Related papers: Noncommutative geometrical structures of entangled…
Non-classical states that are characterized by their non-positive quasi-probabilities in phase space are known to be the basis for various quantum effects. In this work, we investigate the interrelation between the non-classicality and…
We consider a nonrelativistic quantum particle constrained to a curved layer of constant width built over a non-compact surface embedded in $R^3$. We suppose that the latter is endowed with the geodesic polar coordinates and that the layer…
We construct quantum gate entangler for general multipartite states based on topological unitary operators. We show that these operators can entangle quantum states if they satisfy the separability condition that is given by the complex…
The state sums defining the quantum hyperbolic invariants (QHI) of hyperbolic oriented cusped $3$-manifolds can be split in a "symmetrization" factor and a "reduced" state sum. We show that these factors are invariants on their own, that we…
Using measures of entanglement such as negativity and tangles we provide a detailed analysis of entanglement structures in pure states of non-interacting qubits. The motivation for this exercise primarily comes from holographic…
A new framework for noncommutative complex geometry on quantum homogeneous spaces is introduced. The main ingredients used are covariant differential calculi and Takeuchi's categorical equivalence for faithfully flat quantum homogeneous…
We generalize the formulation of non-commutative quantum mechanics to three dimensional non-commutative space. Particular attention is paid to the identification of the quantum Hilbert space in which the physical states of the system are to…
A deformed boson algebra is naturally introduced from studying quantum mechanics on noncommutative phase space in which both positions and momenta are noncommuting each other. Based on this algebra, corresponding intrinsic noncommutative…
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 explore the connection between quantum entanglement and the exchange symmetry of the states of N identical particles. Each particle has n-levels. The N particles span the nN dimensional Hilbert space. We shall call the general state of…
We prove three structural impossibility results demonstrating that fuzzy metric spaces cannot capture essential features of quantum state geometry. First, we show they cannot model destructive interference between concepts due to phase…
We consider a quantum system consisting of N parts, each of which is a "quKit" described by a K dimensional Hilbert space. We prove that in the symmetric subspace, S, a pure state is not globally entangled, if and only if it is a coherent…
We explore the effect of two-dimensional position-space non-commutativity on the bipartite entanglement of continuous variable systems. We first extend the standard symplectic framework for studying entanglement of Gaussian states of…
In this paper, we construct genuinely multipartite entangled bases in $(\mathbb{C}^{3})^{\otimes N}$ for $N\geq3$, where every state is one-uniform state. By modifying this construction, we successfully obtain strongly nonlocal orthogonal…
We use open quantum system techniques to construct one-parameter semigroups of positive maps and apply them to study the entanglement properties of a class of 16-dimensional density matrices, representing states of a 4x4 bipartite system.
Dicke states are completely symmetric states of multiple qubits (2-level systems), and qudit Dicke states are their $d$-level generalization. We define here $q$-deformed qudit Dicke states using the quantum algebra $su_q(d)$. We show that…
Application of the noncommutative geometry to several physical models is considered.
In this paper, the generalized coherent state for quantum systems with degenerate spectra is introduced. Then, the nonclassicality features and number-phase entropic uncertainty relation of two particular degenerate quantum systems are…
We study multi-qubit variational quantum states that can be considered as vertex- and edge-weighted graph. These states are constructed as single-layer variational circuits with $RX$ rotations and $RZZ$ entangling gates, corresponding to…
The concept of quantum geometry for single-particle states has revolutionized our interpretation of several emergent properties in condensed matter. However, a description of the quantum geometry for interacting particles and an…