Quantum privacy amplification and the security of quantum cryptography over noisy channels

Existing quantum cryptographic schemes are not, as they stand, operable in the presence of noise on the quantum communication channel. Although they become operable if they are supplemented by classical privacy-amplification techniques, the resulting schemes are difficult to analyse and have not been proved secure. We introduce the concept of quantum privacy amplification and a cryptographic scheme incorporating it which is provably secure over a noisy channel. The scheme uses an `entanglement purification' procedure which, because it requires only a few quantum Controlled-Not and single-qubit operations, could be implemented using technology that is currently being developed. The scheme allows an arbitrarily small bound to be placed on the information that any eavesdropper may extract from the encrypted message.Comment: 13 pages, Latex including 2 postcript files included using psfig macro

Conditional Quantum Dynamics and Logic Gates

Quantum logic gates provide fundamental examples of conditional quantum dynamics. They could form the building blocks of general quantum information processing systems which have recently been shown to have many interesting non--classical properties. We describe a simple quantum logic gate, the quantum controlled--NOT, and analyse some of its applications. We discuss two possible physical realisations of the gate; one based on Ramsey atomic interferometry and the other on the selective driving of optical resonances of two subsystems undergoing a dipole--dipole interaction.Comment: 5 pages, RevTeX, two figures in a uuencoded, compressed fil

Seewis virus, a genetically distinct hantavirus in the Eurasian common shrew (Sorex araneus)

More than 20 years ago, hantaviral antigens were reported in tissues of the Eurasian common shrew (Sorex araneus), Eurasian water shrew (Neomys fodiens) and common mole (Talpa europea), suggesting that insectivores, or soricomorphs, might serve as reservoirs of unique hantaviruses. Using RT-PCR, sequences of a genetically distinct hantavirus, designated Seewis virus (SWSV), were amplified from lung tissue of a Eurasian common shrew, captured in October 2006 in Graubünden, Switzerland. Pair-wise analysis of the full-length S and partial M and L segments of SWSV indicated approximately 55%–72% similarity with hantaviruses harbored by Murinae, Arvicolinae, Neotominae and Sigmodontinae rodents. Phylogenetically, SWSV grouped with other recently identified shrew-borne hantaviruses. Intensified efforts are underway to clarify the genetic diversity of SWSV throughout the geographic range of the Eurasian common shrew, as well as to determine its relevance to human health

Experimental Demonstration of Greenberger-Horne-Zeilinger Correlations Using Nuclear Magnetic Resonance

The Greenberger-Horne-Zeilinger (GHZ) effect provides an example of quantum correlations that cannot be explained by classical local hidden variables. This paper reports on the experimental realization of GHZ correlations using nuclear magnetic resonance (NMR). The NMR experiment differs from the originally proposed GHZ experiment in several ways: it is performed on mixed states rather than pure states; and instead of being widely separated, the spins on which it is performed are all located in the same molecule. As a result, the NMR version of the GHZ experiment cannot entirely rule out classical local hidden variables. It nonetheless provides an unambiguous demonstration of the "paradoxical" GHZ correlations, and shows that any classical hidden variables must communicate by non-standard and previously undetected forces. The NMR demonstration of GHZ correlations shows the power of NMR quantum information processing techniques for demonstrating fundamental effects in quantum mechanics.Comment: Latex2.09, 8 pages, 1 eps figur

Quantum Clock Synchronization Based on Shared Prior Entanglement

We demonstrate that two spatially separated parties (Alice and Bob) can utilize shared prior quantum entanglement, and classical communications, to establish a synchronized pair of atomic clocks. In contrast to classical synchronization schemes, the accuracy of our protocol is independent of Alice or Bob's knowledge of their relative locations or of the properties of the intervening medium.Comment: 4 page

Elementary gates for quantum computation

We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values $(x,y)$ to $(x,x \oplus y)$) is universal in the sense that all unitary operations on arbitrarily many bits $n$ (U($2^n$)) can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2) transformation to one input bit if and only if the logical AND of all remaining input bits is satisfied. These gates play a central role in many proposed constructions of quantum computational networks. We derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two-and three-bit quantum gates, the asymptotic number required for $n$-bit Deutsch-Toffoli gates, and make some observations about the number required for arbitrary $n$-bit unitary operations.Comment: 31 pages, plain latex, no separate figures, submitted to Phys. Rev. A. Related information on http://vesta.physics.ucla.edu:7777

The mediating effect of task presentation on collaboration and children's acquisition of scientific reasoning

There has been considerable research concerning peer interaction and the acquisition of children's scientific reasoning. This study investigated differences in collaborative activity between pairs of children working around a computer with pairs of children working with physical apparatus and related any differences to the development of children's scientific reasoning. Children aged between 9 and 10 years old (48 boys and 48 girls) were placed into either same ability or mixed ability pairs according to their individual, pre-test performance on a scientific reasoning task. These pairs then worked on either a computer version or a physical version of Inhelder and Piaget's (1958) chemical combination task. Type of presentation was found to mediate the nature and type of collaborative activity. The mixed-ability pairs working around the computer talked proportionally more about the task and management of the task; had proportionally more transactive discussions and used the record more productively than children working with the physical apparatus. Type of presentation was also found to mediated children's learning. Children in same ability pairs who worked with the physical apparatus improved significantly more than same ability pairs who worked around the computer. These findings were partially predicted from a socio-cultural theory and show the importance of tools for mediating collaborative activity and collaborative learning

Information-theoretic interpretation of quantum error-correcting codes

Quantum error-correcting codes are analyzed from an information-theoretic perspective centered on quantum conditional and mutual entropies. This approach parallels the description of classical error correction in Shannon theory, while clarifying the differences between classical and quantum codes. More specifically, it is shown how quantum information theory accounts for the fact that "redundant" information can be distributed over quantum bits even though this does not violate the quantum "no-cloning" theorem. Such a remarkable feature, which has no counterpart for classical codes, is related to the property that the ternary mutual entropy vanishes for a tripartite system in a pure state. This information-theoretic description of quantum coding is used to derive the quantum analogue of the Singleton bound on the number of logical bits that can be preserved by a code of fixed length which can recover a given number of errors.Comment: 14 pages RevTeX, 8 Postscript figures. Added appendix. To appear in Phys. Rev.