The Laplace-Jaynes approach to induction

An approach to induction is presented, based on the idea of analysing the context of a given problem into `circumstances'. This approach, fully Bayesian in form and meaning, provides a complement or in some cases an alternative to that based on de Finetti's representation theorem and on the notion of infinite exchangeability. In particular, it gives an alternative interpretation of those formulae that apparently involve `unknown probabilities' or `propensities'. Various advantages and applications of the presented approach are discussed, especially in comparison to that based on exchangeability. Generalisations are also discussed.Comment: 38 pages, 1 figure. V2: altered discussion on some points, corrected typos, added reference

Numerical Bayesian quantum-state assignment for a three-level quantum system. II. Average-value data with a constant, a Gaussian-like, and a Slater prior

This paper offers examples of concrete numerical applications of Bayesian quantum-state assignment methods to a three-level quantum system. The statistical operator assigned on the evidence of various measurement data and kinds of prior knowledge is computed partly analytically, partly through numerical integration (in eight dimensions) on a computer. The measurement data consist in the average of outcome values of N identical von Neumann projective measurements performed on N identically prepared three-level systems. In particular the large-N limit will be considered. Three kinds of prior knowledge are used: one represented by a plausibility distribution constant in respect of the convex structure of the set of statistical operators; another one represented by a prior studied by Slater, which has been proposed as the natural measure on the set of statistical operators; the last prior is represented by a Gaussian-like distribution centred on a pure statistical operator, and thus reflecting a situation in which one has useful prior knowledge about the likely preparation of the system. The assigned statistical operators obtained with the first two kinds of priors are compared with the one obtained by Jaynes' maximum entropy method for the same measurement situation. In the companion paper the case of measurement data consisting in absolute frequencies is considered.Comment: 10 pages, 4 figures. V2: added "Post scriptum" under Conclusions, slightly changed Acknowledgements, and corrected some spelling error

Numerical Bayesian state assignment for a three-level quantum system. I. Absolute-frequency data; constant and Gaussian-like priors

This paper offers examples of concrete numerical applications of Bayesian quantum-state-assignment methods to a three-level quantum system. The statistical operator assigned on the evidence of various measurement data and kinds of prior knowledge is computed partly analytically, partly through numerical integration (in eight dimensions) on a computer. The measurement data consist in absolute frequencies of the outcomes of N identical von Neumann projective measurements performed on N identically prepared three-level systems. Various small values of N as well as the large-N limit are considered. Two kinds of prior knowledge are used: one represented by a plausibility distribution constant in respect of the convex structure of the set of statistical operators; the other represented by a Gaussian-like distribution centred on a pure statistical operator, and thus reflecting a situation in which one has useful prior knowledge about the likely preparation of the system. In a companion paper the case of measurement data consisting in average values, and an additional prior studied by Slater, are considered.Comment: 23 pages, 14 figures. V2: Added an important note concerning cylindrical algebraic decomposition and thanks to P B Slater, corrected some typos, added reference

Quantum error correction may delay, but also cause, entanglement sudden death

Dissipation may cause two initially entangled qubits to evolve into a separable state in a finite time. This behavior is called entanglement sudden death (ESD). We study to what extent quantum error correction can combat ESD. We find that in some cases quantum error correction can delay entanglement sudden death but in other cases quantum error correction may cause ESD for states that otherwise do not suffer from it. Our analysis also shows that fidelity may not be the best measure to compare the efficiency of different error correction codes since the fidelity is not directly coupled to a state's remaining entanglement.Comment: 3 figure

Tunable effective g-factor in InAs nanowire quantum dots

We report tunneling spectroscopy measurements of the Zeeman spin splitting in InAs few-electron quantum dots. The dots are formed between two InP barriers in InAs nanowires with a wurtzite crystal structure grown by chemical beam epitaxy. The values of the electron g-factors of the first few electrons entering the dot are found to strongly depend on dot size and range from close to the InAs bulk value in large dots |g^*|=13 down to |g^*|=2.3 for the smallest dots. These findings are discussed in view of a simple model.Comment: 4 pages, 3 figure

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

Realistic limits on the nonlocality of an N-partite single-photon superposition

A recent paper [L. Heaney, A. Cabello, M. F. Santos, and V. Vedral, New Journal of Physics, 13, 053054 (2011)] revealed that a single quantum symmetrically delocalized over N modes, namely a W state, effectively allows for all-versus-nothing proofs of nonlocality in the limit of large N. Ideally, this finding opens up the possibility of using the robustness of the W states while realizing the nonlocal behavior previously thought to be exclusive to the more complex class of Greenberger-Horne-Zeilinger (GHZ) states. We show that in practice, however, the slightest decoherence or inefficiency of the Bell measurements on W states will degrade any violation margin gained by scaling to higher N. The non-statistical demonstration of nonlocality is thus proved to be impossible in any realistic experiment.Comment: 6 pages, 6 figure

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

The role of illness perceptions in adherence to surveillance in patients with familial adenomatous polyposis (FAP)

Objective The aim of the study was to examine patients' beliefs about having familial adenomatous polyposis (FAP), a hereditary colorectal cancer syndrome, and how these beliefs are associated with adherence to endoscopic surveillance. Methods Adult patients diagnosed with FAP on the national Swedish polyposis register who had undergone prophylactic colorectal surgery (n 209, response rate 76%) completed the Illness Perception Questionnaire (IPQ). Logistic regression analysis was used to investigate the relationships between illness perceptions and adherence, when controlling for demographic and clinical factors. Results FAP was less distressing in men and those with fewer symptoms, reporting less serious consequences and more coherent understanding of FAP. Non-adherence (14%) to surveillance was associated with being older, having undergone surgery less recently and no history of malignancy. Patients' beliefs about their FAP were able to explain unique variance in non-adherence, in particular those who believed FAP was less distressing. Conclusions Patients who were non-adherent to endoscopic surveillance had more positive perceptions about their FAP and, in particular, were less emotionally affected compared to those who adhered. As non-adherence implies a greater risk of future malignancies, special efforts are required to effectively prevent cancer in all patients with FAP. Those who have lived with the condition for a long time, and are not troubled by gastrointestinal symptoms or worried about their FAP, may be in need of specific information and support. Further prospective research is required to examine emotional predictors and consequences of non-adherence