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We propose an approach to the study of quantum resource manipulation based on the basic observation that quantum channels which preserve certain sets of states are contractive with respect to the base norms induced by those sets. We forgo…
Scrambling unitary dynamics in a quantum system transmutes local quantum information into a non-local web of correlations which manifests itself in a complex spatio-temporal pattern of entanglement. In such a context, we show there can…
We investigate partial functions and computability theory from within a constructive, univalent type theory. The focus is on placing computability into a larger mathematical context, rather than on a complete development of computability…
In this paper we initiate the study of entanglement-breaking (EB) superchannels. These are processes that always yield separable maps when acting on one side of a bipartite completely positive (CP) map. EB superchannels are a generalization…
We provide a quantum statistical basis for (a)a characterisation of a complete set of thermodynamic variables and (b) the differentiability of the entropy function of these variables
In this article we treat the subject of chaotic environments with few degrees of freedom in quantum communication by investigating a conservative dynamical map as a model of a dephasing quantum channel. When the channel's dynamics is…
Differentiable quantum dynamics require automatic differentiation of a complex-valued initial value problem, which numerically integrates a system of ordinary differential equations from a specified initial condition, as well as the…
Mapping the functional connectome has the potential to uncover key insights into brain organisation. However, existing workflows for functional connectomics are limited in their adaptability to new data, and principled workflow design is a…
In the paper, the dynamical additivity of bi-stochastic quantum operations is characterized and the strong dynamical additivity is obtained under some restrictions.
The uncertainty principle is one of quantum theory's most foundational features. It underpins a quantum phenomenon called measurement incompatibility -- two physical observables of a single quantum system may not always be measured…
The theory of noncommutative dynamical entropy and quantum symbolic dynamics for quantum dynamical systems is analised from the point of view of quantum information theory. Using a general quantum dynamical system as a communication channel…
The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…
We consider the learning of algorithmic tasks by mere observation of input-output pairs. Rather than studying this as a black-box discrete regression problem with no assumption whatsoever on the input-output mapping, we concentrate on tasks…
Recently, the entanglement dynamics of two harmonic oscillators initially prepared in a separable-coherent state was demonstrated to offer a pathway for prime number identification. This article presents a generalized approach and outlines…
We study the scaling properties of discontinuous maps by analyzing the average value of the squared action variable $I^2$. We focus our study on two dynamical regimes separated by the critical value $K_c$ of the control parameter $K$: the…
As is well known, unital Pauli maps can be eternally non-CP-divisible. In contrast, here we show that in the case of non-unital maps, eternal non-Markovianity in the non-unital part is ruled out. In the unital case, the eternal…
In classification tasks, it is crucial to meaningfully exploit the information contained in data. While much of the work in addressing these tasks is devoted to building complex algorithmic infrastructures to process inputs in a black-box…
Distinguishability is fundamental to information theory and extends naturally to quantum systems. While quantum state discrimination is well understood, quantum channel discrimination remains challenging due to the dynamic nature of…
We study different characterizations of P-divisibility in two-level open quantum systems whose dynamics are governed by a time-local master equation with time-dependent relaxation rates. Necessary and sufficient conditions for the…
Quantum processors may enhance machine learning by mapping high-dimensional data onto quantum systems for processing. Conventional feature maps, for encoding data onto a quantum circuit are currently impractical, as the number of entangling…