5,145 research outputs found
Eigenlogic: a Quantum View for Multiple-Valued and Fuzzy Systems
We propose a matrix model for two- and many-valued logic using families of
observables in Hilbert space, the eigenvalues give the truth values of logical
propositions where the atomic input proposition cases are represented by the
respective eigenvectors. For binary logic using the truth values {0,1} logical
observables are pairwise commuting projectors. For the truth values {+1,-1} the
operator system is formally equivalent to that of a composite spin 1/2 system,
the logical observables being isometries belonging to the Pauli group. Also in
this approach fuzzy logic arises naturally when considering non-eigenvectors.
The fuzzy membership function is obtained by the quantum mean value of the
logical projector observable and turns out to be a probability measure in
agreement with recent quantum cognition models. The analogy of many-valued
logic with quantum angular momentum is then established. Logical observables
for three-value logic are formulated as functions of the Lz observable of the
orbital angular momentum l=1. The representative 3-valued 2-argument logical
observables for the Min and Max connectives are explicitly obtained.Comment: 11 pages, 2 table
Generalized Quantum Theory: Overview and Latest Developments
The main formal structures of Generalized Quantum Theory are summarized.
Recent progress has sharpened some of the concepts, in particular the notion of
an observable, the action of an observable on states (putting more emphasis on
the role of proposition observables), and the concept of generalized
entanglement. Furthermore, the active role of the observer in the structure of
observables and the partitioning of systems is emphasized.Comment: 14 pages, update in reference
Complete quantum teleportation using nuclear magnetic resonance
Quantum mechanics provides spectacular new information processing abilities
(Bennett 1995, Preskill 1998). One of the most unexpected is a procedure called
quantum teleportation (Bennett et al 1993) that allows the quantum state of a
system to be transported from one location to another, without moving through
the intervening space. Partial implementations of teleportation (Bouwmeester et
al 1997, Boschi et al 1998) over macroscopic distances have been achieved using
optical systems, but omit the final stage of the teleportation procedure. Here
we report an experimental implementation of the full quantum teleportation
operation over inter-atomic distances using liquid state nuclear magnetic
resonance (NMR). The inclusion of the final stage enables for the first time a
teleportation implementation which may be used as a subroutine in larger
quantum computations, or for quantum communication. Our experiment also
demonstrates the use of quantum process tomography, a procedure to completely
characterize the dynamics of a quantum system. Finally, we demonstrate a
controlled exploitation of decoherence as a tool to assist in the performance
of an experiment.Comment: 15 pages, 2 figures. Minor differences between this and the published
versio
Expandable intramedullary nails in lower limb trauma: a systematic review of clinical and radiological outcomes.
This study systematically reviews the evidence-base for the use of expandable nails in the treatment of acute diaphyseal fractures of the lower limb. Both electronic and hand searches were undertaken of the published and grey literature to 1 December 2011. A total of 154 citations were identified, of which 15 were deemed suitable and assessed with the Critical Appraisals Skills Programme tool. A total of 625 nailing procedures were performed in 620 patients: 279 femoral and 346 tibial nails. The expandable nail was found to be significantly quicker to insert than interlocked nails (p < 0.05), and the total incidence of non-union or other complication was 13 and 14 % for expandable femoral and tibial nails, respectively. Notable complications with the expandable nail included fracture propagation on nail inflation in 2.5 % and post-operative shortening in 3.3 %. Device failure secondary to problems with the expansion mechanism was seen in 2.9 %. The rate of non-union and infection following expandable nailing was 3.1 and 1.4 %, respectively. Despite promising initial results, there remains a paucity of good quality studies to support the use of expandable nails over interlocked nails for the treatment of acute diaphyseal fractures of the lower limb
Quantum resource estimates for computing elliptic curve discrete logarithms
We give precise quantum resource estimates for Shor's algorithm to compute
discrete logarithms on elliptic curves over prime fields. The estimates are
derived from a simulation of a Toffoli gate network for controlled elliptic
curve point addition, implemented within the framework of the quantum computing
software tool suite LIQ. We determine circuit implementations for
reversible modular arithmetic, including modular addition, multiplication and
inversion, as well as reversible elliptic curve point addition. We conclude
that elliptic curve discrete logarithms on an elliptic curve defined over an
-bit prime field can be computed on a quantum computer with at most qubits using a quantum circuit of at most Toffoli gates. We are able to classically simulate the
Toffoli networks corresponding to the controlled elliptic curve point addition
as the core piece of Shor's algorithm for the NIST standard curves P-192,
P-224, P-256, P-384 and P-521. Our approach allows gate-level comparisons to
recent resource estimates for Shor's factoring algorithm. The results also
support estimates given earlier by Proos and Zalka and indicate that, for
current parameters at comparable classical security levels, the number of
qubits required to tackle elliptic curves is less than for attacking RSA,
suggesting that indeed ECC is an easier target than RSA.Comment: 24 pages, 2 tables, 11 figures. v2: typos fixed and reference added.
ASIACRYPT 201
On the Trace Anomaly and the Anomaly Puzzle in N=1 Pure Yang-Mills
The trace anomaly of the energy-momentum tensor is usually quoted in the form
which is proportional to the beta function of the theory. However, there are in
general many definitions of gauge couplings depending on renormalization
schemes, and hence many beta functions. In particular, N=1 supersymmetric pure
Yang-Mills has the holomorphic gauge coupling whose beta function is one-loop
exact, and the canonical gauge coupling whose beta function is given by the
Novikov-Shifman-Vainshtein-Zakharov beta function. In this paper, we study
which beta function should appear in the trace anomaly in N=1 pure Yang-Mills.
We calculate the trace anomaly by employing the N=4 regularization of N=1 pure
Yang-Mills. It is shown that the trace anomaly is given by one-loop exact form
if the composite operator appearing in the trace anomaly is renormalized in a
preferred way. This result gives the simplest resolution to the anomaly puzzle
in N=1 pure Yang-Mills. The most important point is to examine in which scheme
the quantum action principle is valid, which is crucial in the derivation of
the trace anomaly.Comment: 25 pages, 1 figure; v2:slight correction in sec.5, minor addition in
appendi
Preparation and Measurement of Three-Qubit Entanglement in a Superconducting Circuit
Traditionally, quantum entanglement has played a central role in foundational
discussions of quantum mechanics. The measurement of correlations between
entangled particles can exhibit results at odds with classical behavior. These
discrepancies increase exponentially with the number of entangled particles.
When entanglement is extended from just two quantum bits (qubits) to three, the
incompatibilities between classical and quantum correlation properties can
change from a violation of inequalities involving statistical averages to sign
differences in deterministic observations. With the ample confirmation of
quantum mechanical predictions by experiments, entanglement has evolved from a
philosophical conundrum to a key resource for quantum-based technologies, like
quantum cryptography and computation. In particular, maximal entanglement of
more than two qubits is crucial to the implementation of quantum error
correction protocols. While entanglement of up to 3, 5, and 8 qubits has been
demonstrated among spins, photons, and ions, respectively, entanglement in
engineered solid-state systems has been limited to two qubits. Here, we
demonstrate three-qubit entanglement in a superconducting circuit, creating
Greenberger-Horne-Zeilinger (GHZ) states with fidelity of 88%, measured with
quantum state tomography. Several entanglement witnesses show violation of
bi-separable bounds by 830\pm80%. Our entangling sequence realizes the first
step of basic quantum error correction, namely the encoding of a logical qubit
into a manifold of GHZ-like states using a repetition code. The integration of
encoding, decoding and error-correcting steps in a feedback loop will be the
next milestone for quantum computing with integrated circuits.Comment: 7 pages, 4 figures, and Supplementary Information (4 figures)
Comparison of Short-Term Estrogenicity Tests for Identification of Hormone-Disrupting Chemicals
The aim of this study was to compare results obtained by eight different short-term assays of estrogenlike actions of chemicals conducted in 10 different laboratories in five countries. Twenty chemicals were selected to represent direct-acting estrogens, compounds with estrogenic metabolites, estrogenic antagonists, and a known cytotoxic agent. Also included in the test panel were 17β-estradiol as a positive control and ethanol as solvent control. The test compounds were coded before distribution. Test methods included direct binding to the estrogen receptor (ER), proliferation of MCF-7 cells, transient reporter gene expression in MCF-7 cells, reporter gene expression in yeast strains stably transfected with the human ER and an estrogen-responsive reporter gene, and vitellogenin production in juvenile rainbow trout. 17β-Estradiol, 17α-ethynyl estradiol, and diethylstilbestrol induced a strong estrogenic response in all test systems. Colchicine caused cytotoxicity only. Bisphenol A induced an estrogenic response in all assays. The results obtained for the remaining test compounds—tamoxifen, ICI 182.780, testosterone, bisphenol A dimethacrylate, 4-n-octylphenol, 4-n-nonylphenol, nonylphenol dodecylethoxylate, butylbenzylphthalate, dibutylphthalate, methoxychlor, o,p′-DDT, p,p′-DDE, endosulfan, chlomequat chloride, and ethanol—varied among the assays. The results demonstrate that careful standardization is necessary to obtain a reasonable degree of reproducibility. Also, similar methods vary in their sensitivity to estrogenic compounds. Thus, short-term tests are useful for screening purposes, but the methods must be further validated by additional interlaboratory and interassay comparisons to document the reliability of the methods
The Regge Limit for Green Functions in Conformal Field Theory
We define a Regge limit for off-shell Green functions in quantum field
theory, and study it in the particular case of conformal field theories (CFT).
Our limit differs from that defined in arXiv:0801.3002, the latter being only a
particular corner of the Regge regime. By studying the limit for free CFTs, we
are able to reproduce the Low-Nussinov, BFKL approach to the pomeron at weak
coupling. The dominance of Feynman graphs where only two high momentum lines
are exchanged in the t-channel, follows simply from the free field analysis. We
can then define the BFKL kernel in terms of the two point function of a simple
light-like bilocal operator. We also include a brief discussion of the gravity
dual predictions for the Regge limit at strong coupling.Comment: 23 pages 2 figures, v2: Clarification of relation of the Regge limit
defined here and previous work in CFT. Clarification of causal orderings in
the limit. References adde
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