Related papers: A lower bound on the dimension of a quantum system…
It has been shown that the conditional probability distributions obtained by performing measurements on an uncharacterized physical system can be used to infer its underlying dimension in a device-independent way both in the classical and…
Quantum devices, such as quantum simulators, quantum annealers, and quantum computers, may be exploited to solve problems beyond what is tractable with classical computers. This may be achieved as the Hilbert space available to perform such…
We discuss properties of probabilistic coding of two qubits to one qutrit and generalize the scheme to higher dimensions. We show that the protocol preservers entanglement between qubits to be encoded and environment and can be also applied…
We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a real Hilbert space. This extends…
We investigate convergence properties of discrete-time semigroup quantum dynamics, including asymptotic stability, probability and speed of convergence to pure states and subspaces. These properties are of interest in both the analysis of…
A natural measure for the amount of quantum information that a physical system E holds about another system A = A_1,...,A_n is given by the min-entropy Hmin(A|E). Specifically, the min-entropy measures the amount of entanglement between E…
Many typical Bell experiments can be described as follows. A source repeatedly distributes particles among two spacelike separated observers. Each of them makes a measurement, using an observable randomly chosen out of several possible…
We improve the upper bound on the minimal resources required for measurement-based quantum computation. Minimizing the resources required for this model is a key issue for experimental realization of a quantum computer based on projective…
We consider methods for obtaining local lower bounds on characteristics of quantum (correspondingly, classical) systems, i.e. lower bounds valid in the trace norm $\epsilon$-neighborhood of a given state (correspondingly, probability…
A `register' in quantum information processing -- is composition of k quantum systems, `qudits'. The dimensions of Hilbert spaces for one qudit and whole quantum register are d and d^k respectively, but we should have possibility to prepare…
Given a random subspace $H_n$ chosen uniformly in a tensor product of Hilbert spaces $V_n\otimes W$, we consider the collection $K_n$ of all singular values of all norm one elements of $H_n$ with respect to the tensor structure. A law of…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…
We introduce the notion of hidden quantum correlations. We present the mean values of observables depending on one classical random variable described by the probability distribution in the form of correlation functions of two (three, etc.)…
We use entropy numbers in combination with the polynomial method to derive a new general lower bound for the n-th minimal error in the quantum setting of information-based complexity. As an application, we improve some lower bounds on…
This article presents general procedures for constructing, estimating, and testing Hilbert space multi-dimensional (HSM) models, which are based on quantum probability theory. HSM models can be applied to collections of K different…
Quantum metrology typically demands the preparation of exotic quantum probe states, such as entangled or squeezed states, to surpass classical limits. However, the need for carefully calibrated system parameters and finely optimized quantum…
We study experimentally accessible lower bounds on entanglement measures based on entropic uncertainty relations. Experimentally quantifying entanglement is highly desired for applications of quantum simulation experiments to fundamental…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
Let X be a real or complex Hilbert space of finite but large dimension d, let S(X) denote the unit sphere of X, and let u denote the normalized uniform measure on S(X). For a finite subset B of S(X), we may test whether it is approximately…