Quantum coherence and correlations in cold atom systems

2001

Entanglement, according to Erwin Schrödinger the essence of quantum mechanics, is at the heart of the Einstein-Podolsky-Rosen paradox and of the so called quantum-nonlocality -the fact that a local realistic explanation of quantum mechanics is not possible as quantitatively expressed by violation of Bell's inequalities. Even as entanglement gains increasing importance in most quantum information processing protocols, its conceptual foundation is still widely debated. Among the open questions are: What is the conceptual meaning of quantum entanglement? What are the most general constraints imposed by local realism? Which general quantum states violate these constraints? Developing Schrödinger's ideas in an information-theoretic context we suggest that a natural understanding of quantum entanglement results when one accepts (1) that the amount of information per elementary system is finite and (2) that the information in a composite system resides more in the correlations than in properties of individuals. The quantitative formulation of these ideas leads to a rather natural criterion of quantum entanglement. Independently, extending Bell's original ideas, we obtain a single general Bell inequality that summarizes all possible constraints imposed by local realism on the correlations for a multi-particle system. Violation of the general Bell inequality results in an independent general criterion for quantum entanglement. Most importantly, the two criteria agree in essence, though the two approaches are conceptually very different. This concurrence strongly supports the information-theoretic interpretation of quantum entanglement and of quantum physics in general.

2013

Entanglement-according to Schrödinger (1935) the essential property of quantum mechanics-teaches us that the properties of individual quantum systems cannot be considered to be (local) elements of physical reality before and independent of observation. Yet it is a widespread point of view that the way the observations on, say, two particles are correlated, i.e. the specific type of their entanglement, can still be considered as a property of the physical world. Here I discuss a previous experiment (Walther et al., 2006) showing that this is explicitly not the case. The correlations between a single particle property, the polarization state of a photon, and a joint property of two particles, the entangled state of a photon pair in a three-photon entangled state, have been measured. It is shown that the correlations between these properties can obey a cosine relation in direct analogy with the polarization correlations in one of the triplet Bell states (Bell, 1964). The cosine correlations between the polarization and entangled state measurements are too strong for any local-realistic explanation and are experimentally exploited to violate a Clauser-Horne-Shimony-Holt (CHSH) Bell inequality (Bell, 1964; Clauser et al., 1969). Thus, entanglement itself can be an entangled property leading to the notion of entangled entanglement.

Actual Problems of Mind, 2024

Idea of quantum entanglement is discussed in the context of debate about the Einstein-Podolsky-Rosen thought experiment and some theoretical studies of quantum systems. It is noted that Schrödinger invented this idea in 1935 in order to fix some features of the quantum-mechanical description of two systems with temporary interaction. However, he did not grasp essence of these features really. In view of the concepts of mixture and statistical operator proposed by von Neumann and adopted by Schrödinger in 1936, it is argued that the idea of entanglement and related terminology are not necessary in quantum mechanics. One can use this idea and terms "entanglement" etc. as "visual" surrogates for the "mixture – statistical operator" pair. Deeper comparative analysis of several theoretical works by Schrödinger, von Neumann, and Landau showed that the modeling of non-trivial complex quantum systems as quasi-classical aggregates has been gradually overcome. Instead, wholeness of such quantum systems was actually recognized step by step. Thus, wholeness is immanent not only to quantum phenomena, as Niels Bohr had argued, but also to the quantum systems themselves, objectively. The pair "mixture – statistical operator" and especially the pair "mixed state – density matrix" similar to it appear to be adequate tools to comprehend and describe wholeness of diverse quantum reality. It is insisted, it is advisable to understand the surrogate idea of entanglement and relevant terminology in the same sense. In mature quantum paradigm, they are possible but not necessary theoretical tools to grasp wholeness of reality. Respectively, acceptable understanding of quantum entanglement must be based on recognition of quantum wholeness. Philosophically speaking, the idea of entanglement is understandable and conditionally acceptable in the view of contemporary rational holism, or holistic rationality. The clarified understanding of quantum entanglement, as well as Bohr's substantiation of wholeness of quantum phenomena, demonstrates irreducibility of the Universe to any quasi-classical aggregate. Moreover, all this supports the view of the Universe as real wholeness, which rational holism intends to grasp. It is concluded, further development and regular implementation of rational holism have the undoubted potential for revolutionary replacement of the hitherto widespread worldview in the spirit of Democritus and pure analytical methodology of knowledge. Key words: quantum entanglement, Einstein-Podolsky-Rosen thought experiment, wholeness of quantum system itself, wholeness of the Universe, contemporary rational holism.

In this work we review and further develop the controversial concept of "classical entanglement" in optical beams. We present a unified theory for different kinds of light beams exhibiting classical entanglement and we indicate several possible extensions of the concept. Our results shed new light upon the physics at the debated border between the classical and the quantum representations of the world.

Foundations of Science, 2021

and the United States, to animate an interdisciplinary dialogue about fundamental issues of science and society. 'Entanglement' is a genuine quantum phenomenon, in the sense that it has no counterpart in classical physics. It was originally identified in quantum physics experiments by considering composite entities made up of two (or more) sub-entities which have interacted in the past but are now sufficiently distant from each other. If joint measurements are performed on the sub-entities when the composite entity is in an 'entangled state', then the sub-entities exhibit, despite their spatial separation, statistical correlations (expressed by the violation of 'Bell inequalities') which cannot be represented in the formalism of classical physics.

Advanced Technologies of Quantum Key Distribution, 2018

Quantum correlations: entanglement and quantumness of correlations are main resource for quantum information theory. In this chapter it is presented the scenarios which quantumness of correlations plays an interesting role in entanglement distillation protocol. By means of Koashi-Winter relation, it is discussed that quantumness of correlations are related to the irreversibility of the entanglement distillation protocol. The activation protocol is introduced, and it is proved that quantumness of correlations can create distillable entanglement between the system and the measurement apparatus during a local measurement process.

2019

Quantum entanglement, a term coined by Erwin Schrodinger in 1935, is a mechanical phenomenon at the quantum level wherein the quantum states of two (or more) particles have to be described with reference to each other though these particles may be spatially separated. This phenomenon leads to paradox and has puzzled us for a long time. The behaviour of entangled particles is apparently inexplicable, incomprehensible and like magic at work. Locality has been a reliable and fruitful principle which has guided us to the triumphs of twentieth century physics. But the consequences of the local laws in quantum theory could seem "spooky" and nonlocal, with some theorists questioning locality itself. Could two subatomic particles on opposite sides of the universe be really instantaneously connected? Is any theory which predicts such a connection essentially flawed or incomplete? Are the results of experiments which demonstrate such a connection being misinterpreted? These questions challenge our most basic concepts of spatial distance and time. Modern physics is in the process of dismantling the space all around us and the universe will never be the same. Quantum entanglement involves the utilisation of cutting edge technology and will bring great benefits to society. This paper traces the development of quantum entanglement and presents some possible explanations for the strange behaviour of entangled particles. This paper is published in an international journal.

2003

The significance of the quantum feature of entanglement between physical systems is investigated in the context of quantum measurements. It is shown that, while there are measurement couplings that leave the object and probe systems nonentangled, no information transfer from object to probe can take place unless there is at least some intermittent period where the two systems are entangled.

All our former experience with application of quantum theory seems to say: what is predicted by quantum formalism must occur in laboratory. But the essence of quantum formalism -entanglement, recognized by Einstein, Podolsky, Rosen and Schrödinger -waited over 70 years to enter to laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including "canonical" ones: quantum cryptography, quantum teleportation and dense coding. However, it appeared that this new resource is very complex and difficult to detect. Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying. In particular, the authors discuss various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, quantum cryptography and point out some interrelations. They also discuss a basic role of entanglement in quantum communication within distant labs paradigm and stress some peculiarities such as irreversibility of entanglement manipulations including its extremal form -bound entanglement phenomenon. A basic role of entanglement witnesses in detection of entanglement is emphasized. quantum computing with quantum data structure 37 IX. Classical algorithms detecting entanglement 37 X. Quantum entanglement and geometry 38 XI. The paradigm of local operations and classical communication (LOCC) 39 A. Quantum channel -the main notion 39 B. LOCC operations 39 XII. Distillation and bound entanglement 41 A. One-way hashing distillation protocol 41 B. Two-way recurrence distillation protocol 42 93 C. Byzantine agreement -useful entanglement for quantum and classical distributed computation 94 ACKNOWLEDGMENTS 94