Related papers: Bures and Hilbert-Schmidt 2 x 2 Determinantal Mome…
In this paper, we study decoherence in Grover's quantum search algorithm using a perturbative method. We assume that each two-state system (qubit) that belongs to a register suffers a phase flip error (\sigma_{z} error) with probability p…
In the present paper, we investigated the distribution of hardness ratio (HR) for short and long gamma-ray bursts (GRBs) in different time scales for the first two seconds. After including and subtracting the background count, we performed…
Statistical properties of ensembles of random density matrices are investigated. We compute traces and von Neumann entropies averaged over ensembles of random density matrices distributed according to the Bures measure. The eigenvalues of…
We propose an interferometric method for statistically discriminating between nonorthogonal states in high dimensional Hilbert spaces for use in quantum information processing. The method is illustrated for the case of photon orbital…
The interplay among differential geometry, statistical physics, and quantum information science has been increasingly gaining theoretical interest in recent years. In this paper, we present an explicit analysis of the Bures and Sjoqvist…
We analytically derive the bit-string probability distributions of subsystems of random pure states and depolarized random states using the Dirichlet distribution. We identify the exact Beta distribution as the universal statistical law of…
In this article, we propose a novel discretization method based on numerical integration for discretizing continuous systems, termed the $\alpha\beta$-approximation or Scalable Bilinear Transformation (SBT). In contrast to existing methods,…
In this paper, we consider the moments of the trace of Frobenius of elliptic curves if the trace is restricted to a fixed arithmetic progression. We determine the asymptotic behavior for the ratio of the $(2k+1)$-th moment to the zeroeth…
We study the question of whether there is a minimum Hilbert functions for double point schemes whose support is $s$ points with the generic Hilbert functions. Previous work shows that the question has an affirmative answer for $s \le 9$ and…
We obtain the asymptotic growth rate of the moments of the Mandelbrot random cascades at critical exponents. The key ingredient is a $q$ to $q/2$ reduction method for the moment-estimation, which is obtained by combining the martingale…
We study the connection between the exponent of the order parameter of the Mott insulator-to-superfluid transition occurring in the two-dimensional Bose-Hubbard model, and the divergence exponents of its one- and two-particle correlation…
For a 1-parametric family $E_k$ of elliptic curves over $\mathbb{Q}$ and a prime $p$, consider the second moment sum $M_{2,p}(E_k)=\sum_{k \in \mathbb{F}_p} a_{k,p}^2$, where $a_{k,p}=p+1-\#E_k(\mathbb{F}_p)$. Inspired by Rosen and…
Qubit-efficient optimization studies how large combinatorial problems can be addressed with quantum circuits whose width is far smaller than the number of logical variables. In quadratic unconstrained binary optimization (QUBO), objective…
The effect of refractory periods in partial resetting processes is studied. Under Poissonian partial resets, a state variable jumps to a value closer to the origin by a fixed fraction at constant rate, $x\to a x$. Following each reset, a…
The purpose of this paper is to pursue our study of rho-estimators built from i.i.d. observations that we defined in Baraud et al. (2014). For a \rho-estimator based on some model S (which means that the estimator belongs to S) and a true…
Hyperspectral measurements from long range sensors can give a detailed picture of the items, materials, and chemicals in a scene but analysis can be difficult, slow, and expensive due to high spatial and spectral resolutions of…
This paper investigates the influences of standard numerical discretizations on hitting probabilities for linear stochastic parabolic system driven by space-time white noises. We establish lower and upper bounds for hitting probabilities of…
In Bayesian multilevel models, the data are structured in interconnected groups, and their posteriors borrow information from one another due to prior dependence between latent parameters. However, little is known about the behaviour of the…
Simulating time evolution is one of the most natural applications of quantum computers and is thus one of the most promising prospects for achieving practical quantum advantage. Here, we develop quantum algorithms to extract thermodynamic…
We imagine an experiment on an unknown quantum mechanical system in which the system is prepared in various ways and a range of measurements are performed. For each measurement M and preparation rho the experimenter can determine, given…