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physica status solidi (b)

On quantum entanglement and quantum communication

Marek Żukowski

Published Apr 3, 2009• 1 citation
Publisher

Abstract

Abstract This article presents a talk given at 23rd International Conference on Theoretical Physics (Ustroń, 2008). A new version of Bell's theorem is presented, with inequalities based on four assumptions: realism, locality and “free will” and “principle of rotational symmetry of physical laws”. The new Bell‐type inequalities are derived using a simple geometrical intuition. The assumptions behind Bell's theorem are discussed. A critique of overinterpretations of violations of Bell inequalities is given. Further on, a new criterion for entanglement is presented, based on simple geometrical ideas. This leads to a new class of entanglement identifiers, which is richer than entanglement witnesses. Finally a link between Bell's theorem and communication complexity problems will be shown. It covers also realizations, which do not involve entanglement (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200881569

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(A) Bell's theorem rests on a conjunction of three assumptions: realism, locality and ``free will''. A discussion of these assumptions will be presented. It will be also shown that, if one adds to the assumptions the principle or rotational symmetry of physical laws, a stronger version of the theorem emerges. (B) A link between Bell's theorem and communication complexity problems will be presented. This also includes experimental realizations, which surprisingly do not involve entanglement. (C) A new sufficient and necessary criterion for entanglement of general (mixed) states is be presented. It is derived using the same geometric starting point as the inclusion of the symmetry in (A). The set of entanglement identifiers (EI's) emerging via this method contains entanglement witnesses (EW's), but they form only a subset of all EI's. Thus the method is more powerful than the one based on EW's.
In the first part of this thesis Bell's theorem is revisited. It points at a difference between the quantum and the classical world. This difference is often behind the advantages of solutions using quantum mechanics. New and more general versions of Bell inequalities are presented. These inequalities involve multiple settings per observer. Compared with the two-setting inequalities, the new ones reveal the non-classical character of a broader class of states. Some of them are also proven to be optimal (tight). Next, we go beyond Bell's theorem. It is shown, both in theory and in experiment, that incompatibility between quantum mechanics and realistic theories can be extended into an important class of nonlocal models. We also show that the violation of Bell inequalities disqualifies local realistic models with a limited lack of the experimenter's freedom. This, at first glance quite philosophical result, has its down-to-earth implications for quantum communication. In the second part of the thesis well-known examples of quantum communication are reviewed. Next, new results concerning quantum cryptography and quantum communication complexity are given.
We discuss general Bell inequalities for bipartite and multipartite systems, emphasizing the connection with convex geometry on the mathematical side, and the communication aspects on the physical side. Known results on families of generalized Bell inequalities are summarized. We investigate maximal violations of Bell inequalities as well as states not violating (certain) Bell inequalities. Finally, we discuss the relation between Bell inequality violations and entanglement properties currently discussed in quantum information theory.
Abstract We investigate the influence of environmental noise on polariton entangled pairs in the self‐stimulated regime. By adopting a recent separability criterion, we show that self‐stimulation may suppress the detrimental influence of noise on entanglement, but once effective, a noise‐equipped classical model of parametric emission provides the same results of quantum theory with respect to the separability criterion. More generally we show that, in the macroscopic limit, it is not possible to observe violations of local realism with measurements of finite order n ‐particle correlations only. These results provide a prototypical case of the emergence of macroscopic local realism in the presence of strong entanglement even in the absence of decoherence. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)