Related papers: Property (T) and exotic quantum group norms
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
If T is an algebraic torus defined over a discretely valued field K with perfect residue field k, we relate the K-cohomology of T to the k-cohomology of certain objects associated to T. When k has cohomological dimension <= 1, our results…
Using a categorial version of Fra\"iss\'e's theorem due to Droste and G\"obel, we derive a criterion for a comma-category to have universal homogeneous objects. As a first application we give new existence result for universal structures…
Thom polynomials of singularities express the cohomology classes dual to singularity submanifolds. A stabilization property of Thom polynomials is known classically, namely that trivial unfolding does not change the Thom polynomial. In this…
We give a complete characterization of connected Lie groups with the Approximation Property for groups (AP). To this end, we introduce a strengthening of property (T), that we call property (T*), which is a natural obstruction to the AP. In…
I give a self-contained introduction to the resource theory approach to quantum thermodynamics. I will introduce in an elementary manner the technical machinery necessary to unpack and prove the core statements of the theory. The topics…
We investigate some properties of topological groups related to disconnectedness or Archimedeanness. We prove or disprove the preservation of those under operations as subgroups, quotients, products, etc. Characterizations of…
We combine aspects of the notions of finite decomposition complexity and asymptotic property C into a notion that we call finite APC-decomposition complexity. Any space with finite decomposition complexity has finite APC-decomposition…
Every discrete group with Kazhdan's Property (T) is a quotient of a torsion-free, word hyperbolic group with Property (T).
We show that if $T$ is any of four semigroups of two elements that are not groups, there exists a finite dimensional associative $T$-graded algebra over a field of characteristic $0$ such that the codimensions of its graded polynomial…
Property testing has been extensively studied and its target is to determine whether a given object satisfies a certain property or it is far from the property. In this paper, we construct an efficient quantum algorithm which tests if a…
The meaning of quantum group transformation properties is discussed in some detail by comparing the (co)actions of the quantum group with those of the corresponding Lie group, both of which have the same algebraic (matrix) form of the…
We formulate and prove an Agreement Theorem for quantum mechanics (QM), describing when two agents, represented by separate laboratories, can or cannot maintain differing probability estimates of a shared quantum property of interest.…
The pursuit of quantum advantage in simulating many-body quantum systems on quantum computers has gained momentum with advancements in quantum hardware. This work focuses on leveraging the symmetry properties of these systems, particularly…
Classical matching theory can be defined in terms of matrices with nonnegative entries. The notion of Positive operator, central in Quantum Theory, is a natural generalization of matrices with nonnegative entries. Based on this point of…
In this article, we consider tensor products of unitary representations by irreducible non-unitary finite dimensional representations of topological groups to define a property that is a twisting of Kazhdan's Property (T). We use the…
We introduce an algebraic framework for interacting quantum systems that enables studying complex phenomena, characterized by the coexistence and competition of various broken symmetry states of matter. The approach unveils the hidden unity…
We analyse some aspects of the notion of algebraic exponentiation introduced by the second author [16] and satisfied by the category of groups. We show how this notion provides a new approach to the categorical-algebraic question of the…
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some…
The physical interpretation of the main notions of the quantum group theory (coproduct, representations and corepresentations, action and coaction) is discussed using the simplest examples of $q$-deformed objects (quantum group…