Related papers: Quantum correlations on quantum spaces
The quantum mechanics of an N=1 supersymmetric dynamical system constrained to a hypersurface embedded in the higher dimensional Euclidean space is investigated by using the projection-operator method (POM) of constrained systems. It is…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
Understanding the role of correlations in quantum systems is both a fundamental challenge as well as of high practical relevance for the control of multi-particle quantum systems. Whereas a lot of research has been devoted to study the…
The absolute/relative debate on the nature of space and time is ongoing for thousands of years. Here we attempt to investigate space and time from the information theoretic point of view to understand spatial and temporal correlations under…
The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…
Measurement-based quantum computation (MQC) is a paradigm for studying quantum computation using many-body entanglement and single-qubit measurements. While MQC has inspired wide-ranging discoveries throughout quantum information, our…
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…
Quantum correlations are interesting resources for modern quantum technologies such as quantum information processing, quantum communication, quantum teleportation, and quantum computation tasks. However, engineering these quantum states…
It is shown that the coordinate algebra of the quantum $2n+1$-dimensional lens space $\mathcal{O}(L^{2n+1}_q(\prod_{i=0}^n m_i; m_0,\ldots, m_n))$ is a principal $\mathbb{Z}$-comodule algebra or the coordinate algebra of a circle principal…
We explore the concept of a graph homomorphism through the lens of C$^*$-algebras and operator systems. We start by studying the various notions of a quantum graph homomorphism and examine how they are related to each other. We then define…
Quantum relations in the sense of Weaver are $M'$-bimodules, for a von Neumann algebra $M$, these generalising actual relations on a set $X$ when $M=\ell^\infty(X)$. Similarly, relations between two sets can be generalised as bimodules over…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
In this work, we present several aspects of the interplay between classical and quantum theories. After reviewing the equivalence between positivity and complete positivity in the commutative setting, we introduce and analyze intermediate…
A quantum mechanical model for the systems consisting of interacting bodies is considered. The model takes into account the noncommutativity of the space and impulse operators and the correlation equations for the indeterminacy of these…
For the O(N) field theory with lambda Phi^4 self-coupling, we construct the two-particle-irreducible (2PI), closed-time-path (CTP) effective action in a general curved spacetime. From this we derive a set of coupled equations for the mean…
We describe a categorical model of MALL (Multiplicative Additive Linear Logic) inspired by the Heisenberg-Schr\"odinger duality of finite-dimensional quantum theory. Proofs of formulas with positive logical polarity correspond to CPTP…
We establish operator structure identities for quantum channels and their error-correcting and private codes, emphasizing the complementarity relationship between the two perspectives. Relevant structures include correctable and private…
An often used model for quantum theory is to associate to every physical system a C*-algebra. From a physical point of view it is unclear why operator algebras would form a good description of nature. In this paper, we find a set of…