Abstract We investigate the extendibility problem for Brauer states, focusing on the symmetric two-sided extendibility and the de Finetti extendibility. By employing the representation theory of the unitary and orthogonal groups, we provide a general recipe for determining the set of -extendible and -de Finetti-extendible Brauer states. From the concrete form of the commutant of the diagonal action of the orthogonal group, we explicitly determine the set of parameters for which the Brauer states are -, - and -extendible in any dimension and find that Brauer states extend with a non-trivial trade-off in and . Using the same recipe we also provide an estimate of the set of -extendible Brauer states for any and dimension . Finally, using the branching rules from to , we obtain the set of -de Finetti-extendible Brauer states in any dimension, and also analytically describe the limiting shape which turns out not to be a polygon for odd dimensions.Abstract We investigate the extendibility problem for Brauer states, focusing on the symmetric two-sided extendibility and the de Finetti extendibility. By employing the representation theory of the unitary and orthogonal groups, we provide a general recipe for determining the set of -extendible and -de Finetti-extendible Brauer states. From the concrete form of the commutant of the diagonal action of the orthogonal group, we explicitly determine the set of parameters for which the Brauer states are -, - and -extendible in any dimension and find that Brauer states extend with a non-trivial trade-off in and . Using the same recipe we also provide an estimate of the set of -extendible Brauer states for any and dimension . Finally, using the branching rules from to , we obtain the set of -de Finetti-extendible Brauer states in any dimension, and also analytically describe the limiting shape which turns out not to be a polygon for odd dimensions.

arXiv:2411.04597Journal of Physics A Mathematical and TheoreticalJun 22, 20260 citations

Quantum cellular automata and invertible phases of matter

Corey Jones, Nikita Sopenko, Ryan Thorngren

We introduce and study (fermionic and bosonic) invertible quasi-local algebras over uniformly locally finite metric spaces $X$ with infinite-dimensional local von Neumann algebras. We show that the group of Brauer equivalence classes of such algebras is isomorphic to both the group of phases of invertible states and the group of stable equivalence classes of quantum cellular automata over $X\times \mathbb{Z}$ . Using K-theory of the symmetric monoidal category of invertible quasi-local algebras and bounded spread isomorphisms, we propose a definition of an $Ω$ -spectrum of invertible phases as conjectured by Kitaev. We then show that the $c=\frac{1}{2}$ chiral Majorana fermion net and the $(E_{8})_{1}$ conformal net provide Brauer non-trivial invertible quasi-local algebras, thus providing explicit constructions of non-trivial invertible states and quantum cellular automata on $\mathbb{Z}^{2}$ . In addition, we show that the time-slice nets of rational diagonal conformal field theories admit lattice degrees of freedom, which implies the discretization of any holomorphic conformal net is invertible.We introduce and study (fermionic and bosonic) invertible quasi-local algebras over uniformly locally finite metric spaces $X$ with infinite-dimensional local von Neumann algebras. We show that the group of Brauer equivalence classes of such algebras is isomorphic to both the group of phases of invertible states and the group of stable equivalence classes of quantum cellular automata over $X\times \mathbb{Z}$. Using K-theory of the symmetric monoidal category of invertible quasi-local algebras and bounded spread isomorphisms, we propose a definition of an $Ω$-spectrum of invertible phases as conjectured by Kitaev. We then show that the $c=\frac{1}{2}$ chiral Majorana fermion net and the $(E_{8})_{1}$ conformal net provide Brauer non-trivial invertible quasi-local algebras, thus providing explicit constructions of non-trivial invertible states and quantum cellular automata on $\mathbb{Z}^{2}$. In addition, we show that the time-slice nets of rational diagonal conformal field theories admit lattice degrees of freedom, which implies the discretization of any holomorphic conformal net is invertible.

math-phCross-listedarXiv:2608.26456Aug 28, 20260 citations

Erwiderung von H. Rechenberg

Physikalische BlätterSep 1, 19910 citations

Conclusion and Further Remarks

Franklin de Lima Marquezino, Renato Portugal, Carlile Lavor

SpringerBriefs in computer scienceJan 1, 20190 citations

Entwicklung von Analogie-Experimenten zum quantenmechanischen Messprozess

Stefan Aehle, Philipp Scheiger, Holger Cartarius

Quantenphysikunterricht steht von Natur aus vor der Herausforderung, den Lernenden ein Themanbsp;näher zu bringen, das scheinbar gegen jede alltägliche Intuition geht. Umso wichtiger scheint es, innbsp;einer multiperspektivischen Herangehensweise verschiedene Repräsentationen für das komplexenbsp;Verhalten von Quantenobjekten zu wählen. Im Folgenden bieten wir eine Repräsentation zum Verhaltennbsp;von Einzelphotonen an Polarisationsfiltern an, die auf der Zusammenarbeit von 3D-Druck,nbsp;Arduino-Microcontrollern und NFC-Chips basiert. Besonderer Fokus dieser Analogie fällt dabei aufnbsp;den quantenphysikalischen Messprozess.Quantenphysikunterricht steht von Natur aus vor der Herausforderung, den Lernenden ein Themanbsp;näher zu bringen, das scheinbar gegen jede alltägliche Intuition geht. Umso wichtiger scheint es, innbsp;einer multiperspektivischen Herangehensweise verschiedene Repräsentationen für das komplexenbsp;Verhalten von Quantenobjekten zu wählen. Im Folgenden bieten wir eine Repräsentation zum Verhaltennbsp;von Einzelphotonen an Polarisationsfiltern an, die auf der Zusammenarbeit von 3D-Druck,nbsp;Arduino-Microcontrollern und NFC-Chips basiert. Besonderer Fokus dieser Analogie fällt dabei aufnbsp;den quantenphysikalischen Messprozess.

PhyDid B - Didaktik der Physik - Beiträge zur DPG-FrühjahrstagungNov 30, 20220 citations

Comment on Torben M. Andersen's Paper

Pekka Ilmakunnas

Physica-Verlag eBooksSep 16, 20050 citations

We introduce and study (fermionic and bosonic) invertible quasi-local algebras over uniformly locally finite metric spaces

X

with infinite-dimensional local von Neumann algebras. We show that the group of Brauer equivalence classes of such algebras is isomorphic to both the group of phases of invertible states and the group of stable equivalence classes of quantum cellular automata over

X\times \mathbb{Z}

. Using K-theory of the symmetric monoidal category of invertible quasi-local algebras and bounded spread isomorphisms, we propose a definition of an

Ω

-spectrum of invertible phases as conjectured by Kitaev. We then show that the

c=\frac{1}{2}

chiral Majorana fermion net and the

(E_{8})_{1}

conformal net provide Brauer non-trivial invertible quasi-local algebras, thus providing explicit constructions of non-trivial invertible states and quantum cellular automata on

\mathbb{Z}^{2}

. In addition, we show that the time-slice nets of rational diagonal conformal field theories admit lattice degrees of freedom, which implies the discretization of any holomorphic conformal net is invertible.