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Frontiers in Optics

TUTORIAL: Entanglement and Quantum Information Theory

S. J. van Enk

Published Jan 1, 2011• 1 citation
Publisher

Abstract

In this tutorial I'll review the old and modern definitions of entanglement, discuss why we think entanglement is useful, and present various methods that can be used to detect entanglement in an experiment. Article not available.
DOI
10.1364/fio.2011.fwn2

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This paper contributes to the proceedings of the Latin-American School of Physics (ELAF-2017) on Quantum Correlations, and is a brief review of quantum entanglement and nonlocality. In such a brief review, only some topics can be covered. The emphasis is on those topics relevant that may be relevant to detecting multi-particle quantum correlations arising in atomic and Bose-Einstein condensate (BEC) experiments. The paper is divided into five sections. In the first section, the historical papers of Einstein-Podolsky-Rosen (EPR), Bell, Schrodinger and Greenberger-Zeilinger-Horne (GHZ) are described in a tutorial fashion. This is followed by an introduction to entanglement and density operators. A discussion of the classes of nonlocality is given in the third section, including the modern interpretation of the correlations of the EPR paradox experiments, known as EPR steering correlations. The fourth section covers the detection and generation of so-called continuous variable entanglement and EPR steering. Various known criteria are derived with the details of the proofs given for tutorial purposes. The final section focuses on the criteria and methods that have been useful to detect quantum correlation in BEC or atomic systems. Recent results relating spin squeezing with quantum correlations, including entanglement and EPR steering, are summarised.
November 1997, “The Radical Eye” Let me send you some prep work…while I'm procrastinating from things I really need to be doing. I'll convey the information in my favorite way: quoting/forwarding old emails! The first, an old – kind of poorly written – note “Dreams of a More Ethereal Quantum,” concerns one aspect of the below-the-water stuff: the idea about distilling the MaxEntlooking part out of quantum theory. It doesn't say much more than I said in the proposal…but you can't expect too much, it's still just a vague program for a program. That stuff is at the bottom of the note; the early part of the note says a few – even more sketchy – things about Mermin and Quantum Probabilities…so I thought I would include it for that reason. The only other readable thing (I think) I've written on this aspect of the below-the-water stuff is on pages 22–26 of my paper with Caves, “Quantum Information: How Much Information in a State Vector” (it's on quant-ph). These same pages also contain an extended discussion on probability. The second note, “Rainy Mondays and Consistent Histories,” is a note I wrote Bob Griffiths concerning what I think of his Consistent History stuff. I think it says quite plainly and clearly what I think about probability in quantum mechanics. It's pretty self-contained (i.e., not referring to old conversations, etc.), so you might find it useful reading.
Quantum Entanglement-one of the weirdest and most exciting aspects of quantum mechanics. Two or more particles become entangled in a way that if the state of one of the particles is measured, then instantaneously the state of another particle is determined even if they are far apart from one another. The content of this paper explores the details of quantum entanglement: where it came from, what the basic principles are, what experiments support this notion, and what experiments we use to study entanglement. The trends of the data are laid out and what it signifies. From here, I then move to what effects quantum entanglement will have on quantum computing, cryptography and communication. I will attempt to justify my arguments through thirteen published academic sources prior to 2019.
Various kinds of methods of entanglement detection and definitions of entanglement measurement in quantum systems were reviewed.For entanglement of two or more particles,some separability criterions were summarized.Their relationships with positive map and the relationships between themselves were also analyzed.Particularly,concentrations on entanglement witness are paid which is a special criterion involving its definition and construction methods.Further,its applications are also investigated from the viewpoint of experiment.Based on axiomatic hypothesis of entanglement measurement,the theoretical definitions of two-particle and multipartite entanglement,and their estimations in experiment were discussed.At last, various nonlinear separability criterions were analyzed.
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.