility, if the visibility is measured in a different manner, and not as contrast. Quanta 2019; 8: 24–35.
Quantum Physics
The notion that particles have properties of waves lies at the heart of quantum mechanics. When quantum systems interact, their interaction can be described in terms of interfering waves, whose coherence is of utmost importance in working out how these waves ultimately interfere. Determining how much coherence there is in a system or how much is required for a particular process is difficult to quantify, though. Baumgratz et al. present a rigorous mathematical framework for the quantification of coherence and identify intuitive and easily computable measures that can be used to compute it. They argue that having such a quantifiable metric will have important implications for describing energy transfer processes or transferring quantum information between quantum elements.
Phys. Rev. Lett. 10.1103/PhysRevLett.113.140401 (2014).
Abstract Discussions about quantum interference, indistinguishability, and superposition between quantum states go back to the beginning of quantum mechanics. However, the theoretical problem, concerning quantitative measures for quantum coherence, was only recently solved by Baumgratz et al (2014 Phys. Rev. Lett. 113 140401). Since then, many works have explored one of the possible coherence measures: the l 1 norm, which has not yet been obtained experimentally for spatial photonic states in high dimensions. In this article, we study the measurement of spatial qudits quantum coherence. We treat the optical measure-operators as path-markers and show in which condition an interference pattern can be used for measure l 1 norm. We analyze the validity of a l 1 norm measurement method, proposed by Paul and Qureshi (2017 Phys. Rev. A 95 042110), implementing it experimentally in qutrit states, and propose an alternative method for qudits states in which one of their assumptions does not apply.
The notion of measurement is of both foundational and instrumental significance in quantum mechanics, and coherence destroyed by measurements (decoherence) lies at the very heart of quantum to classical transition. Qualitative aspects of this spirit have been widely recognized and analyzed ever since the inception of quantum theory. However, axiomatic and quantitative investigations of coherence are attracting great interest only recently with several figures of merit for coherence introduced [Baumgratz, Cramer, and Plenio, Phys. Rev. Lett. 113, 140401 (2014)]. While these resource theoretic approaches have many appealing and intuitive features, they rely crucially on various notions of incoherent operations which are sophisticated, subtle, and not uniquely defined, as have been critically assessed [Chitambar and Gour, Phys. Rev. Lett. 117, 030401 (2016)]. In this paper, we elaborate on the idea that coherence and quantum uncertainty are dual viewpoints of the same quantum substrate, and address coherence quantification by identifying coherence of a state (with respect to a measurement) with quantum uncertainty of a measurement (with respect to a state). Consequently, coherence measures may be set into correspondence with measures of quantum uncertainty. In particular, we take average quantum Fisher information as a measure of quantum uncertainty, and introduce the corresponding measure of coherence, which is demonstrated to exhibit desirable properties. Implications for interpreting quantum purity as maximal coherence, and quantum discord as minimal coherence, are illustrated.
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.