72 research outputs found
Distillation of entanglement by projection on permutationally invariant subspaces
We consider distillation of entanglement from two qubit states which are
mixtures of three mutually orthogonal states: two pure entangled states and one
pure product state. We distill entanglement from such states by projecting n
copies of the state on permutationally invariant subspace and then applying
one-way hashing protocol. We find analytical expressions for the rate of the
protocol. We also generalize this method to higher dimensional systems. To get
analytical expression for two qubit case, we faced a mathematical problem of
diagonalizing a family of matrices enjoying some symmetries w.r.t. to symmetric
group. We have solved this problem in two ways: (i) directly, by use of
Schur-Weyl decomposition and Young symmetrizers (ii) showing that the problem
is equivalent to a problem of diagonalizing adjacency matrices in a particular
instance of a so called algebraic association scheme.Comment: 22 pages, comments welcom
Multipartite Quantum States and their Marginals
Subsystems of composite quantum systems are described by reduced density
matrices, or quantum marginals. Important physical properties often do not
depend on the whole wave function but rather only on the marginals. Not every
collection of reduced density matrices can arise as the marginals of a quantum
state. Instead, there are profound compatibility conditions -- such as Pauli's
exclusion principle or the monogamy of quantum entanglement -- which
fundamentally influence the physics of many-body quantum systems and the
structure of quantum information. The aim of this thesis is a systematic and
rigorous study of the general relation between multipartite quantum states,
i.e., states of quantum systems that are composed of several subsystems, and
their marginals. In the first part, we focus on the one-body marginals of
multipartite quantum states; in the second part, we study general quantum
marginals from the perspective of entropy.Comment: PhD thesis, ETH Zurich. The first part contains material from
arXiv:1208.0365, arXiv:1204.0741, and arXiv:1204.4379. The second part is
based on arXiv:1302.6990 and arXiv:1210.046
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
Applications of coherent classical communication and the Schur transform to quantum information theory
Quantum mechanics has led not only to new physical theories, but also a new
understanding of information and computation. Quantum information began by
yielding new methods for achieving classical tasks such as factoring and key
distribution but also suggests a completely new set of quantum problems, such
as sending quantum information over quantum channels or efficiently performing
particular basis changes on a quantum computer. This thesis contributes two
new, purely quantum, tools to quantum information theory--coherent classical
communication in the first half and an efficient quantum circuit for the Schur
transform in the second half.Comment: 176 pages. Chapters 1 and 4 are a slightly older version of
quant-ph/0512015. Chapter 2 is quant-ph/0205057 plus unpublished extensions
(slightly outdated by quant-ph/0511219) and chapter 3 is quant-ph/0307091,
quant-ph/0412126 and change. Chapters 5-8 are based on quant-ph/0407082, but
go much furthe
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