Related papers: Kronecker product/Direct product/Tensor product in…
We extend the formalism of pure state thermodynamics to matrix product states. In pure state thermodynamics finite temperature properties of quantum systems are derived without the need of statistical mechanics ensembles, but instead using…
Coherent states provide a natural connection of quantum systems to their classical limit and are employed in various fields of physics. Here we derive general systematic expansions, with respect to quantum parameters, of expectation values…
Dirac talked about q-numbers versus c-numbers. Quantum observables are q-number variables that generally do not commute among themselves. He was proposing to have a generalized form of numbers as elements of a noncommutative algebra. That…
Braided tensor products have been introduced by the author as a systematic way of making two quantum-group-covariant systems interact in a covariant way, and used in the theory of braided groups. Here we study infinite braided tensor…
Some fundamental aspects related with the construction of Robertson-Schr\"odinger like uncertainty principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum…
In a quantum computer the hardware and software are intrinsically connected because the quantum Hamiltonian (or more precisely its time development) is the code that runs the computer. We demonstrate this subtle and crucial relationship by…
A classical t-tensor product expander is a natural way of formalising correlated walks of t particles on a regular expander graph. A quantum t-tensor product expander is a completely positive trace preserving map that is a straightforward…
This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…
The Trotter product formula is a key instrument in numerical simulations of quantum systems. However, computers cannot deal with continuous degrees of freedom, such as the position of particles in molecules, or the amplitude of…
We study a uniform matrix product state as a variational state for classical and quantum spin chains in the thermodynamic limit. Under a careful treatment of the translational symmetry, eigen values of the transfer matrix defined in the…
We apply symmetric function theory to study random processes formed by singular values of products of truncations of Haar distributed symplectic and orthogonal matrices. These product matrix processes are degenerations of Macdonald…
Identifying the physiological processes in the central nervous system that underlie our conscious experiences has been at the forefront of cognitive neuroscience. While the principles of classical physics were long found to be…
Motivated by the novel applications of the mathematical formalism of quantum theory and its generalizations in cognitive science, psychology, social and political sciences, and economics, we extend the notion of the tensor product and…
We introduce a new topological coproduct $\Delta^{\psi}_{u}$ for quantum toroidal algebras $U_{q}(\mathfrak{g}_{\mathrm{tor}})$ in all untwisted types, leading to a well-defined tensor product on the category…
In this article we discuss the formal structure of a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly) non-commutative setting. By studying this framework, we argue that quantum…
In this paper we will analyse the inner product for a general tensor field theory. We will first analyse a generalized inner product for scalar field theories. Then we will use it to construct a inner product for tensor field theories. We…
In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…
Given n quaternions we investigate the extent of non-commutativity of their multiple products, commutators and exponential products.
We review some recent results on properties of tensor product and fusion coefficients under complex conjugation of one of the factors. Some of these results have been proven, some others are conjectures awaiting a proof, one of them…
Accurate modeling of driven light-matter interactions is essential for quantum technologies, where natural and synthetic atoms are used to store and process quantum information, mediate interactions between bosonic modes, and enable…