Related papers: Inequalities that Collectively Completely Characte…
Optomechanics is currently believed to provide a promising route towards the achievement of genuine quantum effects at the large, massive-system scale. By using a recently proposed figure of merit that is well suited to address…
An inequality in quantum mechanics, which does not appear to be well known, is derived by elementary means and shown to be quite useful. The inequality applies to 'all' operators and 'all' pairs of quantum states, including mixed states. It…
The field of quantum resource theory (QRT) has emerged as an invaluable framework for the examination of small and strongly correlated quantum systems, surpassing the boundaries imposed by traditional statistical treatments. The fundamental…
Symplectic and optical joint probability representations of quantum mechanics are considered, in which the functions describing the states are the probability distributions with all random arguments (except the argument of time ). The…
Quantum communication theory explores the implications of quantum mechanics to the tasks of information transmission. Many physical channels can be formally described as quantum Gaussian operations acting on bosonic quantum states.…
Many behavioural equivalences or preorders for probabilistic processes involve a lifting operation that turns a relation on states into a relation on distributions of states. We show that several existing proposals for lifting relations can…
Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in \mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of $Y$, given that $X = x$. The goal is to estimate these distributions under the sole assumption…
We construct for a Schur concave function $f$ on the set of quantum states a tight upper bound on the difference $f(\rho)-f(\sigma)$ for a quantum state $\rho$ with finite $f(\rho)$ and any quantum state $\sigma$ $m$-partially majorized by…
The canonical quantization of flux is performed. It is shown that according to the canonical flux quantization there must be a new uncertainty relation: $e \Delta A_m . \Delta x_m \geq \hbar$ where $A_m$ and $\Delta x_m \geq l_B$ are the…
In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it…
Reichenbach's principle asserts that if two observed variables are found to be correlated, then there should be a causal explanation of these correlations. Furthermore, if the explanation is in terms of a common cause, then the conditional…
We describe $\omega$-limit sets of completely positive (CP) maps over finite-dimensional spaces. In such sets and in its corresponding convex hulls, CP maps present isometric behavior and the states contained in it commute with each other.…
Suppose several parties jointly possess a pure multipartite state, |\psi>. Using local operations on their respective systems and classical communication (i.e. LOCC) it may be possible for the parties to transform deterministically |\psi>…
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…
Transition Probability (fidelity) for pairs of density operators can be defined as "functor" in the hierarchy of "all" quantum systems and also within any quantum system. The introduction of "amplitudes" for density operators allows for a…
Complete sets of commutation relations for arbitrary pairs of quantum minors are computed, with explicit coefficients in closed form.
We define an index of compatibility for a probabilistic theory (PT). Quantum mechanics with index 0 and classical probability theory with index 1 are at the two extremes. In this way, quantum mechanics is at least as incompatible as any PT.…
This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…
It is shown that probabilistic treatment of quantum mechanics can be coordinated with causality of all physical processes. The physical interpretation of quantum-mechanical phenomena such as process of measurement and collapse of quantum…
We consider a real random variable X represented through a random pair of real random variables (R,T) and a deterministic function u as X=Ru(T). Under some additional assumptions, we prove a limit theorem for (R,T) given X>x, as x tends to…