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Bound entanglement – mysterious invention of nature

Ryszard Horodecki

Published Nov 1, 2010• 9 citations
Publisher

Abstract

leven years later, on 23 rd August 2009, Nature Physics [1] reported that the researchers of a laboratory in Stockholm had created a four-qubit bound entangled state.Another eight months later, on 30 th April, another team from the laboratory in Dortmund reported the creation of pseudo-bound entanglement [2].When that paper was in preparation, a team of researchers from Waterloo (see Fig. 1) announced [3] that they had managed to experimentally create a genuine bound entangled state.At the same time the Innsbruck group presented an experiment implementing bound entanglement with ions [4].e exciting course of these events already shows that experimental, unrecoverable imprisoning of quantum correlations,even in the simplest (four-qubit) arrangement, is no small challenge.At the current stage, full understanding of bound entanglement -"a mysterious invention of nature"[5] -may be no more than an illusion.Nevertheless, it is interesting to follow the paths that led to that invention in a foggy bush of quantum formalism,in order properly to appreciate the efforts and inventiveness of experimentalists.

DOI
10.1051/epn/2010603

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leven years later, on 23 rd August 2009, Nature Physics [1] reported that the researchers of a laboratory in Stockholm had created a four-qubit bound entangled state.Another eight months later, on 30 th April, another team from the laboratory in Dortmund reported the creation of pseudo-bound entanglement [2].When that paper was in preparation, a team of researchers from Waterloo (see Fig. 1) announced [3] that they had managed to experimentally create a genuine bound entangled state.At the same time the Innsbruck group presented an experiment implementing bound entanglement with ions [4].e exciting course of these events already shows that experimental, unrecoverable imprisoning of quantum correlations,even in the simplest (four-qubit) arrangement, is no small challenge.At the current stage, full understanding of bound entanglement -"a mysterious invention of nature"[5] -may be no more than an illusion.Nevertheless, it is interesting to follow the paths that led to that invention in a foggy bush of quantum formalism,in order properly to appreciate the efforts and inventiveness of experimentalists.
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When two particles are created together in a single quantum event, they can become entangled: their properties remain correlated no matter how far apart they travel. Measure one, and the outcome of measuring the other is no longer independent. This correlation is the central puzzle of quantum mechanics. Classical physics sets a hard limit on how strong such correlations can be. The CHSH inequality (Clauser, Horne, Shimony, and Holt, 1969) formalises that limit: for any theory in which each particle carries its own independent set of predetermined answers, the correlation measure S cannot exceed 2. Bell-type experiments consistently violate this bound, with the maximum ideal value predicted by quantum mechanics being S = 2√2. Something does not fit. Several explanations have been proposed. Some invoke extra dimensions. Others appeal to wormhole geometries connecting the particles. The mainstream position is that the outcomes "collapse and become correlated," which states the observation without explaining the mechanism. All of these either add dramatic ontological furniture or repackage the mystery as an answer. This paper proposes a simpler reading. The value 2√2 is not a mystery to be explained by exotic physics. It is the geometric signature of a jointly structured bipartite state whose correlation was fixed at the source, at the moment of entanglement, not at measurement time. The two particles are not two independent objects that later communicate. They are two readout surfaces of a single joint preparation. The cosine correlation law, the Tsirelson bound, and the full Bell violation follow directly from the geometry of the two-qubit state space and the relative orientation of the measurement settings. No signal, no extra dimension, no new physics is required. Three companion papers in this series explored the opposite hypothesis: The Speed of Light and Its Limits [1] examined whether entanglement could circumvent relativistic constraints; Quantum Entanglement as a Communication Channel [2] proposed a synchronized-clock experiment to detect timing signatures; and Parametrizing Correlation Timing [3] developed a Lorentz-structured ansatz for concurrence-dependent delays. If those experimental proposals return null, the present reading is reinforced: not by proof, but by elimination of the alternatives that require more. A final section develops geometric and regime-based frameworks consistent with the source-structural reading, including the measurement torus as the natural geometry of Bell experiments, a jointness index based on Concurrence, and connections to emergent spacetime programmes. These are offered as directions for future development.
The rapidly developing interdisciplinary field of quantum information, which merges quantum and information science, studies non-classical aspects of quantum systems. These studies are motivated by the promise that the non-classicality can be used to solve tasks more efficiently than classical methods would allow. In many quantum informational studies, non-classical behaviour is attributed to the notion of entanglement. In this thesis we use photons to experimentally investigate fundamental questions such as: What happens to the entanglement in a system when it is affected by noise? In our study of noisy entanglement we pursue the challenging task of creating bound entanglement. Bound entangled states are created through an irreversible process that requires entanglement. Once in the bound regime, entanglement cannot be distilled out through local operations assisted by classical communication. We show that it is possible to experimentally produce four-photon bound entangled states and that a violation of a Bell inequality can be achieved. Moreover, we demonstrate an entanglement-unlocking protocol by relaxing the condition of local operations. We also explore the non-classical nature of quantum mechanics in several single-photon experiments. In these experiments, we show the violation of various inequalities that were derived under the assumption of non-contextuality. Using qutrits we construct and demonstrate the simplest possible test that offers a discrepancy between classical and quantum theory. Furthermore, we perform an experiment in the spirit of the Kochen-Specker theorem to illustrate the state-independence of this theorem. Here, we investigate whether or not measurement outcomes exhibit fully contextual correlations. That is, no part of the correlations can be attributed to the non-contextual theory. Our results show that only a small part of the experimental generated correlations are amenable to a non-contextual interpretation.
From its seemingly non-intuitive and puzzling nature, most evident in numerous EPR-like gedanken experiments to its almost ubiquitous presence in quantum technologies, entanglement is at the heart of modern quantum physics. First introduced by Erwin Schrödinger nearly a century ago, entanglement has remained one of the most fascinating ideas that came out of quantum mechanics. Here, we attempt to explain what makes entanglement fundamentally different from any classical phenomenon. To this end, we start with a historical overview of entanglement and discuss several hidden variables models that were conceived to provide a classical explanation and demystify quantum entanglement. We discuss some inequalities and bounds that are violated by quantum states thereby falsifying the existence of some of the classical hidden variables theories. We also discuss some exciting manifestations of entanglement, such as N00N states and the non-separable single particle states. We conclude by discussing some contemporary results regarding quantum correlations and present a future outlook for the research of quantum entanglement.
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