相关论文: The Relation between Subfactors arising from Confo…
This paper enriches the list of known properties of congruence sequences starting from the universal relation and successively performing the operators lower $k$ and lower $t$. Two series of inverse semigroups, namely…
We define mutation pair in a pseudo-triangulated category. We prove that under certain conditions, for a mutation pair in a pseudo-triangulated category, the corresponding quotient category carries a natural triangulated structure. This…
We explain the quantum structure as due to the presence of two effects, (a) a real change of state of the entity under influence of the measurement and, (b) a lack of knowledge about a deeper deterministic reality of the measurement…
Let $N \subset M$ be an irreducible inclusion of type type II$_1$ factors with finite Jones index. We shall introduce the notion of normality for intermediate subfactors of the inclusion $N \subset M$. If the depth of $N \subset M$ is 2,…
Post-hoc explanations of machine learning models are crucial for people to understand and act on algorithmic predictions. An intriguing class of explanations is through counterfactuals, hypothetical examples that show people how to obtain a…
The notion of quantum matrix pairs is defined. These are pairs of matrices with non-commuting entries, which have the same pattern of internal relations, q-commute with each other under matrix multiplication, and are such that products of…
Some physical implications involved in a new concept, termed the "quantum protectorate" (QP), are developed and discussed. This is done by considering the idea of quantum protectorate in the context of quantum theory of magnetism. It is…
Intervention theories of causality define a relationship as causal if appropriately specified interventions to manipulate a putative cause tend to produce changes in the putative effect. Interventionist causal theories are commonly…
Quantum Measure Theory (QMT) is a generalization of quantum theory where physical predictions are computed from a matrix known as \emph{decoherence functional} (DF). Previous works have noted that, in its original formulation, QMT exhibits…
A group theoretical understanding of the two dimensional fractional supersymmetry is given in terms of the quantum Poincare group at roots of unity. The fractional supersymmetry algebra and the quantum group dual to it are presented and the…
The congruence subgroup property is established for the modular representations associated to any modular tensor category. This result is used to prove that the kernel of the representation of the modular group on the conformal blocks of…
Let Q be any II_1-factor. It is shown that any standard lattice G can be realized as the standard invariant of a free product of (several) rescalings of Q. In particular, if Q has fundamental group equal to the positive reals and if P is…
In this paper, we study the quantum channel on a von Neuamnn algebra $\mathcal{M}$ preserving a von Neumann subalgebra $\mathcal{N}$, namely an $\mathcal{N}$-$\mathcal{N}$-bimodule unital completely positive map. By introducing the relative…
Quantum computing has revolutionized the field of computer science with its extraordinary ability to handle classically intractable problems. To realize its potential, however, quantum computers need to scale to millions of qubits, a feat…
A new quantum mechanical notion -- Conditional Density Matrix -- is discussed and is applied to describe some physical processes. This notion is a natural generalization of von Neumann density matrix for such processes as divisions of…
Evaluating hypothetical statements about how the world would be had a different course of action been taken is arguably one key capability expected from modern AI systems. Counterfactual reasoning underpins discussions in fairness, the…
Various relations between conformal quantum field theories in one, two and four dimensions are explored. The intention is to obtain a better understanding of 4D CFT with the help of methods from lower dimensional CFT.
One of the main technical obstacles in constructing a consistent theory of quantum gravity is that the metric itself defines the causal structure required for quantization. This motivates implementing quantum aspects of gravity through an…
Measurement incompatibility is the most basic resource that distinguishes quantum from classical physics. Contextuality is the critical resource behind the power of some models of quantum computation and is also a necessary ingredient for…
In statistical physics any given system can be either at an equilibrium or away from it. Networks are not an exception. Most network models can be classified as either equilibrium or growing. Here we show that under certain conditions there…