Related papers: A duality between exceptions and states
Exploring quantum phenomena beyond predictions of any classical model has fundamental importance to understand the boundary of classical and quantum descriptions of nature. As a typical property that a quantum system behaves distinctively…
We consider the optomechanical system consisting of an atom-cavity system coupled with a mechanical resonator, and expand the notion of quasi-dark state to the optomechanical system. We theoretically prove that even if both the one-mode…
We consider quantum systems in entangled states post-selected in non-entangled states. Such systems exhibit unusual behavior, in particular when weak measurements are performed at intermediate times.
Intuitionistic logic, in which the double negation law not-not-P = P fails, is dominant in categorical logic, notably in topos theory. This paper follows a different direction in which double negation does hold. The algebraic notions of…
A nonlocality anomaly in which a partially entangled state can outperform a maximally entangled state in a task exploiting nonlocality and several ways to remove the anomaly are discussed. A necessary condition for the anomaly to occur is…
We introduce the mathematical theory of the particle systems that interact via permutations, where the transition rates are assigned not to the jumps from a site to a site, but to the permutations themselves. This permutation processes can…
One advantage of quantum algorithms over classical computation is the possibility to spread out, process, analyse and extract information in multipartite configurations in coherent superpositions of classical states. This will be discussed…
The notion of quantum information related to the two different perspectives of the global and local states is examined. There is circularity in the definition of quantum information because we can speak only of the information of systems…
The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and…
In this article we develop a duality principle suitable for a large class of problems in optimization. The main result is obtained through basic tools of convex analysis and duality theory. We establish a correct relation between the…
Quantum information science is a source of task-related axioms whose consequences can be explored in general settings encompassing quantum mechanics, classical theory, and more. Quantum states are compendia of probabilities for the outcomes…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
We define the notion of duality categories as generalization of duality groups. Two examples are treated. The first is the Serre duality in the categories of strict polynomial functors. The second concerns finite complexes. We show in…
Suppose you receive a sequence of qubits where each qubit is guaranteed to be in one of two pure states, but you do not know what those states are. Your task is to determine the states. This can be viewed as a kind of quantum state learning…
Traditionally categorical data analysis (e.g. generalized linear models) works with simple, flat datasets akin to a single table in a database with no notion of missing data or conflicting versions. In contrast, modern data analysis must…
I conceptualise the role of dualities in quantum gravity, in terms of their functions for theory construction. I distinguish between two functions of duality in physical practice: namely, discovering and describing 'equivalent physics', vs.…
This paper explains why internal and external validity cannot be simultaneously maximised. It introduces "evidential states" to represent the information available for causal inference and shows that routine study operations (restriction,…
Emergence and causality are two fundamental concepts for understanding complex systems. They are interconnected. On one hand, emergence refers to the phenomenon where macroscopic properties cannot be solely attributed to the cause of…
This paper describes how to verify a parser for regular expressions in a functional programming language using predicate transformer semantics for a variety of effects. Where our previous work in this area focused on the semantics for a…
When a quantum system interacts with an external environment, it undergoes the loss of quantum correlation (decoherence) and the loss of energy (relaxation) and eventually all of the quantum information becomes classical. Here we show a…