Related papers: Geometric uncertainty relation for quantum ensembl…
In the following paper, we generalize the geometrical framework of qubit decoherence to higher dimensions. The quantum mixed state is represented by the probability distribution, which is the K\"ahler function on the projective Hilbert…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
The existence of a minimal observable length has long been suggested, in quantum gravity, as well as in string theory. In this context a generalized uncertainty relation has been derived which quantum theoretically describes the minimal…
We investigate the differential geometry of bipartite quantum states. In particular the manifold structures of pure bipartite states are studied in detail. The manifolds with respect to all normalized pure states of arbitrarily given…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum…
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this…
We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
Symmetric states are defined in the kinematical sector of loop quantum gravity and applied to spherical symmetry and homogeneity. Consequences for the physics of black holes and cosmology are discussed.
The set of quantum states consists of density matrices of order $N$, which are hermitian, positive and normalized by the trace condition. We analyze the structure of this set in the framework of the Euclidean geometry naturally arising in…
In this work, we explore the implications of applying the formalism of symplectic geometry to quantum mechanics, particularly focusing on many-particle systems. We extend the concept of a symplectic indicator of entanglement, originally…
An algebraic treatment of shape-invariant potentials in supersymmetric quantum mechanics is discussed. By introducing an operator which reparametrizes wave functions, the shape-invariance condition can be related to a oscillator-like…
In this paper I will investigate geometrical structures of multipartite quantum systems based on complex projective varieties. These varieties are important in characterization of quantum entangled states. In particular I will establish…
This paper addresses the question why quantum mechanics is formulated in a unitary Hilbert space, i.e. in a manifestly complex setting. Investigating the linear dynamics of real quantum theory in a finite-dimensional Euclidean Hilbert space…
In this paper, the quantization and generalized uncertainty relation for some quantum deformed algebras are investigated. For several deformed algebras, the commutation relation between the position and the momentum operator is shown to be…
Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general K x M problem and characterize the set of effectively…
Persistent spin helices are a manifestation of symmetry-protected spin textures in systems with balanced spin-orbit coupling. They enable long-lived spin structures that are of interest for spintronics and coherent spin manipulation. The…
Permutation-symmetric quantum states appear in a variety of physical situations, and they have been proposed for quantum information tasks. This article builds upon the results of [New J. Phys. 12, 073025 (2010)], where the maximally…