Entanglement—A Higher Order Symmetry

Communications in Mathematical Physics, 2010

... E-mail: [email protected]; [email protected] 2 Departamento de Fisica, Universidade Federal de Minas Gerais, Caixa Postal 702, Belo Horizonte, MG 30123-970, Brazil 3 Institut für Theoretische Physik, Universität Ulm, Albert-Einstein-Allee 11, D-89069 ...

2005

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This work is a collection of papers on quantum entanglement. It is intended as a glimpse for the younger colleagues of the author at Ericsson Hungary. Our intention was to introduce as many features as possible, within a readable extent. Our selection criteria are very wide, the work spans the gap from university lecture through research paper to magazine article. Our goal is to illustrate that the topic is very interesting and it covers several unsolved problems. It can be a good basis for research.

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.

2007

The author would like to thank her supervisor Dr. Debasis Sarkar, for proper guidance and help without which it would be truly impossible to pursue the research work. The author is also grateful to all the senior scientists of this field or related areas for various discussions, helpful advices and inspirations. Specially, the author acknoledges Dr. G. Kar and group with all the good-old longtime sessions at ISI, Kolkata. The author would sincerely thank Dr. Arun Pati for invitation at the Institute of Physics. Discussions about the 'No-Go Theorems' at IOP are really open new paths to go on. Its' a pleasure to be in contact with the renowned research personalities like, Prof.

Physical Review A, 2006

In recent years it has become apparent that constraints on possible quantum operations, such as those constraints imposed by superselection rules (SSRs), have a profound effect on quantum information theoretic concepts like bipartite entanglement. This paper concentrates on a particular example: the constraint that applies when the parties (Alice and Bob) cannot distinguish among certain quantum objects they have. This arises naturally in the context of ensemble quantum information processing such as in liquid NMR. We discuss how a SSR for the symmetric group can be applied, and show how the extractable entanglement can be calculated analytically in certain cases, with a maximum bipartite entanglement in an ensemble of N Bell-state pairs scaling as log(N ) as N → ∞. We discuss the apparent disparity with the asymptotic (N → ∞) recovery of unconstrained entanglement for other sorts of superselection rules, and show that the disparity disappears when the correct notion of applying the symmetric group SSR to multiple copies is used. Next we discuss reference frames in the context of this SSR, showing the relation to the work of von Korff and Kempe [Phys. Rev. Lett. 93, 260502 (2004)]. The action of a reference frame can be regarded as the analog of activation in mixed-state entanglement. We also discuss the analog of distillation: there exist states such that one copy can act as an imperfect reference frame for another copy. Finally we present an example of a stronger operational constraint, that operations must be non-collective as well as symmetric. Even under this stronger constraint we nevertheless show that Bell-nonlocality (and hence entanglement) can be demonstrated for an ensemble of N Bell-state pairs no matter how large N is. This last work is a generalization of that of Mermin [Phys. Rev. D 22, 356 (1980)].

New Journal of Physics, 2005

(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.

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.