Related papers: Kronecker product/Direct product/Tensor product in…
We introduced a non-symmetric tensor product of any two states or any two representations of Cuntz-Krieger algebras associated with a certain non-cocommutative comultiplication in previous our work. In this paper, we show that a certain set…
We study a quantum state transfer between two qubits interacting with the ends of a quantum wire consisting of linearly arranged spins coupled by an excitation conserving, time-independent Hamiltonian. We show that if we control the…
We present a manifestly rotational invariant formulation of the matrix product method valid for spin chains and ladders. We apply it to 2 legged spin ladders with spins 1/2, 1 and 3/2 and different magnetic structures labelled by the…
In the quantum logic framework we show that the no-signaling box model is a particular type of tensor product of the logics of single boxes. Such notion of tensor product is too strong to apply in the category of logics of quantum…
We show that two tensor permutation matrices permutate tensor product of rectangle matrices. Some examples, in the particular case of tensor commutation matrices, for studying some linear matrix equations are given.
In a recent paper, the authors introduced a new basis of the ring of symmetric functions which evaluate to the irreducible characters of the symmetric group at roots of unity. The structure coefficients for this new basis are the stable…
In this note, we survey some elementary theorems and proofs concerning dynamical matrices theory. Some mathematical concepts and results involved in quantum information theory are reviewed. A little new result on the matrix representation…
Derksen proved that the spectral norm is multiplicative with respect to vertical tensor products (also known as tensor Kronecker products). We will use this result to show that the nuclear norm and other norms of interest are also…
We propose that a magnetic quantum wire composed of magnetic and non-magnetic atomic sites can be used as a spin filter for a wide range of applied bias voltage. We adopt a simple tight-binding Hamiltonian to describe the model where the…
In this work we present an intuitive construction of the quantum logical axiomatic system provided by George Mackey. The goal of this work is a detailed discussion of the results from the paper 'Physical justification for using the tensor…
We establish a non-commutative version of the Intermediate Factor Theorem for crossed products associated with product lattices. Given an irreducible lattice $\Gamma < G= G_1 \times \dots \times G_d$ in higher rank semisimple algebraic…
Linearity and unitarity are two fundamental tenets of quantum theory. Any consequence that follows from these must be respected in the quantum world. The no-cloning theorem and the no-deleting theorem are the consequences of the linearity…
The quantum Fisher information, the quantum analogue of the classical Fisher information, is a central quantity in quantum metrology and quantum sensing due to its connection to parameter estimation and fidelity susceptibility. Using…
Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…
The evolution of complex correlated quantum systems such as random circuit networks is governed by the dynamical buildup of both entanglement and entropy. We here introduce a real-time field theory approach -- essentially a fusion of the $G…
A coarse-graining of spin networks is expressed in terms of partial tracing, thus allowing to use tools of quantum information theory. This is illustrated by the analysis of a simple black hole model, where the logarithmic correction of the…
We study quantum moment maps of $G$-invariant star products, which are a quantum analogue of the moment map for classical Hamiltonian systems. Introducing an integral representation, we show that any quantum moment map for a $G$-invariant…
We consider the dynamics $t\mapsto\tau_t$ of an infinite quantum lattice system that is generated by a local interaction. If the interaction decomposes into a finite number of terms that are themselves local interactions, we show that…
In this paper, we give a combinatorial rule to calculate the decomposition of the tensor product (Kronecker product) of two irreducible complex representations of the symmetric group ${\mathfrak S}_n$, when one of the representations…
We construct explicit approximating nets for crossed products of C*-algebras by actions of discrete quantum groups. This implies that C*-algebraic approximation properties such as nuclearity, exactness or completely bounded approximation…