Related papers: Improving application performance with biased dist…
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,…
The Bures-Hall ensemble is a unique measure of density matrices that satisfies various distinguished properties in quantum information processing. In this work, we study the statistical behavior of entanglement over the Bures-Hall ensemble…
The randomized quantum marginal problem asks about the joint distribution of the partial traces ("marginals") of a uniform random Hermitian operator with fixed spectrum acting on a space of tensors. We introduce a new approach to this…
Classical computation of electronic properties in large-scale materials remains challenging. Quantum computation has the potential to offer advantages in memory footprint and computational scaling. However, general and practical quantum…
We study the joint distribution of the set of all marginals of a random Wishart matrix acting on a tensor product Hilbert space. We compute the limiting free mixed cumulants of the marginals, and we show that in the balanced asymptotical…
The Kirkwood-Dirac distribution, serving as an informationally complete representation of a quantum state, has recently garnered increasing attention. We investigate the Kirkwood-Dirac classicality with respect to mutually unbiased bases.…
The Schmidt coefficients capture all entanglement properties of a pure bipartite state and therefore determine its usefulness for quantum information processing. While the quantification of the corresponding properties in mixed states is…
Random samples of quantum states are an important resource for various tasks in quantum information science, and samples in accordance with a problem-specific distribution can be indispensable ingredients. Some algorithms generate random…
Channel-state duality is a central result in quantum information science. It refers to the correspondence between a dynamical process (quantum channel) and a static quantum state in an enlarged Hilbert space. Since the corresponding dual…
We study the rates of convergence of the posterior distribution for Bayesian density estimation with Dirichlet mixtures of normal distributions as the prior. The true density is assumed to be twice continuously differentiable. The bandwidth…
The Hellinger distance between quantum states is a significant measure in quantum information theory, known for its Riemannian and monotonic properties. It is also easier to compute than the Bures distance, another measure that shares these…
We discuss a model for quantum computing with initially mixed states. Although such a computer is known to be less powerful than a quantum computer operating with pure (entangled) states, it may efficiently solve some problems for which no…
We discuss quantum state tomography via a stepwise reconstruction of the eigenstates of the mixed states produced in experiments. Our method is tailored to the experimentally relevant class of nearly pure states or simple mixed states,…
The question of the generation of random mixed states is discussed, aiming for the computation of probabilistic characteristics of composite finite dimensional quantum systems. Particularly, we consider the generation of the random…
We show that rate-adaptive multivariate density estimation can be performed using Bayesian methods based on Dirichlet mixtures of normal kernels with a prior distribution on the kernel's covariance matrix parameter. We derive sufficient…
We investigate the intermediate permutational symmetries of a system of qubits, that lie in between the perfect symmetric and antisymmetric cases. We prove that, on average, pure states of qubits picked at random with respect to the uniform…
Hilbert-Schmidt distance is one of the prominent distance measures in quantum information theory which finds applications in diverse problems, such as construction of entanglement witnesses, quantum algorithms in machine learning, and…
Wishart ensemble is a useful and important random matrix model used in diverse fields. By realizing induced random mixed quantum states as Wishart ensemble with the fixed-trace one, using matrix integral technique we give a fast track to…
We demonstrate a close connection between the decoherent histories (DH) approach to quantum mechanics and the quantum state diffusion (QSD) picture, for open quantum systems described by a master equation of Lindblad form. The (physically…
Dirichlet process mixtures are flexible non-parametric models, particularly suited to density estimation and probabilistic clustering. In this work we study the posterior distribution induced by Dirichlet process mixtures as the sample size…