Related papers: A universal state sum
We introduce regular language states, a family of quantum many-body states. They are built from a special class of formal languages, called regular, which has been thoroughly studied in the field of computer science. They can be understood…
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
We introduce a family of operations in quantum mechanics that one can regard as "universal quantum measurements" (UQMs). These measurements are applicable to all finite-dimensional quantum systems and entail the specification of only a…
In this paper the problem of tomographic reconstruction of states is investigated within the so-called Schwinger's picture of Quantum Mechanics in which a groupoid is associated with every quantum system. The attention is focused on spin…
For an arbitrary integer $x$, an integer of the form $T(x)\!=\!\frac{x^2+x}{2}$ is called a triangular number. Let $\alpha_1,\dots,\alpha_k$ be positive integers. A sum $\Delta_{\alpha_1,\dots,\alpha_k}(x_1,\dots,x_k)=\alpha_1…
We define a state as a $[0,1]$-valued, finitely additive function attaining the value $1$ on an EMV-algebra, which is an algebraic structure close to MV-algebras, where the top element is not assumed. We show that states always exist, the…
We discuss the construction of $n$-qubit pure states with maximum bipartite entanglement across all possible choices of $k$ vs $n-k$ bi-partitioning, which implies that the Von Neumann entropy of every $k$-qubit reduced density matrix…
In this paper, we analyze the set of all possible aggregate distributions of the sum of standard uniform random variables, a simply stated yet challenging problem in the literature of distributions with given margins. Our main results are…
The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of n-category suited for this purpose, and…
The evolution of a measured system and an experimental apparatus is presented in an unified form. Conditions under which the state of such a total system forms, evaluates and declines from a superposition of states are defined. The problem…
We construct a family of 3d quantum field theories $\mathcal T_{n,k}^A$ that conjecturally provide a physical realization -- and derived generalization -- of non-semisimple mathematical TQFT's based on the modules for the quantum group…
k-uniform mixed states are a significant class of states characterized by all k-party reduced states being maximally mixed. Novel methodologies are constructed for constructing k-uniform mixed states with the highest possible purity. By…
Quantum state preparation is a fundamental component of quantum algorithms, particularly in quantum machine learning and data processing, where classical data must be encoded efficiently into quantum states. Existing amplitude encoding…
A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields multipartite generalizations of the singular…
For an arbitrary integer $x$, an integer of the form $T(x)=\frac{x^2+x}{2}$ is called a triangular number. For positive integers $\alpha_1,\alpha_2,\dots,\alpha_k$, a sum…
In this paper, we define a parametric variant of generalized Euler sums and call them the (alternating) parametric Euler $T$-sums. By using the contour integration method and residue theorem, we establish several explicit formulae for the…
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.
Squeezed states are one of the most useful quantum optical models having various applications in different areas, especially in quantum information processing. Generalized squeezed states are even more interesting since, sometimes, they…
We give an exact coefficients formula of any infinite product of power series with constant term equal to $1$, by using structures from partitions of integers and permutation groups. This is an universal theorem for various of Binomial-type…
We consider open, oriented 3-manifolds which are infinite connected sums of closed 3-manifolds. We introduce some topological invariants for these manifolds and obtain a classification in the case where there are only finitely many summands…