Related papers: Statistical properties of the truncated state with…
A fundamental task in quantum information is to approximate a pure quantum state in terms of sparse states or, for a bipartite system, states of bounded Schmidt rank. The optimal deterministic approximation in each case is straightforward,…
We study the problem of estimating the parameters of a Gaussian distribution when samples are only shown if they fall in some (unknown) subset $S \subseteq \R^d$. This core problem in truncated statistics has long history going back to…
Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudo-random…
Invariant ensemble, which are characterised by the joint distribution of eigenvalues $P(\lambda_1,\ldots,\lambda_N)$, play a central role in random matrix theory. We consider the truncated linear statistics $L_K = \sum_{n=1}^K f(\lambda_n)$…
We introduce a procedure based on quantum expectation values of measurement observables to characterize quantum coherence. Our measure allows one to quantify coherence without having to perform tomography of the quantum state, and can be…
An oscillator with stochastic frequency is discussed as a model for evaluating the quantum coherence properties of a physical system. It is found that the choice of jump statistics has to be considered with care if unphysical consequences…
Random number has many applications, it plays an important role in quantum information processing. It's not difficult to generate true random numbers, the main difficulty is how to certify the random numbers generated by untrusted devices.…
A possible way of generating nonclassical states of light, especially non-Gaussian states, is via the truncation of a given state in the Fock basis. In recent work, we presented an alternative scheme for such quantum scissors [Phys. Rev. A…
We study the dynamics of condensation for a stochastic continuous mass transport process defined on a one-dimensional lattice. Specifically we introduce three different variations of the truncated random average process. We generalize…
The zero-truncated Poisson distributions are certain discrete probability distributions whose supports are the set of positive integers, which are also known as the conditional Poisson distributions or the positive Poisson distributions. In…
Completely random measures (CRMs) and their normalizations are a rich source of Bayesian nonparametric priors. Examples include the beta, gamma, and Dirichlet processes. In this paper we detail two major classes of sequential CRM…
A class of states of the electromagnetic field involving superpositions of all the excited states above a specified low energy eigenstate of the electromagnetic field is introduced. These states and the photon-added coherent states are…
Mixed state ensembles such as the Bures-Hall and Hilbert-Schmidt measure are probability distributions that characterise the statistical properties of random density matrices and can be used to determine the typical features of mixed…
In this paper we introduce a model which provides a new approach to the phenomenon of stochastic resonance. It is based on the study of the properties of the stationary distribution of the underlying stochastic process. We derive the…
We provide an efficient algorithm to generate random samples from the bounded kth order statistic in a sample of independent, but not necessarily identically distributed, random variables. The bounds can be upper or lower bounds and need…
We study the set of random matrix product states (RMPS) introduced in arXiv:0908.3877 as a tool to explore foundational aspects of quantum statistical mechanics. In the present work, we provide an accurate numerical and analytical…
In this paper, we introduce turnpike arguments in the context of optimal state estimation. In particular, we show that the optimal solution of the state estimation problem involving all available past data serves as turnpike for the…
The observational limitations of astronomical surveys lead to significant statistical inference challenges. One such challenge is the estimation of luminosity functions given redshift $z$ and absolute magnitude $M$ measurements from an…
In the analysis of Markov chains and processes, it is sometimes convenient to replace an unbounded state space with a "truncated" bounded state space. When such a replacement is made, one often wants to know whether the equilibrium behavior…
This is the documentation for generating random samples from the quantum state space in accordance with a specified distribution, associated with this webpage: http://tinyurl.com/QSampling . Ready-made samples (each with at least a million…