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We consider the quantum computational process as viewed by an insider observer: this is equivalent to an isomorphism between the quantum computer and a quantum space, namely the fuzzy sphere. The result is the formulation of a reversible…
A theoretical framework is presented allowing the treatment of quantum messages with components of variable length. To this aim a many-letter space, similiar to the Fock space, is constructed, generalizing the standard quantum information…
We study the two dual quantum information effects to manipulate the amount of information in quantum computation: hiding and allocation. The resulting type-and-effect system is fully expressive for irreversible quantum computing, including…
Quantum information science and intense laser matter interaction are two apparently unrelated fields. Here, we introduce the notion of quantum information theory to intense laser driven processes by providing the quantum mechanical…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…
Quantum information theory is used to analize various non-linear operations on quantum states. The universal disentanglement machine is shown to be impossible, and partial (negative) results are obtained in the state-dependent case. The…
We study determinants of matrices whose entries are powers of Fibonacci numbers. We then extend the results to include entries that are powers of generalized Fibonacci numbers defined as a second-order linear recurrence relation. These…
This is a short review of recent work on fuzzy spaces in their relation to the M(atrix) theory and the quantum Hall effect. We give an introduction to fuzzy spaces and how the limit of large matrices is obtained. The complex projective…
Never is the difference between thermal equilibrium and turbulence so dramatic, as when a quadratic invariant makes the equilibrium statistics exactly Gaussian with independently fluctuating modes. That happens in two very different yet…
Quantum walk is a key operation in quantum computing, simulation, communication and information. Here, we report for the first time the demonstration of quantum walks and localized quantum walks in a new type of optical fibers having a ring…
Many important results in modern quantum information theory have been obtained for an idealized situation when the spacetime dependence of quantum phenomena is neglected. However the transmission and processing of (quantum) information is a…
We define generalised notions of biunitary elements in planar algebras and show that objects arising in quantum information theory such as Hadamard matrices, quantum latin squares and unitary error bases are all given by biunitary elements…
We describe a connection between finite--dimensional representations of quantum affine algebras and affine Hecke algebras.
The tools, ideas, and insights from linear algebra, abstract algebra, and functional analysis can be extremely useful to signal processing and system theory in various areas of engineering, science, and social science including…
We describe a quasiperiodic optical lattice, created by a physical realization of the abstract cut-and-project construction underlying all quasicrystals. The resulting potential is a generalization of the Fibonacci tiling. Calculation of…
Tensors are ubiquitous in statistics and data analysis. The central object that links data science to tensor theory and algebra is that of a model with latent variables. We provide an overview of tensor theory, with a particular emphasis on…
The objective of this series of papers is to recover information regarding the behaviour of FQ operations in the case $n=2$, and FQ conform-operations in the case $n=3$. In this first part we study how the basic invariance properties of FQ…
Using a fermionic renormalization group approach we analyse a model where the electrons diffusing on a quantum dot interact via Fermi-liquid interactions. Describing the single-particle states by Random Matrix Theory, we find that…
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in…
Let $(F_n)_{n\ge 1}$ be the Fibonacci sequence. Define $P(F_n): = (\sum_{i=1}^n F_i)_{n\ge 1}$; that is, the function $P$ gives the sequence of partial sums of $(F_n)$. In this paper, we first give an identity involving $P^k(F_n)$, which is…