Related papers: Algorithmic Randomness and Capacity of Closed Sets
We study algorithmically random closed subsets of $2^\omega$, algorithmically random continuous functions from $2^\omega$ to $2^\omega$, and algorithmically random Borel probability measures on $2^\omega$, especially the interplay between…
Projective measurements with high quantum efficiency is often assumed to be required for efficient circuit based quantum computing. We argue that this is not the case and show that this fact has actually be known previously though not…
Recently the theory of communication developed by Shannon has been extended to the quantum realm by exploiting the rules of quantum theory. This latter stems on complex vector spaces. However complex (as well as real) numbers are just…
In a recent paper, two multi-representations for the measurable sets in a computable measure space have been introduced, which prove to be topologically complete w.r.t. certain topological properties. In this contribution, we show them…
Given a probability measure over a state space, a partial collection (sub-$\sigma$-algebra) of events whose probabilities are known, induces a capacity over the collection of all possible events. The \emph{induced capacity} of an event $F$…
We establish a framework which allows one to construct novel schemes for measurement-based quantum computation. The technique further develops tools from many-body physics - based on finitely correlated or projected entangled pair states -…
This article is a fundamental study in computable measure theory. We use the framework of TTE, the representation approach, where computability on an abstract set X is defined by representing its elements with concrete "names", possibly…
Quantum measurements under realistic conditions reveal only partial information about a system. Yet, by performing sequential measurements on the same system, additional information can be accessed. We investigate this problem in the…
Quantum speed limits are usually regarded as fundamental restrictions, constraining the amount of computation that can be achieved within some given time and energy. Complementary to this intuition, here we show that these limitations are…
We initiate the effective metric structure theory of Keisler randomizations. We show that a classical countable structure $\mathcal{M}$ has a decidable presentation if and only if its Borel randomization $\mathcal{M}^{[0,1)}$ has a…
This paper presents an analysis of the concept of capacity for noisy com- putations, i.e. functions implemented by unreliable or random devices. An information theoretic model of noisy computation of a perfect function f (measurable…
The set $M$ of $d\times d$ Hermitian matrices (observables) is studied as a partially ordered set with the L\"{o}wner partial order. Upper and lower sets in it, define the concept of cumulativeness (used mainly with scalar quantities) in…
We develop a synthesis of Turing's paradigm of computation and von Neumann's quantum logic to serve as a model for quantum computation with recursion, such that potentially non-terminating computation can take place, as in a quantum Turing…
We use machine learning to provide a tractable measure of the amount of predictable variation in the data that a theory captures, which we call its "completeness." We apply this measure to three problems: assigning certain equivalents to…
Quantum coherence characterizes the non-classical feature of a single party system with respect to a local basis. Based on a recently introduced resource framework, coherence can be regarded as a resource and be systematically manipulated…
Recently there have been fruitful results on resource theories of quantum measurements. Here we investigate the number of measurement outcomes as a kind of resource. We cast the robustness of the resource as a semi-definite positive…
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…
We investigate the compression of quantum information with respect to a given set $\mathcal{M}$ of high-dimensional measurements. This leads to a notion of simulability, where we demand that the statistics obtained from $\mathcal{M}$ and an…
The problem of capacity achieving (optimal) input probability measures has been widely investigated for several channel models with constrained inputs. So far, no outstanding generalizations have been derived. This paper does a forward step…
The empty set of course contains no computable point. On the other hand, surprising results due to Zaslavskii, Tseitin, Kreisel, and Lacombe assert the existence of NON-empty co-r.e. closed sets devoid of computable points: sets which are…