Related papers: Observable-geometric phases and quantum computatio…
A proposal for applying non-adiabatic geometric phases to quantum computing, called the double-loop method [S.-L. Zhu and Z. D. Wang, Phys. Rev. A {\bf 67}, 022319 (2003)], is demonstrated in a liquid state NMR quantum computer. Using a…
With approaching quantum/noncommutative models for the deep microscopic spacetime in mind, and inspired by our recent picture of the (projective) Hilbert space as the model of physical space behind basic quantum mechanics, we reformulate…
Quaternion quantum mechanics is examined at the level of unbroken SU(2) gauge symmetry. A general quaternionic phase expression is derived from formal properties of the quaternion algebra.
The questions of describing observables and observation in quantum gravity appear to be centrally important to its physics. A relational approach holds significant promise, and a classification of different types of relational observables…
In this paper, using the concept of Lewis Riesenfeld invariant quantum operator method for finding continuous eigenvalues of quantum mechanical wave functions we derive the analytical expressions for the cosmological geometric phase, which…
The phenomenon of quantum phase transition is considered in the special case in which the evolution laws remain unitary and in which the bound-state energies remain observable. The conventional Hermiticity of observables is lost at the…
Conditional geometric phase shift gate, which is fault tolerate to certain errors due to its geometric property, is made by NMR technique recently under adiabatic condition. By the adiabatic requirement, the result is inexact unless the…
The paper explores the basic geometrical properties of the observables characterizing two-qubit systems by employing a novel projective ring geometric approach. After introducing the basic facts about quantum complementarity and maximal…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
We explore the relation between quantum geometry in non-Hermitian systems and physically measurable phenomena. We highlight various situations in which the behavior of a non-Hermitian system is best understood in terms of quantum geometry,…
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…
The physical phase space in gauge systems is studied. Effects caused by a non-Euclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac…
Experimental realization of a universal set of quantum logic gates is the central requirement for implementation of a quantum computer. An all-geometric approach to quantum computation offered a paradigm for implementation where all the…
In an open system, the geometric phase should be described by a distribution. We show that a geometric phase distribution for open system dynamics is in general ambiguous, but the imposition of reasonable physical constraints on the…
The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an…
Aiming towards a geometric description of quantum theory, we study the coherent states-induced metric on the phase space, which provides a geometric formulation of the Heisenberg uncertainty relations (both the position-momentum and the…
We elucidate the geometry of quantum adiabatic evolution. By minimizing the deviation from adiabaticity we find a Riemannian metric tensor underlying adiabatic evolution. Equipped with this tensor, we identify a unified geometric…
Since Pancharatnam's 1956 discovery of optical geometric phase, and Berry's 1984 discovery of geometric phase in quantum systems, researchers analyzing geometric phase have focused almost exclusively on algebraic approaches using the Jones…
Given a quantum state in the finite-dimensional Hilbert space $ \C^n $, the range of possible values of a quantum observable is usually identified with the discrete spectrum of eigenvalues of a corresponding Hermitian matrix. Here any such…
A model in statistical mechanics, characterised by the corresponding Gibbs measure, is a subset of the totality of probability distributions on the phase space. The shape of this subset, i.e., the geometry, then plays an important role in…