Interest Rates and Information Geometry

The space of probability distributions on a given sample space possesses natural geometric properties. For example, in the case of a smooth parametric family of probability distributions on the real line, the parameter space has a Riemannian structure induced by the embedding of the family into the Hilbert space of square-integrable functions, and is characterised by the Fisher-Rao metric. In the nonparametric case the relevant geometry is determined by the spherical distance function of Bhattacharyya. In the context of term structure modelling, we show that minus the derivative of the discount function with respect to the maturity date gives rise to a probability density. This follows as a consequence of the positivity of interest rates. Therefore, by mapping the density functions associated with a given family of term structures to Hilbert space, the resulting metrical geometry can be used to analyse the relationship of yield curves to one another. We show that the general arbitrage-free yield curve dynamics can be represented as a process taking values in the convex space of smooth density functions on the positive real line. It follows that the theory of interest rate dynamics can be represented by a class of processes in Hilbert space. We also derive the dynamics for the central moments associated with the distribution determined by the yield curve.Comment: 20 pages, 3 figure

Unpolarized light in quantum optics

We present a new derivation of the unpolarized quantum states of light, whose general form was first derived by Prakash and Chandra [Phys. Rev. A 4, 796 (1971)]. Our derivation makes use of some basic group theory, is straightforward, and offers some new insights.Comment: 3 pages, REVTeX, presented at ICQO'200

Amino acid residues of the Escherichia coli tRNA(m5U54)methyltransferase (TrmA) critical for stability, covalent binding of tRNA and enzymatic activity

The Escherichia coli trmA gene encodes the tRNA(m5U54)methyltransferase, which catalyses the formation of m5U54 in tRNA. During the synthesis of m5U54, a covalent 62-kDa TrmA-tRNA intermediate is formed between the amino acid C324 of the enzyme and the 6-carbon of uracil. We have analysed the formation of this TrmA-tRNA intermediate and m5U54 in vivo, using mutants with altered TrmA. We show that the amino acids F188, Q190, G220, D299, R302, C324 and E358, conserved in the C-terminal catalytic domain of several RNA(m5U)methyltransferases of the COG2265 family, are important for the formation of the TrmA-tRNA intermediate and/or the enzymatic activity. These amino acids seem to have the same function as the ones present in the catalytic domain of RumA, whose structure is known, and which catalyses the formation of m5U in position 1939 of E. coli 23 S rRNA. We propose that the unusually high in vivo level of the TrmA-tRNA intermediate in wild-type cells may be due to a suboptimal cellular concentration of SAM, which is required to resolve this intermediate. Our results are consistent with the modular evolution of RNA(m5U)methyltransferases, in which the specificity of the enzymatic reaction is achieved by combining the conserved catalytic domain with different RNA-binding domains

Simultaneous minimum-uncertainty measurement of discrete-valued complementary observables

We have made the first experimental demonstration of the simultaneous minimum uncertainty product between two complementary observables for a two-state system (a qubit). A partially entangled two-photon state was used to perform such measurements. Each of the photons carries (partial) information of the initial state thus leaving a room for measurements of two complementary observables on every member in an ensemble.Comment: 4 pages, 4 figures, REVTeX, submitted to PR

Experimental determination of the degree of quantum polarisation of continuous variable states

We demonstrate excitation-manifold resolved polarisation characterisation of continuous-variable (CV) quantum states. In contrast to traditional characterisation of polarisation that is based on the Stokes parameters, we experimentally determine the Stokes vector of each excitation manifold separately. Only for states with a given photon number does the methods coincide. For states with an indeterminate photon number, for example Gaussian states, the employed method gives a richer and more accurate description. We apply the method both in theory and in experiment to some common states to demonstrate its advantages.Comment: 5 page

Diet-dependent depletion of queuosine in tRNAs in Caenorhabditis elegans does not lead to a developmental block

Queuosine (Q), a hypermodified nucleoside, occurs at the wobble position of transfer RNAs (tRNAs) with GUN anticodons. In eubacteria, absence of Q affects messenger RNA (mRNA) translation and reduces the virulence of certain pathogenic strains. In animal cells, changes in the abundance of Q have been shown to correlate with diverse phenomena including stress tolerance, cell proliferation and tumour growth but the function of Q in animals is poorly understood. Animals are thought to obtain Q (or its analogues) as a micronutrient from dietary sources such as gut microflora. However, the difficulty of maintaining animals under bacteria-free conditions on Q-deficient diets has severely hampered the study of Q metabolism and function in animals. In this study, we show that as in higher animals, tRNAs in the nematode Caenorhabditis elegans are modified by Q and its sugar derivatives. When the worms were fed on Q-deficient Escherichia coli, Q modification was absent from the worm tRNAs suggesting that C. elegans lacks a de novo pathway of Q biosynthesis. The inherent advantages of C. elegans as a model organism, and the simplicity of conferring a Q-deficient phenotype on it make it an ideal system to investigate the function of Q modification in tRNA

Entanglement measure for general pure multipartite quantum states

We propose an explicit formula for an entanglement measure of pure multipartite quantum states, then study a general pure tripartite state in detail, and at end we give some simple but illustrative examples on four-qubits and m-qubits states.Comment: 5 page

Imaging a 1-electron InAs quantum dot in an InAs/InP nanowire

Nanowire heterostructures define high-quality few-electron quantum dots for nanoelectronics, spintronics and quantum information processing. We use a cooled scanning probe microscope (SPM) to image and control an InAs quantum dot in an InAs/InP nanowire, using the tip as a movable gate. Images of dot conductance vs. tip position at T = 4.2 K show concentric rings as electrons are added, starting with the first electron. The SPM can locate a dot along a nanowire and individually tune its charge, abilities that will be very useful for the control of coupled nanowire dots

Quantum point contact due to Fermi-level pinning and doping profiles in semiconductor nanocolumns

We show that nanoscale doping profiles inside a nanocolumn in combination with Fermi-level pinning at the surface give rise to the formation of a saddle-point in the potential profile. Consequently, the lateral confinement inside the channel varies along the transport direction, yielding an embedded quantum point contact. An analytical estimation of the quantization energies will be given

Certainty relations between local and nonlocal observables

We demonstrate that for an arbitrary number of identical particles, each defined on a Hilbert-space of arbitrary dimension, there exists a whole ladder of relations of complementarity between local, and every conceivable kind of joint (or nonlocal) measurements. E.g., the more accurate we can know (by a measurement) some joint property of three qubits (projecting the state onto a tripartite entangled state), the less accurate some other property, local to the three qubits, become. We also show that the corresponding complementarity relations are particularly tight for particles defined on prime dimensional Hilbert spaces.Comment: 4 pages, no figure