Related papers: Finite de Finetti theorem for conditional probabil…
Robin (or mixed) boundary conditions in quantum mechanics have received considerable attention in the last two decades, in particular, for applications to nanoscale systems. However, their utility has remained obscure to the larger physics…
Fine's theorem concerns the question of determining the conditions under which a certain set of probabilities for pairs of four bivalent quantities may be taken to be the marginals of an underlying probability distribution. The eight CHSH…
We construct minimum-uncertainty states and a non-negative quasi probability distribution for quantum systems on a finite-dimensional space. We reexamine the theorem of Massar and Spindel for the uncertainty relationof the two unitary…
An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…
For a class of random partitions of an infinite set a de Finetti-type representation is derived, and in one special case a central limit theorem for the number of blocks is shown.
Approximating a quantum state by the convex mixing of some given states has strong experimental significance and provides potential applications in quantum resource theory. Here we find a closed form of the minimal distance in the sense of…
Finite physical systems have only a finite amount of distinct state. This finiteness is fundamental in statistical mechanics, where the maximum number of distinct states compatible with macroscopic constraints defines entropy. Here we show…
The Glivenko--Cantelli theorem is a uniform version of the strong law of large numbers. It states that for every IID sequence of random variables, the empirical measure converges to the underlying distribution (in the sense of uniform…
Time-symmetric cosmological theories, in which the initial and final states are arranged to have similar features or are independently fixed, have been quite extensively discussed in the literature. However, a more general and perhaps more…
We obtain a necessary and sufficient condition for a finite set of states of a finite dimensional multiparticle quantum system to be amenable to unambiguous discrimination using local operations and classical communication. This condition…
Quantum theory is indeterministic, but not completely so. When a system is in a pure state there are properties it possesses with certainty, known as actual properties. The actual properties of a quantum system (in a pure state) fully…
A classic and fundamental result about the decomposition of random sequences into a mixture of simpler ones is de Finetti's Theorem. In its original form it applies to infinite 0-1 valued exchangeable sequences. Later it was extended and…
We point out that the quantum de Finetti representation, unique for infinitely extendable exchangeable systems, assigns a non-zero Quantum Discord to uncorrelated systems and thus cannot serve as an universal prior distribution in the…
In this paper, we show that the methods of mathematical statistical physics can be successfully applied to random fields in finite volumes. As a result, we obtain simple necessary and sufficient conditions for the existence and uniqueness…
It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of…
We present a novel proof of de Finetti's Theorem characterizing permutation-invariant probability measures of infinite sequences of variables, so-called exchangeable measures. The proof is phrased in the language of Markov categories, which…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
A remarkable feature of quantum theory is that particles with identical intrinsic properties must be treated as indistinguishable if the theory is to give valid predictions. In the quantum formalism, indistinguishability is expressed via…
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…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…