Quantum measurements with prescribed symmetry

We introduce a method to determine whether a given generalised quantum measurement is isolated or it belongs to a family of measurements having the same prescribed symmetry. The technique proposed reduces to solving a linear system of equations in some relevant cases. As consequence, we provide a simple derivation of the maximal family of Symmetric Informationally Complete measurements (SIC)-POVM in dimension 3. Furthermore, we show that the following remarkable geometrical structures are isolated, so that free parameters cannot be introduced: (a) maximal sets of mutually unbiased bases in prime power dimensions from 4 to 16, (b) SIC-POVM in dimensions from 4 to 16 and (c) contextuality Kochen-Specker sets in dimension 3, 4 and 6, composed of 13, 18 and 21 vectors, respectively.Comment: 10 pages, 2 figure

Induced Ginibre ensemble of random matrices and quantum operations

A generalisation of the Ginibre ensemble of non-Hermitian random square matrices is introduced. The corresponding probability measure is induced by the ensemble of rectangular Gaussian matrices via a quadratisation procedure. We derive the joint probability density of eigenvalues for such induced Ginibre ensemble and study various spectral correlation functions for complex and real matrices, and analyse universal behaviour in the limit of large dimensions. In this limit the eigenvalues of the induced Ginibre ensemble cover uniformly a ring in the complex plane. The real induced Ginibre ensemble is shown to be useful to describe statistical properties of evolution operators associated with random quantum operations, for which the dimensions of the input state and the output state do differ.Comment: 2nd version, 34 pages, 5 figure

Random Bistochastic Matrices

Ensembles of random stochastic and bistochastic matrices are investigated. While all columns of a random stochastic matrix can be chosen independently, the rows and columns of a bistochastic matrix have to be correlated. We evaluate the probability measure induced into the Birkhoff polytope of bistochastic matrices by applying the Sinkhorn algorithm to a given ensemble of random stochastic matrices. For matrices of order N=2 we derive explicit formulae for the probability distributions induced by random stochastic matrices with columns distributed according to the Dirichlet distribution. For arbitrary $N$ we construct an initial ensemble of stochastic matrices which allows one to generate random bistochastic matrices according to a distribution locally flat at the center of the Birkhoff polytope. The value of the probability density at this point enables us to obtain an estimation of the volume of the Birkhoff polytope, consistent with recent asymptotic results.Comment: 22 pages, 4 figure

Experimentally feasible measures of distance between quantum operations

We present two measures of distance between quantum processes based on the superfidelity, introduced recently to provide an upper bound for quantum fidelity. We show that the introduced measures partially fulfill the requirements for distance measure between quantum processes. We also argue that they can be especially useful as diagnostic measures to get preliminary knowledge about imperfections in an experimental setup. In particular we provide quantum circuit which can be used to measure the superfidelity between quantum processes. As the behavior of the superfidelity between quantum processes is crucial for the properties of the introduced measures, we study its behavior for several families of quantum channels. We calculate superfidelity between arbitrary one-qubit channels using affine parametrization and superfidelity between generalized Pauli channels in arbitrary dimensions. Statistical behavior of the proposed quantities for the ensembles of quantum operations in low dimensions indicates that the proposed measures can be indeed used to distinguish quantum processes.Comment: 9 pages, 4 figure

Random repeated quantum interactions and random invariant states

We consider a generalized model of repeated quantum interactions, where a system $\mathcal{H}$ is interacting in a random way with a sequence of independent quantum systems $\mathcal{K}_n, n \geq 1$. Two types of randomness are studied in detail. One is provided by considering Haar-distributed unitaries to describe each interaction between $\mathcal{H}$ and $\mathcal{K}_n$. The other involves random quantum states describing each copy $\mathcal{K}_n$. In the limit of a large number of interactions, we present convergence results for the asymptotic state of $\mathcal{H}$. This is achieved by studying spectral properties of (random) quantum channels which guarantee the existence of unique invariant states. Finally this allows to introduce a new physically motivated ensemble of random density matrices called the \emph{asymptotic induced ensemble}

One-component plasma on a spherical annulus and a random matrix ensemble

The two-dimensional one-component plasma at the special coupling \beta = 2 is known to be exactly solvable, for its free energy and all of its correlations, on a variety of surfaces and with various boundary conditions. Here we study this system confined to a spherical annulus with soft wall boundary conditions, paying special attention to the resulting asymptotic forms from the viewpoint of expected general properties of the two-dimensional plasma. Our study is motivated by the realization of the Boltzmann factor for the plasma system with \beta = 2, after stereographic projection from the sphere to the complex plane, by a certain random matrix ensemble constructed out of complex Gaussian and Haar distributed unitary matrices.Comment: v2, typos and references corrected, 24 pages, 1 figur

On Some Problems in Discrete Wavelet Analysis of Bivariate Spectra with an Application to Business Cycle Synchronization in the Euro Zone

The paper considers some of the problems emerging from discrete wavelet analysis of popular bivariate spectral quantities like the coherence and phase spectra and the frequency-dependent time delay. The approach taken here, introduced by Whitcher and Craigmile (2004), is based on the maximal overlap discrete Hilbert wavelet transform (MODHWT). Firstly, we point at a deficiency in the implementation of the MODHWT and suggest using a modified implementation scheme resembling the one applied in the context of the dual-tree complex wavelet transform of Kingsbury (see Selesnick et al., 2005). Secondly, via a broad set of simulation experiments we examine small and large sample properties of two wavelet estimators of the scale-dependent time delay. The estimators are: the wavelet cross-correlator and the wavelet phase angle-based estimator. Our results provide some practical guidelines for empirical examination of short- and medium-term lead-lag relations for octave frequency bands. Besides, we show how the MODHWT-based wavelet quantities can serve to approximate the Fourier bivariate spectra and discuss certain issues connected with building confidence intervals for them. The discrete wavelet analysis of coherence and phase angle is illustrated with a scale-dependent examination of business cycle synchronization between 11 euro zone member countries. The study is supplemented with wavelet analysis of variance and covariance of the euro zone business cycles. The empirical examination underlines good localization properties and high computational efficiency of the wavelet transformations applied, and provides new arguments in favour of the endogeneity hypothesis of the optimum currency area criteria as well as a wavelet evidence on dating the Great Moderation in the euro zone

Fecal Glucocorticoid Metabolites as Biomarkers in Equids: Assay Choice Matters

From Wiley via Jisc Publications RouterHistory: received 2020-05-06, rev-recd 2021-03-29, accepted 2021-04-09, pub-electronic 2021-06-01Article version: VoRPublication status: PublishedFunder: Royal Society; Id: http://dx.doi.org/10.13039/501100000288; Grant(s): UF110641Funder: Chester Zoo; Id: http://dx.doi.org/10.13039/501100005359; Grant(s): Conservation FellowshipABSTRACT: Free ranging animals are exposed to environmental, demographic, and ecological challenges over time, which can affect their health and fitness. Non‐invasive biomarkers can provide insight into how animals cope with these challenges and assess the effectiveness of conservation management strategies. We evaluated how free ranging ponies (Equus ferus caballus) on the Carneddau Mountain range, North Wales respond to 2 stimuli: an acute stressor of an annual roundup event in November 2014, and spatial and temporal variation in ecological factors in 2018. We evaluated fecal glucocorticoid metabolites using 2 enzyme immunoassays (EIAs): an 11‐oxoetiocholanolone EIA (measuring 11,17‐dioxoandrostanes [11,17‐DOAs]) and a corticosterone EIA. The former assay has been validated in equids, whereas there is limited evidence for the suitability of the latter. We used an additional parent testosterone EIA to measure fecal androgen metabolites in response to the ecological challenges. Following the roundup, the metabolite concentrations measured by the 2 glucocorticoid EIAs were not correlated. The 11,17‐DOAs were elevated from the second day following the roundup and then slowly returned to pre‐round levels over the next 2 weeks. In contrast, the metabolites measured by the corticosterone assay showed no response to the roundup. For the ecological data, all 3 assays detected a positive correlation between metabolites and social group size in males but not in females. The metabolite concentrations measured by the testosterone and corticosterone assays were highly correlated and were temporally associated with the onset of the breeding season, whereas the 11,17‐DOAs were not. The co‐variance of metabolites measured by the corticosterone and testosterone assays, and the lack of an acute response in the corticosterone assay to the roundup, suggests that metabolites detected by the corticosterone assay were not primarily associated with increased glucocorticoid production. We recommend using well‐validated fecal biomarker assays of hypothalamus‐pituitary‐adrenal axis activity to evaluate and compare the effect of different management interventions and environmental change. © 2021 The Authors. The Journal of Wildlife Management published by Wiley Periodicals LLC on behalf of The Wildlife Society

Interface design in lightweight SiC/TiSi2 composites fabricated by reactive infiltration process: Interaction phenomena between liquid Si-rich Si-Ti alloys and glassy carbon

To properly design and optimize liquid-assisted processes, such as reactive infiltration for fabricating lightweight and corrosion resistant SiC/TiSi2 composites, the extensive knowledge about the interfacial phenomena taking place when liquid Si-rich Si-Ti alloys are in contact with glassy carbon (GC) is of primary importance. To this end, the wettability of GC by two different Si-rich Si-Ti alloys was investigated for the first time by both the sessile and pendant drop methods at T = 1450 C. The results obtained, in terms of contact angle values, spreading kinetics, reactivity, and developed interface microstructures, were compared with experimental observations previously obtained for the liquid Si-rich Si-Ti eutectics processed under the same operating conditions. As the main outcome, a different Si content did not seem to affect the final contact angle values. Contrarily, the final developed microstructure at the interface and the spreading kinetics were observed as weakly dependent on the composition. From a practical point of view, Si-Ti alloy compositions with a Si content falling in the simple eutectic region of the Si-Ti phase diagram might be potentially used as infiltrating materials of C- and SiC-based composites

Wetting behavior of Si-13.5B alloy on polycrystalline h-BN-based substrates

In this work, for the first time the results of an experimental evaluation of the high temperature behavior of molten Si-B alloy in contact with refractory materials at temperatures up to 1750°C, under static argon atmosphere (p = 850– 900 mbar), is shown. The material investigated, having a nominal chemical composition of Si-13.5B (at. %), was fabricated by using the crucible-less electric arc-melting process assisted by the levitation drop method. The wettability of the molten alloy in contact with commercial hexagonal boron nitride (h-BN) substrates was evaluated by means of especially developed sessile drop technique combined with a contact heating procedure. It was found that both couples show a lack of wettability in the whole tested temperature range (the measured contact angle was θ > 130°). The more stable behavior in contact with molten Si-13.B alloy, evidenced by higher θ values and a lack of drop vibration during the high temperature exposition, was observed for the h-BN based composite substrate