Related papers: Universal Properties in Quantum Theory
Do correctness and completeness of quantum mechanics jointly imply that quantum state vectors are necessarily in one-to-one correspondence with elements of the physical reality? In terms of category theory, such a correspondence would stand…
Quantum theory is a well-defined local theory with a clear interpretation. No "measurement problem" or any other foundational matters are waiting to be settled.
The theory of symmetry of quantum mechanical systems is applied to study the structure and properties of several classes of relevant maps in quantum information theory: CPTP, PPT and Schwarz maps. First, we develop the general structure…
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…
A quantum set is defined to be simply a set of nonzero finite-dimensional Hilbert spaces. Together with binary relations, essentially the quantum relations of Weaver, quantum sets form a dagger compact category. Functions between quantum…
A version of quantum theory is derived from a set of plausible assumptions related to the following general setting: For a given system there is a set of experiments that can be performed, and for each such experiment an ordinary…
The existence of indistinguishable quantum particles provides an explanation for various physical phenomena we observe in nature. We lay out a path for the study of indistinguishable particles in general probabilistic theories (GPTs) via…
In this work we present a general mathematical framework to deal with Quantum Networks, i.e. networks resulting from the interconnection of elementary quantum circuits. The cornerstone of our approach is a generalization of the Choi…
We define a loop to be quantum nullhomotopic if and only if it admits a nonempty quantum set of extensions to the unit disk. We show that the canonical loop in the unit circle is not quantum nullhomotopic, but that every loop in the real…
The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…
We briefly review a number of major features of the approach to quantum measurement theory based on environment-induced decoherence of the measuring apparatus, and summarize our observations in the form of a couple of general principles…
We introduce the framework of general probabilistic theories (GPTs for short). GPTs are a class of operational theories that generalize both finite-dimensional classical and quantum theory, but they also include other, more exotic theories,…
The long lasting discussion on the completeness of quantum theory (QT) has not yet come to an end. The discussion is impeded by the lack of a clear understanding of what makes up the contents of a theory of physics in general and of QT…
We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the…
We consider single-particle quantum transport on parametrized complex networks. Based on general arguments regarding the spectrum of the corresponding Hamiltonian, we derive bounds for a measure of the global transport efficiency defined by…
Gluing two manifolds M_1 and M_2 with a common boundary S yields a closed manifold M. Extending to formal linear combinations x=Sum_i(a_i M_i) yields a sesquilinear pairing p=<,> with values in (formal linear combinations of) closed…
The physically allowed quantum evolutions on a single qubit can be described in terms of their geometry. From a simple parameterisation of unital single-qubit channels, the canonical form of all such channels can be given. The related…
A generalized channel is a completely positive map that preserves trace on a given subspace. We find conditions under which a generalized channel with respect to a positively generated subspace J is an extreme point in the set of all such…
In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. We, then, unearth the structure of the convex set of covariant…
We explore the implications of restricting the framework of quantum theory and quantum computation to finite fields. The simplest proposed theory is defined over arbitrary finite fields and loses the notion of unitaries. This makes such…