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The first part of the paper centers in the study of embeddability between partially commutative groups. In [KK], for a finite simplicial graph $\Gamma$, the authors introduce an infinite, locally infinite graph $\Gamma^e$, called the…
We provide a classification of compact quantum groups, which can be obtained by the Woronowicz construction, when the arrays used in the twisted determinant condition are extensions of functions on permutations. General properties of such…
The exponential convergence to invariant subspaces of quantum Markov semigroups plays a crucial role in quantum information theory. One such example is in bosonic error correction schemes, where dissipation is used to drive states back to…
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…
Explicit embeddings of the group $\mathbb{Q}$ into a finitely presented group $\mathcal{Q}$ and into a $2$-generator finitely presented group $T_{\mathcal{Q}}$ are suggested. The constructed embeddings reflect questions mentioned by…
This report continues the discussion of unitary error bases and quantum codes begun in "Non-binary Unitary Error Bases and Quantum Codes". Nice error bases are characterized in terms of the existence of certain characters in a group. A…
We introduce the notion of Benjamini-Schramm convergence for quantum graphs. This notion of convergence, intended to play the role of the already existing notion for discrete graphs, means that the restriction of the quantum graph to a…
The study of entanglement properties of multi-qubit states that are invariant under permutations of qubits is motivated by potential applications in quantum computing, quantum communication, and quantum metrology. In this work, we…
We introduce a quantum automorphism group for hypergraphs, which turns out to generalize the quantum automorphism group of Bichon for classical graphs. Further, we show that our quantum automorphism group acts on hypergraph C*-algebras as…
This paper presents the Quanta Prime Sequence (QPS) and its foundational theorem, showcasing a unique class of polynomials with substantial implications. The study uncovers profound connections between Quanta Prime numbers and essential…
Quantum systems invariant under particle exchange are either Bosons or Fermions, even though quantum theory in principle admits more general behavior under permutations. But why do we not observe such "paraparticles" in nature? The analysis…
The emergence of quantum computing enables for researchers to apply quantum circuit on many existing studies. Utilizing quantum circuit and quantum differential programming, many research are conducted such as \textit{Quantum Machine…
The quantization of the continous cat maps on the torus has led to rather pathological quantum objects [6]. The non-generic behaviour of this model has led some to conclude that the Correspondence Principle fails in this case [2]. In this…
We study quantum corrections to hypersurfaces of dimension $d+1>2$ embedded in generic higher-dimensional spacetimes. Manifest covariance is maintained throughout the analysis and our methods are valid for arbitrary co-dimension and…
The quantum mechanics is proved to admit no hidden-variable in 1960s, which means the quantum systems are contextual. Revealing the mathematical structure of quantum mechanics is a significant task. We develop the approach of partial…
Quantum entanglement is a foundational resource in quantum information science, underpinning applications across physics. However, detecting and quantifying entanglement remains a significant challenge. In this article, we introduce a…
To study the convergence to equilibrium in random maps we developed the spectral theory of the corresponding transfer (Perron-Frobenius) operators acting in a certain Banach space of generalized functions. The random maps under study in a…
We give examples of finite quantum permutation groups which arise from the twisting construction or as bicrossed products associated to exact factorizations in finite groups. We also give examples of finite quantum groups which are not…
We study the quantum groups appearing via models $C(G)\subset M_K(C(X))$ which are "stationary", in the sense that the Haar integration over $G$ is the functional $tr\otimes\int_X$. Our results include a number of generalities, notably with…
The Fibonacci cube $\Gamma_n$ is the subgraph of the hypercube $Q_n$ induced by vertices with no consecutive $1$s. Munarini introduced Pell graphs, a variation of Fibonacci cubes defined on ternary strings. A generalization of Pell graphs…