730 research outputs found

    Experimental GHZ Entanglement beyond Qubits

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    The Greenberger-Horne-Zeilinger (GHZ) argument provides an all-or-nothing contradiction between quantum mechanics and local-realistic theories. In its original formulation, GHZ investigated three and four particles entangled in two dimensions only. Very recently, higher dimensional contradictions especially in three dimensions and three particles have been discovered but it has remained unclear how to produce such states. In this article we experimentally show how to generate a three-dimensional GHZ state from two-photon orbital-angular-momentum entanglement. The first suggestion for a setup which generates three-dimensional GHZ entanglement from these entangled pairs came from using the computer algorithm Melvin. The procedure employs novel concepts significantly beyond the qubit case. Our experiment opens up the possibility of a truly high-dimensional test of the GHZ-contradiction which, interestingly, employs non-Hermitian operators.Comment: 6+6 pages, 8 figure

    Tracing the cryptic Sardic (Ordovician) metamorphism across Alpine Europe: the Krndija region in the Slavonian Mountains, Croatia

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    Results of a combined petrological, geochemical and geochronological study suggest that metasedimentary rock units in the Krndija region of the Slavonian Mountains, Croatia, were affected by at least three major tectonometamorphic imprints: during the Middle Ordovician (Sardic event), the early Carboniferous (Variscan event), and the Cretaceous (Alpine event). All three metamorphic phases are established by electron microprobe-based in-situ U–Th–Pb dating of monazite grains. The Sardic metamorphic event is additionally confirmed by a precise Lu–Hf garnet-whole-rock isochron age of 466.0 ± 2.3 Ma. Taken together, the data unveil a relatively large and well-preserved piece of the cryptic Sardic orogen in central Krndija, that we name the Kutjevo Zone. A Sardic subduction-related metamorphic event (ca. 540-580 ℃, 8–11 kbar) at ca. 466 Ma is manifested in the mineral paragenesis Ca-rich garnet plus rutile. A low degree of retrograde reequilibration suggests a subsequent fast exhumation. Low-Ca cores in some garnets and staurolite relics record a pre-HP metamorphic event that involves isobaric heating from 570 to 610 ℃ at ~ 7 kbar. We attribute this (so far undated) event to mid-crustal contact metamorphism caused by early Sardic magmatism. Southern parts of Krndija (the Gradište Zone) experienced an (additional?) clockwise PT evolution in Variscan times at ca. 350 Ma. Garnet formed with ilmenite during a PT increase from 580 ℃/5 kbar to 600 ℃/6 kbar and underwent later strong retrograde resorption. Slow Variscan exhumation resulted in andalusite formation at < 550 ℃/ < 3.8 kbar. Penetrative Alpine metamorphism was observed in low-grade phyllites in the north. The lithology and metamorphic history of the Kutjevo Zone is similar to what has been reported from the Sardic Strona-Ceneri Zone in the western Alps. Both areas expose metapelitic (metagreywacke) rocks with a pre-middle Ordovician formation age. These metasedimentary rocks are inter-layered with numerous small amphibolitic units as well as metagranitoids and were likely deposited along the active Gondwana margin, perhaps in a fore-arc position, prior to their subduction during the middle Ordovician. According to recent palaeogeographic reconstructions, both the Kutjevo Zone and the Strona-Ceneri Zone have once resided in an eastern sector of the northern Gondwana margin (i.e., in E-Armorica). We conclude that in the Middle Ordovician, important subduction activities took place in this E-Armorican segment of north Gondwana, which is today exposed in the Alps. The W-Armorican segment of north Gondwana (now exposed in the French, German, and Czech Variscides) had probably already mutated from a (Cadomian) subduction setting to an extensional (transtensional–transpressional) setting by the late Cambrian

    Modulus Computational Entropy

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    The so-called {\em leakage-chain rule} is a very important tool used in many security proofs. It gives an upper bound on the entropy loss of a random variable XX in case the adversary who having already learned some random variables Z1,…,ZℓZ_{1},\ldots,Z_{\ell} correlated with XX, obtains some further information Zℓ+1Z_{\ell+1} about XX. Analogously to the information-theoretic case, one might expect that also for the \emph{computational} variants of entropy the loss depends only on the actual leakage, i.e. on Zℓ+1Z_{\ell+1}. Surprisingly, Krenn et al.\ have shown recently that for the most commonly used definitions of computational entropy this holds only if the computational quality of the entropy deteriorates exponentially in ∣(Z1,…,Zℓ)∣|(Z_{1},\ldots,Z_{\ell})|. This means that the current standard definitions of computational entropy do not allow to fully capture leakage that occurred "in the past", which severely limits the applicability of this notion. As a remedy for this problem we propose a slightly stronger definition of the computational entropy, which we call the \emph{modulus computational entropy}, and use it as a technical tool that allows us to prove a desired chain rule that depends only on the actual leakage and not on its history. Moreover, we show that the modulus computational entropy unifies other,sometimes seemingly unrelated, notions already studied in the literature in the context of information leakage and chain rules. Our results indicate that the modulus entropy is, up to now, the weakest restriction that guarantees that the chain rule for the computational entropy works. As an example of application we demonstrate a few interesting cases where our restricted definition is fulfilled and the chain rule holds.Comment: Accepted at ICTS 201

    Momentum transfer for momentum transfer-free which-path experiments

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    We analyze the origin of interference disappearance in which-path double aperture experiments. We show that we can unambiguously define an observable momentum transfer between the quantum particle and the path detector and we prove in particular that the so called ``momentum transfer free'' experiments can be in fact logically interpreted in term of momentum transfer.Comment: to appear in Phys. Rev . A (2006). (7 pages, 2 figures
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