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Studies in Classical and Quantum Correlations and their Evolution in Physical Systems

Asma Al-Qasimi

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

More than a century ago, starting with Michelson, the field of classical coherence has developed rapidly. By studying and uncovering the coherence properties of light, many useful applications were discovered. In modern times, these applications have seen large use in fields like astronomy, where the properties of light can be used to discover stars and determine their radius, for example. Another class of correlations, namely quantum correlations, which were discovered in the beginning of the twentieth century, have gained much attention from the scientific community in the last two decades. In particular, the field of quantum information developed, promising great computational power by using quantum correlations to build computers. Currently, quantum computation is a very active field bringing together physicists, mathematicians, engineers, chemists, and computer scientists to find solutions to the problems encountered in building quantum computers.\n\nI consider some classical coherence effects of the degree of cross polarization (DCP) on the Hanbury-Brown Twiss effect, with a specific focus on Gaussian Schell-model beams. I show that the DCP is necessary, in general, to determine the correlations in intensity fluctuations of a beam at two different points. As for quantum correlations, I consider entanglement in realistic systems: one in two-qubit systems, and the other in continuous variable quantum systems. In the former case, when the temperature of the system is finite, entanglement always decays in a finite time. However, in the latter case, entanglement is long-lived, although in the long run it is not of much practical use. Finally, I unravel the relationship between quantum discord and quantum entanglement, as well as quantum discord and entropy for the most general two-qubit systems, and I identify the states that define the boundaries of these relationships.

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More than a century ago, starting with Michelson, the field of classical coherence has developed rapidly. By studying and uncovering the coherence properties of light, many useful applications were discovered. In modern times, these applications have seen large use in fields like astronomy, where the properties of light can be used to discover stars and determine their radius, for example. Another class of correlations, namely quantum correlations, which were discovered in the beginning of the twentieth century, have gained much attention from the scientific community in the last two decades. In particular, the field of quantum information developed, promising great computational power by using quantum correlations to build computers. Currently, quantum computation is a very active field bringing together physicists, mathematicians, engineers, chemists, and computer scientists to find solutions to the problems encountered in building quantum computers.\n\nI consider some classical coherence effects of the degree of cross polarization (DCP) on the Hanbury-Brown Twiss effect, with a specific focus on Gaussian Schell-model beams. I show that the DCP is necessary, in general, to determine the correlations in intensity fluctuations of a beam at two different points. As for quantum correlations, I consider entanglement in realistic systems: one in two-qubit systems, and the other in continuous variable quantum systems. In the former case, when the temperature of the system is finite, entanglement always decays in a finite time. However, in the latter case, entanglement is long-lived, although in the long run it is not of much practical use. Finally, I unravel the relationship between quantum discord and quantum entanglement, as well as quantum discord and entropy for the most general two-qubit systems, and I identify the states that define the boundaries of these relationships.
I briefly review second order or two-photon correlations starting from the Hanbury Brown-Twiss correlations to its modern versions in quantum optics studies. With this background, I address some foundational issues in the physics of quantum correlations and quantum entanglement and argue in favour of the validity of Einstein locality, to settle a long-standing debate. Understanding entanglement from this perspective has applications in quantum information theory, especially in gaining intuition about the relation between different measures of entanglement and its time evolution. Some examples are highlighted. I discuss how ideas on photon correlations applied to squeezing fluctuations in coherent light have become important in metrology, and perhaps crucial, in the successful operation of high sensitivity gravitational wave detectors.
In this review we discuss intriguing properties of apparently classical optical fields, that go beyond purely classical context and allow us to speak about quantum characteristics of such fields and about their applications in quantum technologies. We briefly define the genuinely quantum concepts of entanglement and steering. We then move to the boarder line between classical and quantum world introducing quantum discord, a more general concept of quantum coherence, and finally a controversial notion of classical entanglement. To unveil the quantum aspects of often classically perceived systems, we focus more in detail on quantum discordant correlations between the light modes and on nonseparability properties of optical vector fields leading to entanglement between different degrees of freedom of a single beam. To illustrate the aptitude of different types of correlated systems to act as quantum or quantum-like resource, entanglement activation from discord, high-precision measurements with classical entanglement and quantum information tasks using intra-system correlations are discussed. The common themes behind the versatile quantum properties of seemingly classical light are coherence, polarization and inter and intra-mode quantum correlations.
Quantum discord is a more general measure of quantum correlations than entanglement and has been proposed as a resource in certain quantum information processing tasks. The computation of discord is mostly confined to two-qubit systems for which an analytical calculational scheme is available. The utilization of quantum correlations in quantum information-based applications is limited by the problem of decoherence, i.e., the loss of coherence due to the inevitable interaction of a quantum system with its environment. The dynamics of quantum correlations due to decoherence may be studied in the Kraus operator formalism for different types of quantum channels representing system-environment interactions. In this review, we describe the salient features of the dynamics of classical and quantum correlations in a two-qubit system under Markovian (memoryless) time evolution. The two-qubit state considered is described by the reduced density matrix obtained from the ground state of a spin model. The models considered include the transverse-field XY model in one dimension, a special case of which is the transverse-field Ising model, and the XXZ spin chain. The quantum channels studied include the amplitude damping, bit-flip, bit-phase-flip and phase-flip channels. The Kraus operator formalism is briefly introduced and the origins of different types of dynamics discussed. One can identify appropriate quantities associated with the dynamics of quantum correlations which provide signatures of quantum phase transitions in the spin models. Experimental observations of the different types of dynamics are also mentioned.
Quantum information theory (QIT) is an emerging field of physics which aims to develop new methods of dealing with information by harnessing the power of quantum mechanics. Besides its potential to revolutionize the techniques of information processing and communication, it also provides novel approaches to better comprehend the foundations of quantum mechanics. Among many important problems in QIT, manipulation and dynamical characterization of correlations present in quantum systems stand out due to their relevance for the practical applications of the theory. This thesis intends to explore such correlations of quantum and classical nature from various perspectives. In particular, our discussions involve the investigation of local transformations among a class of entangled states and the examination of correlation measures in some physical models. We first examine the classification of the flip (0-1) and exchange symmetric (FES) states under local quantum operations. We study the optimal local one-shot conversions of FES states to determine the entanglement transformations that relate multiqubit FES states with the maximum possible probability of success. Next, we investigate the exchange symmetry properties of certain symmetric states when the qubits evolve according to a dephasing model which is also invariant under swap operation. We find that there exist states which do not preserve the exchange symmetry with unit probability during the time evolution, leading to the spontaneous breaking of exchange symmetry. Later, we turn our attention to the dynamics of quantum and classical correlations for qubit-qutrit systems in independent and global dephasing environments. In these cases, we demonstrate several interesting phenomena such as the transition from classical to quantum decoherence. Lastly, we investigate the thermal quantum and total correlations in the one-dimensional anisotropic XY model in transverse field. We discuss the ability of different measures to estimate the critical point of the quantum phase transition at finite temperature. We also consider the relation between correlations and the factorized ground state in this model. Furthermore, we study the effect of temperature on long-range correlations.
Intensity-interferometry based on Hanbury-Brown and Twiss's seminal experiment for determining the radius of the star Sirius formed the basis for developing the quantum theory of light. To date, the principle of this experiment is used in various forms across different fields of quantum optics, imaging and astronomy. Though, the technique is powerful, it has not been generalized for objects at different temperatures. Here, we address this problem using a generating functional formalism by employing the P-function representation of quantum-thermal light. Specifically, we investigate the photon coincidences of a system of two extended objects at different temperature using this theoretical framework. We show two unique aspects in the second-order quantum coherence function - interference oscillations and a long-baseline asymptotic value that depends on the observation frequency, temperatures and size of both objects. We apply our approach to the case of binary stars and discuss the advantages of measuring these two features in an experiment. In addition to the estimation of the radii of each star and the distance between them, we also show that the present approach is suitable for the estimation of temperatures as well. To this end, we apply it to the practical case of binary stars Luhman 16 and Spica ααα Vir. We find that for currently available telescopes, an experimental demonstration is feasible in the near term. Our work contributes to the fundamental understanding of intensity interferometry of quantum-thermal light and can be used as a tool for studying two-body thermal emitters - from binary stars to extended objects.
Quantum coherence and quantum correlations are of fundamental and practical significance for the development of quantum mechanics.They are also cornerstones of quantum computation and quantum communication theory. Searching physically meaningful and mathematically rigorous quantifiers of them are long-standing concerns of the community of quantum information science, and various faithful measures have been introduced so far. We review in this paper the measures of discordlike quantum correlations for bipartite and multipartite systems, the measures of quantum coherence for any single quantum system, and their relationship in different settings. Our aim is to provide a full review about the resource theory of quantum coherence, including its application in many-body systems, and the discordlike quantum correlations which were defined based on the various distance measures of states. We discuss the interrelations between quantum coherence and quantum correlations established in an operational way, and the fundamental characteristics of quantum coherence such as their complementarity under different basis sets, their duality with path information of an interference experiment, their distillation and dilution under different operations, and some new viewpoints of the superiority of the quantum algorithms from the perspective of quantum coherence. Additionally, we review properties of geometric quantum correlations and quantum coherence under noisy quantum channels. Finally, the main progresses for the study of quantum correlations and quantum coherence in the relativistic settings are reviewed. All these results provide an overview for the conceptual implications and basic connections of quantum coherence, quantum correlations, and their potential applications in various related subjects of physics.