Related papers: Local Operations and Completely Positive Maps in A…
We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier…
We investigate whether commutativity is necessary to represent relativistic locality for localization observables of relativistic quantum systems in Minkowski spacetime. A well known no-go theorem by Halvorson and Clifton shows that…
In the work it is shown that the principles "the objective local theory" and corollaries of the standard quantum mechanics are not in such antagonistic inconsistency as it is usually supposed. In the framework of algebraic approach, the…
The debate on the nature of quantum probabilities in relation to Quantum Non Locality has elevated Quantum Mechanics to the level of an "Operational Epistemic Theory". In such context the quantum superposition principle has an extraneous…
Quantum mechanics is commonly accepted as a complete theory thanks to experimental tests of non-locality based on Bell's theorem. However, we discover that the completeness of the quantum theory practically suffered from detrimental…
We give an example of fulfillment of the condition of locality--no information transfer between certain subsystems--in a tripartite quantum system whose dynamics can not be decomposed (non-sequential dynamics of the system). The three…
The localization phenomenon for periodic unitary transition operators on a Hilbert space consisting of square summable functions on an integer lattice with values in a complex vector space, which is a generalization of the discrete-time…
We describe the structure of all bijective maps on the cone of positive definite operators acting on a finite and at least two-dimensional complex Hilbert space which preserve the quantum $\chi_\alpha^2$-divergence for some $\alpha \in…
Quantum field theory unifies concepts from quantum theory and from special relativity. Its mathematically rigorous description is quite intricate and is only partially understood; this is particularly true for the construction of operators…
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…
Quantum information has become a powerful tool for probing the structure of quantum field theories, yet its application to gauge theories remains subtle. On the one hand, quantum information theory assumes subsystem locality, i.e.~the…
The term 'locality' is used in different contexts with different meanings. There have been claims that relational quantum mechanics is local, but it is not clear then how it accounts for the effects that go under the usual name of quantum…
A theory governing the metric and matter fields in spacetime is {\it locally causal} if the probability distribution for the fields in any region is determined solely by physical data in the region's past, i.e. it is independent of events…
Any quantum resource theory is based on free states and free operations, i.e., states and operations which can be created and performed at no cost. In the resource theory of coherence free states are diagonal in some fixed basis, and free…
In nonrelatistic quantum mechanics, Born's principle of localistion is as follows: For a single particle, if a wave function $\psi_K$ vanishes outside a spatial region $K$, it is said to be localised in $K$. In particular if a spatial…
String-local fields constitute a relatively new tool for solving quantum field theory, stressing and embodying locality and positivity. We examine here their usefulness -- as well as some drawbacks. Starting from just the physical masses…
Deutsch and Hayden have proposed an alternative formulation of quantum mechanics which is completely local. We argue that their proposal must be understood as having a form of `gauge freedom' according to which mathematically distinct…
For two symmetric quantum states one may be interested in maximizing the overlap under local operations applied to one of them. The question arises whether the maximal overlap can be obtained by applying the same local operation to each…
We briefly review the current status of the algebraic approach to quantum field theory on globally hyperbolic spacetimes, both axiomatic -- for general field theories, and constructive -- for a linear Klein-Gordon model. We recall the…
In these proceedings we summarize previous work where we formalize a general concept of algebraic field theories using operads. After giving a gentle reminder of algebraic quantum field theory, operads and their algebras, we construct field…