Related papers: Resource dependent undecidability: computability l…
The power of quantum computers is still somewhat speculative. While they are certainly faster than classical ones at some tasks, the class of problems they can efficiently solve has not been mapped definitively onto known classical…
A major signature of quantum mechanics beyond classical physics is coherence, the existence of superposition states. The recently developed resource theory of quantum coherence allows the formalisation of incoherent operations -- those…
$\textit{Magic: The Gathering}$ is a popular and famously complicated trading card game about magical combat. In this paper we show that optimal play in real-world $\textit{Magic}$ is at least as hard as the Halting Problem, solving a…
On the real numbers, the notions of a semi-decidable relation and that of an effectively enumerable relation differ. The second only seems to be adequate to express, in an algorithmic way, non deterministic physical theories, where…
Recent tremendous development of quantum information theory led to a number of quantum technological projects, e.g., quantum random generators. This development stimulates a new wave of interest in quantum foundations. One of the most…
The abelian sandpile model is a simple combinatorial model for critical behaviour which has the "abelian property" that the order in which we make moves does not change the final outcome of the game. This might seem to restrict the model's…
In laboratory and numerical experiments, physical quantities are known with a finite precision and described by rational numbers. Based on this, we deduce that quantum control problems both for open and closed systems are in general not…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
The notion of computability is stable (i.e. independent of the choice of an indexing) over infinite-dimensional vector spaces provided they have a finite "tensorial dimension". Such vector spaces with a finite tensorial dimension permit to…
Discordant states appear in a large number of quantum phenomena and seem to be a good indicator of divergence from classicality. While there is evidence that they are essential for a quantum algorithm to have an advantage over a classical…
Quantum coherence is an essential feature of quantum mechanics which is responsible for the departure between classical and quantum world. The recently established resource theory of quantum coherence studies possible quantum technological…
It is well known that the verification of resource-constrained multiagent systems is undecidable in general. In many such settings, resources are private to agents. In this paper, we investigate the model checking problem for a resource…
Among the most fundamental questions in the manipulation of quantum resources such as entanglement is the possibility of reversibly transforming all resource states. The key consequence of this would be the identification of a unique…
Understanding the role that quantum entanglement plays as a resource in various information processing tasks is one of the crucial goals of quantum information theory. Here we propose a new perspective for studying quantum entanglement:…
The query containment problem is a fundamental algorithmic problem in data management. While this problem is well understood under set semantics, it is by far less understood under bag semantics. In particular, it is a long-standing open…
We present a resource theory of stinginess, first in a classical scenario, and then, point to a possible quantum version of the same.
In this article, we investigate the arithmetical hierarchy from the perspective of realizability theory. An experimental observation in classical computability theory is that the notion of degrees of unsolvability for natural arithmetical…
We consider two aspects of quantum game theory: the extent to which the quantum solution solves the original classical game, and to what extent the new solution can be obtained in a classical model.
We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely…
The nature of quantum computation is discussed. It is argued that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum…