arXiv subjects

Heide Narnhofer

Publications and source records attributed to Heide Narnhofer.

29 records · Page 2Linked to original sources

arXiv2008

Analysis of quantum semigroups with GKS--Lindblad generators II. General

Semigroups describing the time evolution of open quantum systems in finite-dimensional spaces have generators of a special form, known as Lindblad generators. These generators and the corresponding processes of time evolution are analyzed, characterized as Decay, Dissipation and Dephasing. In relation to these processes the Hilbert space of the system is equipped with a special structure, a decomposition into a sum of mutually orthogonal subspaces. The complete set of all the stationary states and the asymptotic behavior of the evolutions are presented in detail. Some unusual special facts about invariant operators and symmetries are studied, examples are demonstrated. Perturbation theory for the structure and for the stationary states is discussed and performed in case studies.

quant-ph↗

arXiv2007

Analysis of quantum semigroups with GKS-Lindblad generators I. Simple generators

Semigroups describing the time evolution of open quantum systems in finite dimensional spaces have generators of a special form, known as Lindblad generators. The simple generators, characterized by only one operator, are analyzed. The complete set of all the stationary states is presented in detail, including a formula to calculate a stationary state from the generating operator. Also the opposite task can be fulfilled, to construct an evolution leading to a prescribed stationary state.

math-ph↗

arXiv2007

A special simplex in the state space for entangled qudits

Focus is on two parties with Hilbert spaces of dimension d, i.e. "qudits". In the state space of these two possibly entangled qudits an analogue to the well known tetrahedron with the four qubit Bell states at the vertices is presented. The simplex analogue to this magic tetrahedron includes mixed states. Each of these states appears to each of the two parties as the maximally mixed state. Some studies on these states are performed, and special elements of this set are identified. A large number of them is included in the chosen simplex which fits exactly into conditions needed for teleportation and other applications. Its rich symmetry - related to that of a classical phase space - helps to study entanglement, to construct witnesses and perform partial transpositions. This simplex has been explored in details for d=3. In this paper the mathematical background and extensions to arbitrary dimensions are analysed.

quant-ph↗

arXiv2006

The state space for two qutrits has a phase space structure in its core

We investigate the state space of bipartite qutrits. For states which are locally maximally mixed we obtain an analog of the ``magic'' tetrahedron for bipartite qubits--a magic simplex W. This is obtained via the Weyl group which is a kind of ``quantization'' of classical phase space. We analyze how this simplex W is embedded in the whole state space of two qutrits and discuss symmetries and equivalences inside the simplex W. Because we are explicitly able to construct optimal entanglement witnesses we obtain the border between separable and entangled states. With our method we find also the total area of bound entangled states of the parameter subspace under intervestigation. Our considerations can also be applied to higher dimensions.

quant-ph↗

arXiv2006

Maximizing nearest neighbour entanglement in finitely correlated qubit--chains

We consider translationally invariant states of an infinite one dimensional chain of qubits or spin-1/2 particles. We maximize the entanglement shared by nearest neighbours via a variational approach based on finitely correlated states. We find an upper bound of nearest neighbour concurrence equal to C=0.434095 which is 0.09% away from the bound C_W=0.434467 obtained by a completely different procedure. The obtained state maximizing nearest neighbour entanglement seems to approximate the maximally entangled mixed states (MEMS). Further we investigate in detail several other properties of the so obtained optimal state.

quant-ph↗

arXiv2005

Supersymmetric Models for Fermions on a Lattice

We investigate the large-N behaviour of simple examples of supersymmetric interactions for fermions on a lattice. Witten's supersymmetric quantum mechanics and the BCS model appear just as two different aspects of one and the same model. For the BCS model, supersymmetry is only respected in a coherent superposition of Bogoliubov states. In this coherent superposition mesoscopic observables show better stability properties than in a Bogoliubov state.

quant-ph↗

arXiv2004

Finite Supersymmetry Transformations

We investigate simple examples of supersymmetry algebras with real and Grassmann parameters. Special attention is payed to the finite supertransformations and their probability interpretation. Furthermore we look for combinations of bosons and fermions which are invariant under supertransformations. These combinations correspond to states that are highly entangled.

quant-ph↗

arXiv2003

Strategies to measure a quantum state

We consider the problem of determining the mixed quantum state of a large but finite number of identically prepared quantum systems from data obtained in a sequence of ideal (von Neumann) measurements, each performed on an individual copy of the system. In contrast to previous approaches, we do not average over the possible unknown states but work out a ``typical'' probability distribution on the set of states, as implied by the experimental data. As a consequence, any measure of knowledge about the unknown state and thus any notion of ``best strategy'' (i.e. the choice of observables to be measured, and the number of times they are measured) depend on the unknown state. By learning from previously obtained data, the experimentalist re-adjusts the observable to be measured in the next step, eventually approaching an optimal strategy. We consider two measures of knowledge and exhibit all ``best'' strategies for the case of a two-dimensional Hilbert space. Finally, we discuss some features of the problem in higher dimensions and in the infinite dimensional case.

quant-ph↗

arXiv2002

The Structure of State Space with Respect to Imbedding

The entanglement of formation as well as the conditional entropy can be used to define leaves in the state space, given by a linear superposition of their extremal points. Examples are presented, where these leaves can be specified and can be used to calculate the entanglement respectively the conditional entropy. The definition of entanglement is generalized to infinite systems and allows again to define a leaf structure. Finally we remark on the additivity property of both expressions, offering a counter example to the additivity of the conditional entropy.

math-ph↗

arXiv2002

Entanglement of mesoscopic systems

The entanglement of clouds of atoms recently experimentally verified is expressed in terms of the fluctuation algebra introduced by Goderis, Verbeure and Vets. A mean field Hamiltonian describing the coupling to a laser beam leads to different time evolutions if considered on microscopic or mesoscopic operators. Only the latter creates non trivial correlations that finally after a measurement lead to entanglement between the clouds.

math-ph↗

arXiv2000

On the Additivity of Entanglement of Formation

We study whether the entanglement of formation is additive over tensor products and derive a necessary and sufficient condition for optimality of vector states that enables us to show additivity in two special cases.

quant-ph↗