Related papers: De Finetti theorems for a Boolean analogue of easy…

We prove general de Finetti type theorems for classical and free independence. The de Finetti type theorems work for all non-easy quantum groups, which generalize a recent work of Banica, Curran and Speicher. We determine maximal…

We study sequences of noncommutative random variables which are invariant under "quantum transformations" coming from an orthogonal quantum group satisfying the "easiness" condition axiomatized in our previous paper. For 10 easy quantum…

We prove various finite de Finetti theorems for non-commutative distributions which are invariant under the free easy quantum group actions. This complements the free de Finetti theorems by Banica, Curran and Speicher, which mostly focus on…

We introduce a family of quantum semigroups and their natural coactions on noncommutative polynomials. We present three invariance conditions, associated with these coactions, for the joint distribution of sequences of selfadjoint…

What does it mean for a causal structure to be `unknown'? Can we even talk about `repetitions' of an experiment without prior knowledge of causal relations? And under what conditions can we say that a set of processes with arbitrary,…

For the quantum stochastic processes generated by the Boolean Commutation Relations, we prove the following version of De Finetti Theorem: each of such Boolean process is exchangeable if and only if it is independent and identically…

We consider compact matrix quantum groups whose fundamental corepresentation matrix has entries which are partial isometries with central support. We show that such quantum groups have a simple representation as semi-direct product quantum…

The classical de Finetti theorem in probability theory relates symmetry under the permutation group with the independence of random variables. This result has application in quantum information. Here we study states that are invariant with…

De Finetti theorems tell us that if we expect the likelihood of outcomes to be independent of their order, then these sequences of outcomes could be equivalently generated by drawing an experiment at random from a distribution, and…

When analysing quantum information processing protocols one has to deal with large entangled systems, each consisting of many subsystems. To make this analysis feasible, it is often necessary to identify some additional structure. de…

Woronowicz proved the existence of the Haar state for compact quantum groups under a separability assumption later removed by Van Daele in a new existence proof. A minor adaptation of Van Daele's proof yields an idempotent state in any…

We prove several de Finetti theorems for the unitary dual group, also called the Brown algebra. Firstly, we provide a finite de Finetti theorem characterizing $R$-diagonal elements with an identical distribution. This is surprising, since…

We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical…

Markov categories have recently emerged as a powerful high-level framework for probability theory and theoretical statistics. Here we study a quantum version of this concept, called involutive Markov categories. These are equivalent to…

Quantum versions of de Finetti's theorem are powerful tools, yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing to bound the error made by mean-field approaches. Such…

Given a suitable collection of partitions of sets, there exists a connection to easy quantum groups via intertwiner maps. A sufficient condition for this correspondence to be one-to-one are particular linear independences on the level of…

We show that the classical de Finetti theorem has a canonical noncommutative counterpart if we strengthen `exchangeability' (i.e., invariance of the joint distribution of the random variables under the action of the permutation group) to…

Idempotent states on locally compact quantum semigroups with weak cancellation properties are shown to be Haar states on a certain sub-object described by an operator system with comultiplication. We also give a characterization of the…

We introduce new families of pure quantum states that are constructed on top of the well-known Gilmore-Perelomov group-theoretic coherent states. We do this by constructing unitaries as the exponential of operators quadratic in Cartan…

The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, towards probabilistic mixtures of independent and…