Related papers: Infinitely divisible states on finite quantum grou…
The multiplicative group of a finite field is well known to be cyclic; in this note, we determine the finite fields whose multiplicative groups are direct sum indecomposable. We obtain our classification using a direct argument and also as…
Starting from arbitrary Hilbert spaces, we reduce the problem to verify entanglement of any bipartite quantum state to finite dimensional subspaces. Hence, entanglement is a finite dimensional property. A generalization for multipartite…
Retrieving classical information from quantum systems is central to quantum information processing. As a more general task than quantum state discrimination, which focuses on identifying the exact state, quantum state exclusion only…
Schmidt's theorem is significantly generalized, to partitions in which periodic but otherwise arbitrary subsets of parts are counted or uncounted. The identification of such sets of partitions with colored partitions satisfying certain…
We propose isomorphism type identities for nonlinear functionals of general infinitely divisible processes. Such identities can be viewed as an analogy of the Cameron-Martin formula for Poissonian infinitely divisible processes but with…
We study lattice operations on the set of idempotent states on a locally compact quantum group corresponding to the operations of intersection of compact subgroups and forming the subgroup generated by two compact subgroups. Normal…
The paper extends earlier results from \cite{SK}, \cite{SKS} about infinite-volume quantum bosonic states (FK-DLR states) to the case of multi-type particles with non-negative interactions. (An example is a quantum Widom--Rowlinson model.)…
Quantum systems can be prepared in an infinite continuum of states, but only some of them can be used as resources for quantum technologies. Discerning whether a specific quantum state falls into this class, is often a challenging task. We…
The completeness of quantum state space, is usually expressed as \sum_{m=0}^{\infty}|m><m|=1, where {|m>} is selected set of quantum states (basis). Density matrix |m><m| describes a pure quantum state. In this paper, by virtue of the…
The positivity of the partial transpose is in general only a necessary condition for separability. There exist quantum states that are not separable, but nevertheless are positive under partial transpose. States of this type are known as…
We study certain quantum states for which the PPT criterion is both sufficient and necessary for separability. A class of $n\times n$ bipartite mixed states is presented and the conditions of PPT for these states are derived. The separable…
A fundamental problem in quantum physics is to establish whether a multiparticle quantum state can be uniquely determined from its local marginals. In theory, this problem has been addressed in the exact case where the marginals are…
We show that Ramsey theory, a domain presently conceived to guarantee the existence of large homogeneous sets for partitions on k-tuples of words (for every natural number k) over a finite alphabet, can be extended to one for partitions on…
Let $G$ be a group acting properly and essentially on an irreducible, non-Euclidean finite dimensional CAT(0) cube complex $X$ without fixed points at infinity. We show that for any finite collection of simultaneously inessential subgroups…
Shumyatsky and the second author proved that if G is a finitely generated residually finite p-group satisfying a law, then, for almost all primes, the fact that a normal and commutator-closed set of generators satisfies a positive law…
We prove a complete class theorem that characterizes \emph{all} stationary time reversible Markov processes whose finite dimensional marginal distributions (of all orders) are infinitely divisible. Aside from two degenerate cases (iid and…
The idempotent problem of a finitely generated inverse semigroup is the formal language of all words over the generators representing idempotent elements. This note proves that a finitely generated inverse semigroup with regular idempotent…
Every partition of [[omega_1]^{< omega}]^2 into finitely many pieces has a cofinal homogeneous set. Furthermore, it is consistent that every directed partially ordered set satisfies the partition property if and only if it has finite…
Local actions of $\mathbb{P}_\mathbb{N}$, the group of finite permutations on $\mathbb{N}$, on quasi-local algebras are defined and proved to be $\mathbb{P}_\mathbb{N}$-abelian. It turns out that invariant states under local actions are…
Compact-group representations on Banach spaces are known to be norm-continuous precisely when they have finite spectra. For a quantum group with continuous-function algebra $\mathcal{C}(\mathbb{G})$ norm continuity can be cast analogously…