Quantum leap: how to complete a quantum walk in a single step

Quantum walks provide simple models of various fundamental processes. It is pivotal to know when the dynamics underlying a walk lead to quantum advantages just by examining its statistics. A walk with many indistinguishable particles and measurements of non-classical multi-particle correlations is likely to reveal the quantum nature. The number of elements $O(n)$ in a setup realizing walks grows with their length or spread $n$. We introduce the concept of a quantum leap, a process which can be achieved with fewer or complementary resources and which in a single step simulates another long process. The process and its leap are described by the same Hamiltonian but, the latter parametrizes the evolution with a tunable parameter of a setup. In the case of walks, a leap immediately gives a probability distribution which results only after many steps. This may be appealing for simulation of processes which are lengthy or require dynamical control. We discuss a leap based on the multi-particle Hong--Ou--Mandel interference, an inherently quantum phenomenon. It reproduces a quantum walk enabling perfect state transfer through spin chains. It requires a beam splitter, two detectors and $n$ particles to mimic a walk on a chain of size $O(n)$, for time fixed by beam-splitter's reflectivity. Our results apply to a broad class of systems where the HOM-like effects can be observed, and may constitute a new approach to simulation of complex Hamiltonians with passive interferometers

Is there contextuality for a single qubit?

It was presented by Cabello and Nakamura [A. Cabello, Phys. Rev. Lett. 90, 190401 (2003)], that the Kochen-Specker theorem applies to two dimensions if one uses Positive Operator-Valued Measures. We show that contextuality in their models is not of the Kochen-Specker type. It is rather the result of not keeping track of the whole system on which the measurement is performed. This is connected to the fact that there is no one-to-one correspondence between POVM elements and projectors on the extended Hilbert space and the same POVM element has to originate from two different projectors when used in Cabello's and Nakamura's models. Moreover, we propose a hidden-variable formulation of the above models.Comment: 4 pages, 1 figure, comments welcom

Basal-plane Incommensurate Phases in HCP Structures

An Ising model with competing interaction is used to study the appearance of incommensurate phases in the basal plane of an hexagonal closed-packed structure. The calculated mean-field phase diagram reveals various 1q-incommensurate and lock-in phases. The results are applied to explain the basal-plane incommensurate phase in some compounds of the A'A"BX_4 family, like K_2MoO_4, K_2WO_4, Rb_2WO4 and to describe the sequence of high-temperature phase transitions in other compounds of this family.Comment: 8 pages, RevTeX + 4 ps figure

Thermodynamics of the incommensurate state in Rb_2WO_4: on the Lifshitz point in A`A``BX_4 compounds

We consider the evolution of the phase transition from the parent hexagonal phase $P6_{3}/mmc$ to the orthorhombic phase $Pmcn$ that occurs in several compounds of $A'A''BX_{4}$ family as a function of the hcp lattice parameter $c/a$. For compounds of $K_{2}SO_{4}$ type with $c/a$ larger than the threshold value 1.26 the direct first-order transition $Pmcn-P6_{3}/mmc$ is characterized by the large entropy jump $Rln2$. For compounds $Rb_{2}WO_{4}$, $K_{2}MoO_{4}$, $K_{2}WO_{4}$ with $c/a<1.26$ this transition occurs via an intermediate incommensurate $(Inc)$ phase. DSC measurements were performed in $Rb_{2}WO_{4}$ to characterize the thermodynamics of the $Pmcn-Inc-P6_{3}/mmc$ transitions. It was found that both transitions are again of the first order with entropy jumps $0.2Rln2 and$0.3Rln2$. Therefore, at$c/a ~ 1.26$the$A'A''BX_{4}$compounds reveal an unusual Lifshitz point where three first order transition lines meet. We propose the coupling of crystal elasticity with$BX_{4}$ tetrahedra orientation as a possible source of the transitions discontinuity.Comment: 13 pages,1 Postscript figure. Submitted as Brief Report to Phys. Rev. B, this paper reports a new work in Theory and Experiment, directed to Structural Phase Transition

Particle addition and subtraction as a test of bosonic quality

We propose a test to measure the bosonic quality of particles with respect to physical operations of single-particle addition and subtraction. We apply our test to investigate bosonic properties of composite particles made of an even number of fermions and suggest its experimental implementation. Furthermore, we discuss features of the processes of particle addition and subtraction in terms of optimal quantum operations.Comment: 5 page

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

Hysteresis in Pressure-Driven DNA Denaturation

In the past, a great deal of attention has been drawn to thermal driven denaturation processes. In recent years, however, the discovery of stress-induced denaturation, observed at the one-molecule level, has revealed new insights into the complex phenomena involved in the thermo-mechanics of DNA function. Understanding the effect of local pressure variations in DNA stability is thus an appealing topic. Such processes as cellular stress, dehydration, and changes in the ionic strength of the medium could explain local pressure changes that will affect the molecular mechanics of DNA and hence its stability. In this work, a theory that accounts for hysteresis in pressure-driven DNA denaturation is proposed. We here combine an irreversible thermodynamic approach with an equation of state based on the Poisson-Boltzmann cell model. The latter one provides a good description of the osmotic pressure over a wide range of DNA concentrations. The resulting theoretical framework predicts, in general, the process of denaturation and, in particular, hysteresis curves for a DNA sequence in terms of system parameters such as salt concentration, density of DNA molecules and temperature in addition to structural and configurational states of DNA. Furthermore, this formalism can be naturally extended to more complex situations, for example, in cases where the host medium is made up of asymmetric salts or in the description of the (helical-like) charge distribution along the DNA molecule. Moreover, since this study incorporates the effect of pressure through a thermodynamic analysis, much of what is known from temperature-driven experiments will shed light on the pressure-induced melting issue

Fuzzy reasoning applied to multistage diagnosis of acute renal failure in children

The paper deals with fuzzy inference systems for multistage recognition based on a decision tree scheme. Two conceptually different fuzzy methods are presented and discussed for the given learning set. The first method is developed according to the multistage approach known as the Mamdani inference engine, with rules generated from the learning set. In the second approach, we first construct a fuzzy relation between the decision set and the feature space, which is then used for decision making. Both methods were practically applied to computer-aided medical diagnosis of acute renal failure. Results of comparative experimental analysis are given

On new methods of dynamic ensemble selection based on randomized reference classifier

In the paper two dynamic ensemble selection (DES) systems are proposed. Both systems are based on a probabilistic model and utilize the concept of Randomized Reference Classifier (RRC) to determine the competence function of base classifiers. In the first system in the selection procedure of base classifiers the dynamic threshold of competence is applied. In the second DES system, selected classifiers are combined using weighted majority voting rule with continuous-valued outputs, where the weights are equal to the class-dependent competences. The performance of proposed MCSs were tested and compared against DES system with better-than-random selection rule using eleven databases taken from the UCI Machine Learning Repository. The experimental results clearly show the effectiveness of the proposed methods