Related papers: Toric varieties: Simple combinatorial and geometri…
The space of non-resultant systems of bounded multiplicity for a toric variety X is a generalization of the space of rational curves on it. In our earlier work we proved a homotopy stability theorem and determined explicitly the homotopy…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
Classical simulation of quantum physics is a central approach to investigating physical phenomena. Quantum computers enhance computational capabilities beyond those of classical resources, but it remains unclear to what extent existing…
A conception of virtual quantum information bit - virtual qubit - is introduced. It is shown by means of virtual qubit representation that four states of a single quantum particle is enough for implementation of full set of the gates, which…
Two important classes of quantum structures, namely orthomodular posets and orthomodular lattices, can be characterized in a classical context, using notions like partial information and points of view. Using the formalism of representation…
In this paper we present several multipartite quantum systems featuring the same type of genuine (tripartite) entanglement. Based on a geometric interpretation of the so-called $|W\rangle$ and $|GHZ\rangle$ states we show that the…
The partial states of a multipartite quantum state may carry a lot of information: in some cases, they determine the global state uniquely. This result is known for tomographic information, that is for fully characterized measurements. We…
In this paper, a characterization of maps between quantum states that preserve pure states and strict convex combinations is obtained. Based on this characterization, a structural theorem for maps between multipartite quantum states that…
We present a construction of genuinely entangled multipartite quantum states based on the group theory. Analyzed states resemble the Dicke states, whereas the interactions occur only between specific subsystems related by the action of the…
We generalize categories of spatial partitions in the sense of C\'ebron-Weber by introducing new base partitions. This allows us to construct additional examples of free orthogonal quantum groups but yields the same class of spatial…
We discuss the tomography of $N$-qubit states using collective measurements. The method is exact for symmetric states, whereas for not completely symmetric states the information accessible can be arranged as a mixture of irreducible SU(2)…
We introduce several classes of quantum combinatorial designs, namely quantum Latin squares, cubes, hypercubes and a notion of orthogonality between them. A further introduced notion, quantum orthogonal arrays, generalizes all previous…
Understanding the structure of multi-qubit quantum states is essential for both quantum information research and education, yet intuitive visualization beyond the single-qubit Bloch sphere remains challenging. In this work, we propose a…
We develop a method for visualizing the internal structure of multipartite entanglement in pure stabilizer states. Our algorithm graphically organizes the many-body correlations in a hierarchical structure. This provides a rich taxonomy…
Linear maps preserving pure states of a quantum system of any dimension are characterized. This is then used to establish a structure theorem for linear maps that preserve separable pure states in multipartite systems. As an application, a…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
This thesis presents a study of the structure of bipartite quantum states. In the first part, the representation theory of the unitary and symmetric groups is used to analyse the spectra of quantum states. In particular, it is shown how to…
In this paper we illustrate an algorithmic procedure which allows to build projective wonderful models for the complement of a toric arrangement in a n-dimensional algebraic torus T. The main step of the construction is a combinatorial…
We study $G$-equivariant birational geometry of toric varieties, where $G$ is a finite group.
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings [A. Shimony, Ann. NY.…