Related papers: Quasirandom estimations of two-qubit operator-mono…
This work studies the convergence and finite sample approximations of entropic regularized Wasserstein distances in the Hilbert space setting. Our first main result is that for Gaussian measures on an infinite-dimensional Hilbert space,…
In the standard geometric approach to a measure of entanglement of a pure state, $\sin^2\theta$ is used, where $\theta$ is the angle between the state to the closest separable state of products of normalized qubit states. We consider here a…
This paper is devoted to the stochastic approximation of entropically regularized Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal…
We consider Gaussian measures $\mu, \tilde{\mu}$ on a separable Hilbert space, with fractional-order covariance operators $A^{-2\beta}$ resp. $\tilde{A}^{-2\tilde{\beta}}$, and derive necessary and sufficient conditions on $A, \tilde{A}$…
We propose an information-theoretic framework for analog signal separation. Specifically, we consider the problem of recovering two analog signals, modeled as general random vectors, from the noiseless sum of linear measurements of the…
We examine the problem of estimating the expectation values of two observables when we have a finite number of copies of an unknown qubit state. Specifically we examine whether it is better to measure each of the observables separately on…
The well-known Robertson-Schroedinger uncertainty relations miss an irreducible lower bound. This is widely attributed to the lower bound's state-dependence. Therefore, Abbott \emph{et al.} introduced a general approach to derive tight…
We first show that partial transposition for pure and mixed two-particle states in a discrete $N$-dimensional Hilbert space is equivalent to a change in sign of the momentum of one of the particles in the Wigner function for the state. We…
In view of the photon-number tomograms of two-mode light states, using the qubit-portrait method for studying the probability distributions with infinite outputs, the separability and entanglement detection of the states are studied.…
We derive several uncertainty relations for two arbitrary unitary operators acting on physical states of a Hilbert space. We show that our bounds are tighter in various cases than the ones existing in the current literature. Using the…
We propose a new approach to the problem of defining the degree of entanglement between two particles in a pure state with Hilbert spaces of arbitrary finite dimensions. The central idea is that entanglement gives rise to correlations…
We analyze entropic uncertainty relations for two orthogonal measurements on a $N$-dimensional Hilbert space, performed in two generic bases. It is assumed that the unitary matrix $U$ relating both bases is distributed according to the Haar…
We study the discrimination of N mixed quantum states in an optimal measurement that maximizes the probability of correct results while the probability of inconclusive results is fixed at a given value. After considering the discrimination…
Explicitly separable density matrices are constructed for all separable two-qubits states based on Hilbert-Schmidt (HS) decompositions. For density matrices which include only two-qubits correlations the number of HS parameters is reduced…
We ask to what extent an isolated quantum system can eventually "contract" to be contained within a given Hilbert subspace. We do this by starting with an initial random state, considering the probability that all the particles will be…
Peculiarities of multiqubit measurement are for the most part similar to peculiarities of measurement for qudit -- quantum object with finite-dimensional Hilbert space. Three different interpretations of measurement concept are analysed.…
Separability and entanglement for n-qubits systems are quantified by using Hilbert-Schmidt (HS) decompositions in which the density matrices are decomposed into various terms representing certain one qubit, two-qubits,and larger qubits…
The estimation of covariance operators of spatio-temporal data is in many applications only computationally feasible under simplifying assumptions, such as separability of the covariance into strictly temporal and spatial factors.Powerful…
It $d-$pends. Wigner's symmetry theorem implies that transformations that preserve transition probabilities of pure quantum states are linear maps on the level of density operators. We investigate the stability of this implication. On the…
The ability of matter to be superposed at two different locations while being intrinsically connected by a quantum phase is among the most counterintuitive predictions of quantum physics. While such superpositions have been created for a…