4 research outputs found
Equivalence of Decoupling Schemes and Orthogonal Arrays
We consider the problem of switching off unwanted interactions in a given
multi-partite Hamiltonian. This is known to be an important primitive in
quantum information processing and several schemes have been presented in the
literature to achieve this task. A method to construct decoupling schemes for
quantum systems of pairwise interacting qubits was introduced by M.
Stollsteimer and G. Mahler and is based on orthogonal arrays. Another approach
based on triples of Hadamard matrices that are closed under pointwise
multiplication was proposed by D. Leung. In this paper, we show that both
methods lead to the same class of decoupling schemes. Moreover, we establish a
characterization of orthogonal arrays by showing that they are equivalent to
decoupling schemes which allow a refinement into equidistant time-slots.
Furthermore, we show that decoupling schemes for networks of higher-dimensional
quantum systems with t-local Hamiltonians can be constructed from classical
error-correcting codes.Comment: 26 pages, latex, 1 figure in tex
Efficient decoupling schemes with bounded controls based on Eulerian orthogonal arrays
The task of decoupling, i.e., removing unwanted interactions in a system
Hamiltonian and/or couplings with an environment (decoherence), plays an
important role in controlling quantum systems. There are many efficient
decoupling schemes based on combinatorial concepts like orthogonal arrays,
difference schemes and Hadamard matrices. So far these (combinatorial)
decoupling schemes have relied on the ability to effect sequences of
instantaneous, arbitrarily strong control Hamiltonians (bang-bang controls). To
overcome the shortcomings of bang-bang control Viola and Knill proposed a
method called Eulerian decoupling that allows the use of bounded-strength
controls for decoupling. However, their method was not directly designed to
take advantage of the composite structure of multipartite quantum systems. In
this paper we define a combinatorial structure called an Eulerian orthogonal
array. It merges the desirable properties of orthogonal arrays and Eulerian
cycles in Cayley graphs (that are the basis of Eulerian decoupling). We show
that this structure gives rise to decoupling schemes with bounded-strength
control Hamiltonians that can be applied to composite quantum systems with few
body Hamiltonians and special couplings with the environment. Furthermore, we
show how to construct Eulerian orthogonal arrays having good parameters in
order to obtain efficient decoupling schemes.Comment: 8 pages, revte
Randomized Dynamical Decoupling Strategies and Improved One-Way Key Rates for Quantum Cryptography
The present thesis deals with various methods of quantum error correction. It
is divided into two parts. In the first part, dynamical decoupling methods are
considered which have the task of suppressing the influence of residual
imperfections in a quantum memory. The suppression is achieved by altering the
dynamics of an imperfect quantum memory with the help of a sequence of local
unitary operations applied to the qudits. Whereas up to now the operations of
such decoupling sequences have been constructed in a deterministic fashion,
strategies are developed in this thesis which construct the operations by
random selection from a suitable set. Furthermore, it is investigated if and
how the discussed decoupling strategies can be employed to protect a quantum
computation running on the quantum memory.
The second part of the thesis deals with quantum error-correcting codes and
protocols for quantum key distribution. The focus is on the BB84 and the
6-state protocol making use of only one-way communication during the error
correction and privacy amplification steps. It is shown that by adding
additional errors to the preliminary key (a process called noisy preprocessing)
followed by the use of a structured block code, higher secure key rates may be
obtained. For the BB84 protocol it is shown that iterating the combined
preprocessing leads to an even higher gain.Comment: PhD thesis, 223 pages, TU Darmstadt;
http://tuprints.ulb.tu-darmstadt.de/1389