Related papers: The Functional Analysis of Quantum Information The…
We demonstrate that quantum information processing (QIP) completely rests on quantum Fourier transform (QFT), and 190 years after his death, the work of Jean-Baptiste Joseph Fourier is more present than ever in Physics, constituting the…
In this paper, a novel class of quantum fractal functions is introduced based on the Meyer-K\"onig-Zeller operator $M_{q,n}$. These quantum Meyer-K\"onig-Zeller (MKZ) fractal functions employ $M_{q,n} f$ as the base function in the iterated…
In this paper we first introduce the Fock-Guichardet formalism for the quantum stochastic integration, then the four fundamental processes of the dynamics are introduced in the canonical basis as the operator-valued measures of the QS…
We introduce the functional field integral approach to study the statistics of quantum work under nonequilibrium conditions and derive the general formalism for a bilinear Hamiltonian with arbitrary time dependence. The method is then…
These are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.
Learning tasks play an increasingly prominent role in quantum information and computation. They range from fundamental problems such as state discrimination and metrology over the framework of quantum probably approximately correct (PAC)…
An extension of the method and results of A. Schwarz for evaluating the partition function of a quadratic functional is presented. This enables the partition functions to be evaluated for a wide class of quadratic functionals of interest in…
Recent developments on holography and quantum information physics suggest that quantum information theory come to play a fundamental role in understanding quantum gravity. Cosmology, on the other hand, plays a significant role in testing…
This is my talk delivered at the workshop 'Automorphic L-Functions and related prpblems' (March 10--13, 2012, Tokyo University). We showed an instance of applications of the theory of automorphic representations to a genuinely traditional…
We investigate fundamental connections between thermodynamics and quantum information theory. First, we show that the operational framework of thermal operations is nonequivalent to the framework of Gibbs-preserving maps, and we comment on…
Let R be an integral domain, let a non-zero h in R be such that k := R/hR is a field, and let HA be the category of torsionless (or flat) Hopf algebras over R. We call H in HA a "quantized function algebra" (=QFA), resp. "quantized…
We review recent results in the theory of numbers and single-valued functions on the complex plane which arise in quantum field theory. We use the results to calculate the renormalization functions $\beta$, $\gamma$, $\gamma_m$ of…
In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of…
Understanding the electron clock and the role of complex numbers in quantum mechanics is grounded in the geometry of spacetime, and best expressed with Spacetime Algebra (STA). The efficiency of STA is demonstrated with coordinate-free…
Informationally complete measurements allow the estimation of expectation values of any operator on a quantum system, by changing only the data-processing of the measurement outcomes. In particular, an informationally complete measurement…
Quantum field theory (QFT) on fractal spacetimes is a program aiming at quantizing the gravitational interaction consistently at all energy scales thanks to an intrinsically or dynamically induced multiscale or multifractal-like spacetime…
Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cram\'{e}r-Rao bound in quantum parameter estimation. However, studies in recent years have revealed…
We review Schmidt and Kraus decompositions in the form of singular value decomposition using operations of reshaping, vectorization and reshuffling. We use the introduced notation to analyse the correspondence between quantum states and…
The complexity class NP is quintessential and ubiquitous in theoretical computer science. Two different approaches have been made to define "Quantum NP," the quantum analogue of NP: NQP by Adleman, DeMarrais, and Huang, and QMA by Knill,…
The subject of the work is short description of huge amount of n-point information (n-pi) about the system. Methods for solving equations that satisfy such information are considered. Possible interpretation of left and right invertible…