cm(ρ)e ) which offers an exponential convergence in the φ direction and is naturally applicable for polar coordinates system. The coefficients (cm(ρ)) are then calculated by Finite Difference Method (FDM) in the ρ direction. We adopt the Crank-Nicholson method for the temporal propagation. The final linear system consists of a set of independent one-dimensional (ρ) linear systems and the matrix...

With any state of a multipartite quantum system its separability polytope is associated. This is an algebro-topological object (nontrivial only for mixed states) which captures the localisation of entanglement of the state. Particular examples of separabilty polytopes for 3-partite systems are explicitly provided. It turns out that this characterisation of entanglement is associated with simula...

The geometric phase for a pure quantal state undergoing an arbitrary evolution is a "memory" of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution depends not only on the geometry of the path of the system alone but also on a constrained bilocal unitary evolution of the purified en...

We provide a general and consistent formulation for linear subsystem quantum dynamical maps, developed from a minimal set of postulates, primary among which is a relaxation of the usual, restrictive assumption of uncorrelated initial system-bath states. We describe the space of possibilities admitted by this formulation, namely that, far from being limited to only completely positive (CP) maps,...

In this paper we generalize the usual model of quantum computer to a model in which the state is an operator of density matrix and the gates are general superoperators (quantum operations), not necessarily unitary. A mixed state (operator of density matrix) of n twolevel quantum system (open or closed n-qubit system) is considered as an element of 4dimensional operator Hilbert space (Liouville ...

We discuss special perturbations of the gauged level k WZNW model inspired by the σ-model perturbation of the nonunitary WZNW model. In the large k limit there is a second conformal point in the vicinity of the ultarviolet fixed point. At the second critical point the conformal model has a rational Virasoro central charge which no longer corresponds to a coset construction. In spite of this fac...

A non-Hermitian operator with a real spectrum and a complete set of eigenvectors may serve as the Hamiltonian operator for a unitary quantum system provided that one makes an appropriate choice for the defining the inner product of physical Hilbert state. We study the consequences of such a choice for the representation of states in terms of projection operators and the geometry of the state sp...

In this paper we treat the time evolution of unitary elements in the N level system and consider the reduced dynamics from the unitary group U(N) to flag manifolds of the second type (in our terminology). Then we derive a set of differential equations of matrix Riccati types interacting with one another and present an important problem on a nonlinear superposition formula that the Riccati equat...

In this paper two kinds of two-boson realizations of the Higgs algebra are obtained by generalizing the well known Jordan-Schwinger realizations of the SU(2) and SU(1,1) algebras. In each kind, an unitary realization and two nonunitary realizations, together with the properties of their respective acting spaces are discussed in detail. Furthermore, similarity transformations, which connect the ...

A quantum cellular automaton (QCA) is a discrete dynamical system with exactly unitary local evolution. Failure to find homogenous scalar QCAs in one dimension led to consideration of only “approximately unitary” CAs—until recently, when we proved both a No-go Lemma in one dimension and then showed how it may be evaded. In this note we extend the one dimensional result to prove the absence of n...