Quan Chen
We prove that if a finite group $G$ acts outerly on a McDuff $\rm II_1$ factor $M$, then $\mathsf{Rep}(G/KL)$ is a braided monoidal full subcategory of the categorical Connes' $\tildeχ(M\rtimes G)$ defined in arXiv:2111.06378, where $K$ and $L$ are the centrally trivial and approximately inner parts in $G$ respectively. When $L$ is trivial, we give an explicit formula for the $G/K$-gauging procedure on $\tildeχ(M\rtimes G)$. This is the categorical generalization of Connes' short exact sequence on $χ(M\rtimes G)$. Using this machinery, for any finite group $G$, we construct a McDuff $\rm II_1$ factor $M$, whose $\tildeχ(M)$ is braided equivalent to $\mathsf{Rep}(G)$. This is the first example of a braided fusion category which is not modular as $\tildeχ$.
Melchior Wirth
We establish a relation between the exponential decay rates of quantum Markov semigroups with respect to different inner products. More precisely, it was conjectured by Fagnola, Poletti, Sasso and Umanità that for a Gaussian quantum Markov semigroup, the exponential decay rate with respect to the KMS inner product is bounded below by the exponential decay rate for the GNS inner product. We show that this is indeed the case and not limited to Gaussian quantum Markov semigroups, but holds for quantum Markov semigroups with a faithful normal invariant state on arbitrary von Neumann algebras. Additionally, the KMS inner product can be replaced by a whole class of inner products induced by operator monotone functions.
Minghui Ma, Rui Shi, Shanshan Yang
An operator $T$ in a separable factor $\mathcal{M}$ is said to be irreducible in $\mathcal{M}$ if the von Neumann subalgebra $W^*(T)$ generated by $T$ is an irreducible subfactor of $\mathcal{M}$, i.e., $W^*(T)'\cap\mathcal{M}=\mathbb{C}I$. We say that $T$ is a single generator of $\mathcal{M}$ if $W^*(T)=\mathcal{M}$. In this paper, we study generators of separable factors related to maximal abelian self-adjoint subalgebras. As an application, we obtain a complete characterization of normal operators in separable factors which are similar to irreducible operators.
Charles Starling
Spielberg's construction of C*-algebras from left cancellative small categories is a common generalization for most C*-algebras one would consider to come from ``combinatorial data,'' including graph and $k$-graph C*-algebras, Li's semigroup C*-algebras, Nekrashevych's self-similar action algebras, and more. We use known groupoid models of these algebras and Exel's theory of tight representations of inverse semigroups to prove uniqueness theorems for these C*-algebras. As applications, we improve on our previous uniqueness theorem for the boundary quotient C*-algebras of right LCM monoids, and we also generalize the uniqueness theorem of Brown, Nagy, and Reznikoff for row-finite higher-rank graphs to the finitely aligned case.
Christos P. Tantalakis, Michał Wojciechowski
We demonstrate a construction of products on the quantum torus $\mathbb{T}_θ^2$ that generalises the usual construction of finite Riesz products on the commutative torus $\mathbb{T}^2$. We explain why the former constitutes a natural analogue of the latter in the non-commutative setting and, based on this construction, as well as on previous results by K. Kazaniecki and the second author, we prove a non-commutative version of an Ornstein non-inequality.
Guillaume Dumas, Jingyin Huang, Srivatsav Kunnawalkam Elayavalli, Lizzy Teryoshin
The number of connected components can be remembered by the von Neumann algebra among Artin groups, the only possible exception being the case that corresponds to the free group factor problem. In the case of Coxeter groups, this result is obtained in the absence of relatively hyperbolicity. We also discuss a specific case of the analogous problem in measure equivalence where each factor group is a product of nonabelian free groups.
Jacqueline Caminiti, Federico Capeccia, Jonathan Sorce
In quantum field theory, it is not always possible to excite one state out of another using only local operators. This paper establishes abstract algebraic criteria for (local) excitability in general quantum theories, and computes these criteria explicitly for zero-mean Gaussian states in (generalized) free field theories. We find that in this context, due to the special nature of Gaussian states, one-way excitability always implies two-way excitability, and our results generalize the "quasiequivalence theorems" of Powers, Stormer, van Daele, Araki, and Yamagami. A key role in our proof is played by the information-theoretic tool of canonical purification. In appendices, we provide a pedagogical introduction to the algebraic formulation of (generalized) free field theory.
Theodoros Anastasiadis, George Androulakis
Apr 21, 2026·quant-ph·PDF In this article, we prove that the quantum $f$-divergence between two normal states on a semifinite von~Neumann algebra is equal to the classical $f$-divergence between two corresponding classical states, which are called Nussbaum-Szkoła distributions. This result has been proved by the second named author and T.C.~John for normal states on the von~Neumann algebra $\mathbb{B}(\mathscr{H})$ of all bounded operators on a Hilbert space $\mathscr{H}$. We extend their result for normal states on any semifinite von~Neumann algebra, not only $\mathbb{B}(\mathscr{H})$.
Tattwamasi Amrutam, Yongle Jiang
We introduce the notion of confined subalgebras in the context of the group von Neumann algebra. We also define Uniformly Recurrent States -- an operator-algebraic analog of Uniformly Recurrent Subgroups. Using this framework, we show that a countable discrete group is $C^*$-simple if and only if it admits no non-trivial amenable confined subalgebras. This generalizes the well-known result of Kennedy that characterizes $C^*$-simplicity in terms of trivial amenable uniformly recurrent subgroups.
Nicholas R. Allgood
We study the preservation and stability of synchronization subspaces in tensor products of finite-dimensional Hilbert spaces. Given self-adjoint operators $T_A$ and $T_B$ on local subsystems, the synchronization subspace is defined as the kernel of the difference operator $K = T_A \otimes I - I \otimes T_B$. We establish two main results: First for $ε$-compatible dynamics satisfying $||[H,K]|| \leq ε$, we prove a sharp drift bound where any initially synchronized state deviates from the kernel at a rate at most linear in time with slope $ε$. We show by explicit construction that this estimate is optimal to leading order. Second in the presence of finite group symmetry, we show that the synchronization subspace coincides with the diagonal isotypic component in the tensor product decomposition and we characterize the algebra of synchronization-preserving dynamics as the intersection of the commutants of the group action and synchronization operator.
Jamie Bell
We examine crossed product C*-algebras associated with non-minimal free actions of countably infinite discrete abelian groups on the circle, extending the work of Putnam, Schmidt, and Skau. We obtain a large class of unital separable nuclear and non-simple C*-algebras that are quasidiagonal, have stable rank one, and admit a unique tracial state. We determine their ideal structure and establish an improved uniform upper bound for their nuclear dimension. Finally, in the case $G = \mathbb{Z}^d$, we compute the ordered K-theory and its trace pairing.
Pere Ara
We introduce $C^*$-algebras associated with directed graphs, along with two generalizations of this concept, namely Exel-Pardo $C^*$-algebras associated with a self-similar action of a group on a directed graph, and the $C^*$-algebras associated with separated graphs. These constructions have in common that they have a dynamical behavior, being the groupoid $C^*$-algebras associated to certain topological groupoids, which are built from the combinatorial structure. An important invariant one may associate to these dynamical systems is the so-called type semigroup. We will find a formula to compute the type semigroup for a general self-similar action of a group on a row-finite graph $E$ without sources, following a recent paper by Kwaśniewski, Meyer and Prasad, and for any finite bipartite separated graph, following a paper by Exel and the author. In addition, we will review various results concerning the structure of the type semigroup for different dynamical systems.
Alexandros Chatzinikolaou, Gage Hoefer, Nikolaos Koutsonikos-Kouloumpis, Ioannis Apollon Paraskevas
We introduce an operator-algebraic framework for Morita equivalence of quantum graphs based on $Δ$-equivalence of operator systems introduced by Eleftherakis, Kakariadis and Todorov. Adopting the perspective of Weaver, we view quantum graphs as quantum relations, that is, operator systems endowed with a bimodule structure over the commutant of a von Neumann algebra. Within this framework, we show that two irreducibly acting quantum graphs are Morita equivalent if and only if they are both full pullbacks of a common quantum graph. This extends a result of Eleftherakis, Kakariadis and Todorov for graph operator systems to the quantum graph setting. In passing we construct a true-twin reduction analogue for an irreducibly acting quantum graph. We further characterise the case where we have simultaneous TRO-equivalence of the quantum graphs and their associated algebras, thus giving a second, stronger notion of Morita equivalence. In the special case of noncommutative graphs, corresponding to the zero-error quantum communication setting, the two notions coincide and we obtain a characterisation in terms of strong co-homomorphisms of noncommutative graphs. Finally, we show that connectivity, the independence number, Shannon capacity, quantum complexity and subcomplexity, Haemers bound, and the Lovász number are invariant under Morita equivalence.
Alcides Buss, Julian Kranz
We construct the first explicit examples of locally compact Hausdorff étale groupoids that are not inner amenable and that do not arise as transformation groupoids associated to partial actions of discrete groups. This answers questions of Anantharaman--Delaroche and Exel. Our examples include all Higson--Lafforgue--Skandalis groupoids associated to non-amenable residually finite groups, as well as their principal variants constructed by Alekseev--Finn--Sell. These can be chosen to be second countable, ample, and in the latter case even principal. We also show that large classes of Deaconu--Renault groupoids with connected unit space do not arise from partial actions of discrete groups, including cases whose $C^*$-algebras are Kirchberg algebras in the UCT class. We contrast this with the totally disconnected case by giving ample transformation groupoid models for all unital Kirchberg algebras in the UCT class as well as many higher rank graph algebras. Finally, we characterize precisely when coarse groupoids arise from partial actions of discrete groups in terms of coarse embeddings into groups.
Gautier-Edouard Edouard Filardo
We introduce a traceable operator-algebraic framework for incompressible transport on M= T3 (and, more generally, compact Riemannian manifolds endowed with a smooth invariant probability measure). Given an autonomous divergence-free velocity field u, the time-1 map $Φ$ induces the Koopman unitary U on L2(M) and the crossed-product finite von Neumann algebra Mu\,:= L$\infty$(M) ___$α$ Z= W$\star$(L$\infty$(M),U), equipped with its canonical faithful normal trace $τ$u. Within Mu we define tracial complexity functionals from commutators [U,Mf] (with Mf the multiplication operators) and associated positive elements, and we connect these quantities to Fuglede--Kadison determinants and entropy-like tracial functionals. In parallel, we introduce bounded regularized advection operators T(s) u\,:= KsTuKs as differential-level probes of transport oncommutativity, and we recall the Lie-bracket commutator identity at the formal generator level. This provides a natural algebraic setting in which tracial invariants are well posed and, in principle, computable on discretizations (e.g. cavity flow and vortex benchmarks).
Aissa Bouhali, Issam Louhichi, Abdelrahman Yousef
We investigate the commutant problem for Toeplitz operators on the Bergman space of the unit disk whose symbols belong to a subclass of biharmonic functions. We obtain a complete characterization of when two such Toeplitz operators commute. As a consequence, we derive a full description of normal Toeplitz operators with symbols in this class.
Shuyuan Yang, Jinchuan Hou, Kan He
Apr 20, 2026·quant-ph·PDF Employing mutually-commuting von Neumann algebras to represent the algebra of observables on quantum systems provides a framework for studying quantum information theory in systems with infinite degrees of freedom and quantum field theory, yielding many profound results that differ from non-relativistic quantum systems. In this paper, we establish a mutually-commuting von Neumann algebra model of quantum networks with arbitrary structures. We derive Bell-type inequalities on this model, and determine various bounds for Bell-type inequalities based on the structure of underline von Neumann algebras, and identify the algebraic structural conditions required for their violation. The conditions on the algebraic structure of observables for maximal violation of Bell-type inequalities, which we discovered in the context of von Neumann algebra models, can in turn guide the search for measurements in the non-relativistic setting.
Zhen Wang
The aim of this paper is to study Takesaki duality for weak* closed $L^p$-operator crossed product $W^*_p(G,A,α)$, where $G$ is a countable discrete Abelian group, $A$ is a unital separable weak* closed $L^p$-operator algebra ($p>1$), and $α$ is a weak* continuous $p$-completely isometric action of $G$ on $A$. In this paper, we construct a weak* continuous homomorphism $Φ$ from $W^*_p(\hat{G},W^*_p(G,A,α),\hatα)$ to $\mathcal{B}(l^{p}(G))\bar{\otimes}A$. We show that $Φ$ is an isomorphism if and only if either $p=2$ or $G$ is finite, and $Φ$ is an isometric isomorphism if either $p=2$ or $G$ is trivial. It is also proved that $Φ$ is equivariant for the double dual action $\hat{\hatα}$ of $G$ on $W^*_p(\hat{G},W^*_p(G,A,α),\hatα)$ and the action $\mathrm{Ad}ρ_p\otimesα$ of $G$ on $\mathcal{B}(l^p(G))\bar{\otimes} A$. Furthermore, we prove that $W^*_p(\hat{G},W^*_p(G,A,α),\hatα)$ is weak* continuous isometrically isomorphic to $\mathcal{B}(l^{p}(G))\bar{\otimes}A$ if and only if either $p=2$ or $G$ is trivial, and $W^*_p(\hat{G},W^*_p(G,A,α),\hatα)$ is weak* continuous isomorphic to $\mathcal{B}(l^{p}(G))\bar{\otimes}A$ if and only if either $p=2$ or $G$ is finite when $A=M_n^p$. This shows that Takesaki duality theorem of von Neumann algebras can be generalized to weak* closed $L^2$-operator algebras, and this theorem can not be generalized to weak* closed $L^p$-operator algebras when $p\in (1,\infty)\setminus\{2\}$.
Samuel Tiersma
We give an order-theoretic characterization of the essential image of the forgetful functor from the category of real/complex unital C*-algebras to the category of real/complex unital operator systems. It is based on the characterization of JB-algebras among the order unit spaces in terms of the existence of gauge-reversing bijections obtained by M. Roelands and the author in arXiv:2507.09526. To this end, we show that a unital operator system is completely order isomorphic to a C*-algebra if and only if each of its matrix spaces admits a compatible JB-algebra structure. As an application, we prove that for $n\ge 4$ the range of a unital n-positive projection on a unital real C*-algebra is unitally n-order isomorphic to a unital real C*-algebra, which is the analogue of a result proven for complex C*-algebras by Choi--Effros.
Tamara Bottazzi, Alejandro Varela
We study the minimality of $n\times n$ Hermitian matrices $A$ respect to a $C^*$-subalgebra $\mathcal{B}$ of $M_n(\mathbb{C})$ in the spectral norm, that is \[\|A\|\leq \|A+B\|,\ \text{ for every } B\in \mathcal{B}.\] We generalize the notion of the moment of a subspace and relate it to the joint numerical range and the subdifferentials of the maximum eigenvalue. We extend results previously known for the subalgebra of diagonal operators and describe the subdifferential of the maximum eigenvalue in terms of the moment of the corresponding eigenspace. We also characterize $\mathcal{B}$-minimality via moments and subdifferentials, and provide examples.