Entanglement, the quantum formalism and the classical world

2013

In [M. Piani et al., arXiv:1103.4032 (2011)] an activation protocol was introduced which maps the general non-classical (multipartite) correlations between given systems into bipartite entanglement between the systems and local ancillae by means of a potentially highly entangling interaction. Here, we study how this activation protocol can be used to entangle the starting systems themselves via entanglement swapping through a measurement on the ancillae. Furthermore, we bound the relative entropy of quantumness (a naturally arising measure of non-classicality in the scheme of Piani et al. above) for a special class of separable states, the so-called classical-quantum states. In particular, we fully characterize the classical-quantum two-qubit states that are maximally non-classical.

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.

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.

Physical Review A, 2002

We show that quantum entanglement has a very close classical analogue, namely secret classical correlations. The fundamental analogy stems from the behavior of quantum entanglement under local operations and classical communication and the behavior of secret correlations under local operations and public communication. A large number of derived analogies follow. In particular teleportation is analogous to the one-time-pad, the concept of "pure state" exists in the classical domain, entanglement concentration and dilution are essentially classical secrecy protocols, and single copy entanglement manipulations have such a close classical analog that the majorization results are reproduced in the classical setting. This analogy allows one to import questions from the quantum domain into the classical one, and vice-versa, helping to get a better understanding of both. Also, by identifying classical aspects of quantum entanglement it allows one to identify those aspects of entanglement which are uniquely quantum mechanical. The analogy we suggest is summarized in the following table: quantum secret classical entanglement correlations quantum secret classical communication communication classical public classical communication communication local actions local actions

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.

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

Physical Review A, 2005

We analyze the quantum-to-classical transition ͑QCT͒ for coupled bipartite quantum systems for which the position of one of the two subsystems is continuously monitored. We obtain the surprising result that the QCT can emerge concomitantly with the presence of highly entangled states in the bipartite system. Furthermore, the changing degree of entanglement is associated with the backaction of the measurement on the system and is itself an indicator of the QCT. Our analysis elucidates the role of entanglement in von Neumann's paradigm of quantum measurements comprised of a system and a monitored measurement apparatus.

2011

Entanglement is one of the most intriguing features of quantum mechanics. It gives rise to peculiar correlations which cannot be reproduced by a large class of alternative theories, the so-called hidden-variable models, that use parameters in addition to the wave-function. This incompatibility was quantified through the celebrated Bell inequalities [1-3], and more recently through new inequalities due to . Experiments confirm the predictions of quantum mechanics . However, this does not imply that quantum mechanics is the ultimate theory, unsusceptible of improvement, nor that quantum mechanics is essentially non-local. The theories ruled out by Bell and Leggett inequalities are required to satisfy some hypotheses, none of which is implied by locality alone. By dropping one or more hypotheses, it is possible not only to violate said inequalities, but to reproduce the quantum mechanical predictions altogether . So far, the models proposed were only mathematical constructs. In this paper we provide a classical realization of two of these models, using local classical resources, without recurring to any type of communication among the involved parties. The resources consist in two baseballs, two bats, and a number of synchronized watches. Our results demonstrate the possibility of reproducing the quantum mechanical correlations, and even creating stronger correlations which provide the maximum violation of the Bell inequality, beyond the Cirel'son bound for quantum mechanics.

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.

(Typo Corrections and minor revisions 5-10-23) The conventional analysis of both quantum product states and quantum entanglement is shown to be consistent with a local, hidden variable (LHV) model, where two spatially separated observers make independent local measurements on local wave functions that share a common random hidden source variable. A conventional quantum mechanical LHV derivation also suggests that four quanta are required to truly measure a "zero spin" singlet state, with two quanta detected by each observer. In contrast, Bell local hidden variable (BLHV) models and inequalities assume one quantum detection by each observer, which does accurately model product states, but NOT entangled states. It is also shown that quantum entanglement can be viewed as an interference phenomenon, and can be factored into a "disentangled" product of local wave functions at the two spatially separated observers. Experimental measurements of quantum entanglement appear to be measuring Bell product states, and yet see quantum entanglement; which may suggest a non-local hidden variable (NLHV) process, where a detection by one observer instantaneously modifies the wave function in transit to the other observer. However, this proposed non-local process has serious potential flaws. Alternatively, it is shown that "coincidence of clicks" measurements on local, hidden variable (LHV) entangled or product states can approximate the experimentally reported entangled behavior. Additional experiments could potentially discriminate between these interpretations of the experimental data.