Related papers: Quantum version of the Euler's problem: a geometri…
Quantum Entanglement is one of the key manifestations of quantum mechanics that separate the quantum realm from the classical one. Characterization of entanglement as a physical resource for quantum technology became of uppermost…
A number of recent studies have focused on novel features in game theory when the games are played using quantum mechanical toolbox (entanglement, unitary operators, measurement). Researchers have concentrated in two-player-two strategy,…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
The existence of $k$-uniform states has been a widely studied problem due to their applications in several quantum information tasks and their close relation to combinatorial objects like Latin squares and orthogonal arrays. With the…
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 is explored for bi-partite and multi-partite pure and mixed states.…
The way in which geometry encodes entanglement is a topic of much recent interest in quantum many-body physics and the AdS/CFT duality. This relation is particularly pronounced in the case of topological quantum field theories, where…
In holographic quantum gravity, Euclidean pieces of the spacetime appear in the large N limit as representing semi-classical states of the theory. In this essay, we argue that the duals of entangled states are spacetime geometries that…
In this contribution, we discuss three situations in which complete integrability of a three dimensional classical system and its quantum version can be achieved under some conditions. The former is a system with axial symmetry. In the…
We investigate the complexity of finding an embedded non-orientable surface of Euler genus $g$ in a triangulated $3$-manifold. This problem occurs both as a natural question in low-dimensional topology, and as a first non-trivial instance…
In this paper we study Spectral Decomposition Theorem [1] and translate it to quantum language by means of the Wigner transform. We obtain a quantum version of Spectral Decomposition Theorem (QSDT) which enables us to achieve three distinct…
Hybrid algorithms that combine quantum and classical resources have become commonplace in quantum computing. The variational quantum eigensolver (VQE) is routinely used to solve prototype problems. Currently, hybrid algorithms use no more…
Quantum entanglement, a cornerstone of quantum mechanics, remains challenging to classify, particularly in multipartite systems. Here, we present a new interpretation of entanglement classification by revealing a profound connection to…
The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them.…
We investigate the geometry of the four qubit systems by means of algebraic geometry and invariant theory, which allows us to interpret certain entangled states as algebraic varieties. More precisely we describe the nullcone, i.e., the set…
Inspired by ER=EPR conjecture we present a mathematical tool providing a link between quantum entanglement and the geometry of spacetime. We start with the idea of operators in extended Hilbert space which, by definition, has no positive…
Quantum entanglement plays an important role in quantum information processes, such as quantum computation and quantum communication. Experiments in laboratories are unquestionably crucial to increase our understanding of quantum systems…
The quantum measurement problem, the unresolved conflict between the unitary evolution of the wave function and the postulate of wave function collapse, remains the most profound conceptual challenge in quantum foundations. While…
One of the most exciting quantum emulation [1] breakthroughs was the first analog signal-based emulation of a universal quantum computer [2]. This yielded a very interesting paper, but no practical use - even for theorists. The reason for…
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…
Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…