Related papers: State Property Systems and Closure Spaces: Extract…

Schmidt decomposition is a powerful tool in quantum information. While Schmidt decomposition is universal for bipartite states, its not for multipartite states. In this article, we review properties of bipartite Schmidt decompositions and…

It is shown how classical states, meant as states representing a classical object, can be produced in the thermodynamic limit, retaining the unitary evolution of quantum mechanics. Besides, using a simple model of a single spin interacting…

We introduce a general notion of covering property, of which many classical definitions are particular instances. Notions of closure under various sorts of convergence, or, more generally, under taking kinds of accumulation points, are…

A composite quantum system has properties that are incompatible with every property of its parts. The existence of such global properties incompatible with all local properties constitutes what I call "mereological holism"--the distinctive…

The split property of a pure state for a certain cut of a quantum spin system can be understood as the entanglement between the two subsystems being weak. From this point of view, we may say that if it is not possible to transform a state…

In this paper, we consider a subclass of quantum states in the multipartite system, namely, the supersymmetric states. We investigate the problem whether they admit the symmetrically separable decomposition, i.e., each term in this…

We explore the relation between classical and quantum states in both open and closed (super)strings discussing the relevance of coherent states as a semiclassical approximation. For the closed string sector a gauge-fixing of the residual…

Entanglement characteristics of a pair coherent state is studied using entanglement of superposition. It is demonstrated only few states in the expansion of a pair coherent state, in a harmonic oscillator basis, contribute significantly to…

Quantum entanglement describes superposition states in multi-dimensional systems, at least two partite, which cannot be factorized and are thus non-separable. Non-separable states exist also in classical theories involving vector spaces. In…

The quantum superposition principle has been extensively utilized in the quantum mechanical description of the bonding phenomenon. It explains the emergence of delocalized molecular orbitals and provides a recipe for the construction of…

The goal of this note is to compare two notions, one coming from the theory of rewrite systems and the other from proof theory: confluence and cut elimination. We show that to each rewrite system on terms, we can associate a logical system:…

In this paper, we intend to generalize the classical set theory as much as possible. we will do this by freeing sets from the regular properties of classical sets; e.g., the law of excluded middle, the law of non-contradiction, the…

To better understand quantum computation we can search for its limits or no-gos, especially if analogous limits do not appear in classical computation. Classical computation easily implements and extensively employs the addition of two bit…

Transition systems (TS) and Petri nets (PN) are important models of computation ubiquitous in formal methods for modeling systems. An important problem is how to extract from a given TS a PN whose reachability graph is equivalent (with a…

This work exploits a framework whereby a graph (in the mathematical sense) serves to connect a classical system to a state space that we call `quantum-like' (QL). The QL states comprise arbitrary superpositions of states in a tensor product…

We introduce the split principles and show that they bear tight connections to large cardinal properties such as inaccessibility, weak compactness, subtlety, almost ineffability and ineffability, as well as classical combinatorial objects…

Superselection rules severely alter the possible operations that can be implemented on a distributed quantum system. Whereas the restriction to local operations imposed by a bipartite setting gives rise to the notion of entanglement as a…

We present a new set of inseparabilty inequalities to detect entanglement in $N$-spin states. These are based on negative partial transposition and involve collective spin-spin correlations of any two partitions of the entire system. They…

Several definitions of classicality are considered, such as P-representability, generalized coherent states and separable states. These notions are treated under a simple and general definition based on convex sets, which enables the use of…

The superposition principle lies at the heart of many non-classical properties of quantum mechanics. Motivated by this, we introduce a rigorous resource theory framework for the quantification of superposition of a finite number of linear…