Although the foundations of quantum and classical physics are much different, it is often difficult to pinpoint which features of a particular system are intrinsically "quantum". Perhapse, the most clear-cut distinction between "classical" and "quantum" can be made for systems composed of many particles when the properties of the ensemble are determined by the correlations between the constituents. The issue of grasping the nature of entanglement (i.e. quantum correlations) lies in its formal, discriminative definition: "if state is not classical then it is entangled". A possible remedy would be to approach the problem from the utilitarian point of view. The idea is that certain tasks can be performed better when entangled states are used instead of states that are only classically correlated. An example of such task is an entanglement-enhanced interferometer utilizing ensembles of ultra-cold atoms. This line of reasoning leads to the concept of classification of entanglement by the degree of usefulness and allows to relate it to certain well-defined physical properties of the state. The aim of this work is to formalize this abstraction and build upon it an intuitive picture which can help us understand what the entanglement is.
Although the foundations of quantum and classical physics are much different, it is often difficult to pinpoint which features of a particular system are intrinsically "quantum". Perhapse, the most clear-cut distinction between "classical" and "quantum" can be made for systems composed of many particles when the properties of the ensemble are determined by the correlations between the constituents. The issue of grasping the nature of entanglement (i.e. quantum correlations) lies in its formal, discriminative definition: "if state is not classical then it is entangled". A possible remedy would be to approach the problem from the utilitarian point of view. The idea is that certain tasks can be performed better when entangled states are used instead of states that are only classically correlated. An example of such task is an entanglement-enhanced interferometer utilizing ensembles of ultra-cold atoms. This line of reasoning leads to the concept of classification of entanglement by the degree of usefulness and allows to relate it to certain well-defined physical properties of the state. The aim of this work is to formalize this abstraction and build upon it an intuitive picture which can help us understand what the entanglement is.
Entanglement, a defining property of quantum mechanics in which two physical subsystems cannot be seen as independent entities, challenges our everyday experience and classical intuition. However, only such strong quantum correlations enable quantum technologies, including quantum computing or communication, while revealing the limits of our classical worldview by violating local realism. Given its importance in modern quantum science, we present this tutorial addressing the questions: What is entanglement, how does it differ from classical correlations, and how can it be experimentally verified? Using celebrated examples, such as Schrödinger's cat, we highlight the distinction between classical and quantum correlations and illustrate the definition of entangled and separable states. We review entanglement criteria by discussing Heisenberg-type uncertainty relations for continuous variables and the CHSH inequality for discrete systems. Focusing on concepts of quantum correlations and operational entanglement witnesses, we provide accessible tools and illustrative examples aimed at demystifying entanglement for a broad readership.
Abstract Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating information, such as quantum cryptography, teleportation, and quantum computing. We now know that there is potentially much more than entanglement behind the power of quantum information processing. There exist more general forms of non-classical correlations, stemming from fundamental principles such as the necessary disturbance induced by a local measurement, or the persistence of quantum coherence in all possible local bases. These signatures can be identified and are resilient in almost all quantum states, and have been linked to the enhanced performance of certain quantum protocols over classical ones in noisy conditions. Their presence represents, among other things, one of the most essential manifestations of quantumness in cooperative systems, from the subatomic to the macroscopic domain. In this work we give an overview of the current quest for a proper understanding and characterisation of the frontier between classical and quantum correlations (QCs) in composite states. We focus on various approaches to define and quantify general QCs, based on different yet interlinked physical perspectives, and comment on the operational significance of the ensuing measures for quantum technology tasks such as information encoding, distribution, discrimination and metrology. We then provide a broader outlook of a few applications in which quantumness beyond entanglement looks fit to play a key role.
Theory and experiment have not fully resolved the apparent dichotomy , which has agonized physics for the past eighty years: on the one hand, the description of microsystems by quantum mechanics and, on the other, the description of macrosystems by classical dynamics or statistical mechanics. Derivations of the time-irreversible Liouville equation for an open quantum system, based on projecting out its environment, have narrowed the gap between the quantum and classical descriptions. Yet our `classical' intuition continues to be confronted by quantum-mechanical results like the Einstein--Podolsky--Rosen paradox that challenges the classical notion of locality, or the quantum Zeno effect which suggests that the isolation of a system is not the only way to preserve its quantum state. There are two key concepts in any discussion of such issues. The first, which is responsible for the most salient nonclassical properties, is entanglement , that is partial or complete correlation or, more generally, inseparability of the elements comprising a quantum ensemble . Even after their interaction has ceased, this inseparability, originating from their past interaction, can affect the state of one element when another element is subject to a nonunitary action, such as its measurement, tracing- out, or thermalization. The second key concept is decoherence of open quantum systems, which is the consequence of their entanglement with their environment, a `meter' or a thermal `reservoir', followed by the tracing-out of the latter. Despite new insights into entanglement and decoherence, there are still no complete, unequivocal answers to the fundamental questions of the transition from quantal to classical behaviour: how do irreversibility and classicality emerge from unitarity as systems and their environments become increasingly complex ? At what stage does system--meter entanglement give rise to a classical readout of the meter? Is there an upper limit on the size or complexity of systems displaying entanglement? Major developments have opened new vistas into controlled entanglement , which is the resource of quantum information processing. However, these developments have mainly focused on ensembles of simple two- and three-level systems that are thoroughly isolated from their environments. Treatments of coherence in quantum computing have mostly assumed that only a single or a few the elements of the quantum ensemble may simultaneously undergo an uncontrolled intervention---a quantum error. Decoherence-control protocols for more general types of errors are still incomplete. In order to resolve the outstanding issues of the quantum--classical transition, and study the control of entanglement and decoherence without the foregoing restrictions, we must venture into the domain of Quantum Complex Systems (QUACS), either consisting of a large number of inseparable elements or having many coupled degrees of freedom. Our conviction is that fundamental understanding and manipulation of entanglement within QUACS or their entanglement with the environment or a meter, call for the creation of a new conceptual framework or paradigm, that would encompass phenomena common to cold atoms in laser fields, large molecules, Josephson junctions, quantum gases and solids, with the view of employing these systems for quantum information processing and computing. Progress within this paradigm should allow us to answer the questions: does entanglement play an essential role in the evolution of large collections of complex systems? What are the size and complexity limits of systems and ensembles still controllable by an external intervention? What are the most appropriate decoherence protection schemes and control algorithms? This special issue addresses the challenge of understanding in depth and manipulating the basic quantum properties of optical, atomic, molecular and condensed-matter QUACS, and large ensembles thereof. In view of the interdisciplinary character of this issue, we find it expedient to look at the presented articles not only according to the physical objects they describe, but also from a unifying standpoint. Several unifying themes may be discerned: memory effects in dephasing and relaxation; protection of quantum information by its distribution throughout the ensemble; control of decoherence and entanglement by time-dependent interventions or measurements; manifestations of entanglement in scattering off statistical ensembles; measurment-induced dynamics. The concerted discussion of the topics outlined above should help us advance the new paradigm that addresses our abilities to diagnose and manipulate the entangled states of complex quantum objects and their robustness against decoherence. These abilities are required for quantum information (QI) applications in matter--wave interferometry in molecular, semiconducting or superconducting systems. On the fundamental level, this book may help establish the notion of dynamical information exchange between quantum systems and chart in detail the route from unitarity to classicality. Further developments within the outlined paradigm should yield novel, advantageous QI processing schemes and high-sensitivity interferometers, owing to decoherence suppression and effective control of many degrees of freedom. In the long run, these strategies may prove to be the first step towards the (hitherto unattempted) use of entanglement in nanotechnology, metrology and chemistry, with potentially remarkable novel applications.
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.
The description of a quantum system follows a fundamentally different paradigm to that of a classical system, leading to unique yet counter-intuitive properties. In this thesis we consider some of these unique properties, here termed simply the quantum. We focus on understanding some important types of the quantum: quantum coherence and quantum correlations, as well as quantum entanglement as an important subclass of quantum correlations. Our objective is to investigate how to quantify the quantum, what it can be used for, and how it can be preserved in the adverse presence of noise. These findings help to clarify the frontier between quantum and classical systems, a crucial endeavour for understanding the applications and advantageous features of the quantum world.
Classical objects have been excluded as subjects of the observed quantum properties, and the related problem of quantum objects nature has been suspended since the early days of Quantum Theory. Recent experiments show that the problem could be reasonably revisited. The outlined model indicates new issues, which could result from following and exploring the canonical idea of Dirac. Topological defects in solids are considered as an example. The aim is helping to grasp the underlying pre-theoretical new intuitions, which should replace the old ones attached to the background of classical physics.