66 research outputs found
Geometric quantum computation using fictitious spin- 1/2 subspaces of strongly dipolar coupled nuclear spins
Geometric phases have been used in NMR, to implement controlled phase shift
gates for quantum information processing, only in weakly coupled systems in
which the individual spins can be identified as qubits. In this work, we
implement controlled phase shift gates in strongly coupled systems, by using
non-adiabatic geometric phases, obtained by evolving the magnetization of
fictitious spin-1/2 subspaces, over a closed loop on the Bloch sphere. The
dynamical phase accumulated during the evolution of the subspaces, is refocused
by a spin echo pulse sequence and by setting the delay of transition selective
pulses such that the evolution under the homonuclear coupling makes a complete
rotation. A detailed theoretical explanation of non-adiabatic geometric
phases in NMR is given, by using single transition operators. Controlled phase
shift gates, two qubit Deutsch-Jozsa algorithm and parity algorithm in a
qubit-qutrit system have been implemented in various strongly dipolar coupled
systems obtained by orienting the molecules in liquid crystal media.Comment: 37 pages, 17 figure
Simple test for quantum channel capacity
Basing on states and channels isomorphism we point out that semidefinite
programming can be used as a quick test for nonzero one-way quantum channel
capacity. This can be achieved by search of symmetric extensions of states
isomorphic to a given quantum channel. With this method we provide examples of
quantum channels that can lead to high entanglement transmission but still have
zero one-way capacity, in particular, regions of symmetric extendibility for
isotropic states in arbitrary dimensions are presented. Further we derive {\it
a new entanglement parameter} based on (normalised) relative entropy distance
to the set of states that have symmetric extensions and show explicitly the
symmetric extension of isotropic states being the nearest to singlets in the
set of symmetrically extendible states. The suitable regularisation of the
parameter provides a new upper bound on one-way distillable entanglement.Comment: 6 pages, no figures, RevTeX4. Signifficantly corrected version. Claim
on continuity of channel capacities removed due to flaw in the corresponding
proof. Changes and corrections performed in the part proposing a new upper
bound on one-way distillable etanglement which happens to be not one-way
entanglement monoton
Affine Constellations Without Mutually Unbiased Counterparts
It has been conjectured that a complete set of mutually unbiased bases in a
space of dimension d exists if and only if there is an affine plane of order d.
We introduce affine constellations and compare their existence properties with
those of mutually unbiased constellations, mostly in dimension six. The
observed discrepancies make a deeper relation between the two existence
problems unlikely.Comment: 8 page
Dipole Blockade and Quantum Information Processing in Mesoscopic Atomic Ensembles
We describe a technique for manipulating quantum information stored in
collective states of mesoscopic ensembles. Quantum processing is accomplished
by optical excitation into states with strong dipole-dipole interactions. The
resulting ``dipole blockade'' can be used to inhibit transitions into all but
singly excited collective states. This can be employed for a controlled
generation of collective atomic spin states as well as non-classical photonic
states and for scalable quantum logic gates. An example involving a cold
Rydberg gas is analyzed
Multiparticle entanglement with quantum logic networks: Application to cold trapped ions
We show how to construct a multi-qubit control gate on a quantum register of
an arbitrary size N. This gate performs a single-qubit operation on a specific
qubit conditioned by the state of other N-1 qubits. We provide an algorithm how
to build up an array of networks consisting of single-qubit rotations and
multi-qubit control-NOT gates for the synthesis of an arbitrary entangled
quantum state of N qubits. We illustrate the algorithm on a system of cold
trapped ions. This example illuminates the efficiency of the direct
implementation of the multi-qubit CNOT gate compared to its decomposition into
a network of two-qubit CNOT gates.Comment: 13 pages, Revtex4, 10 eps figures, 2 tables, to appear in Phys. Rev.
Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem
In classical information theory, entropy rate and Kolmogorov complexity per
symbol are related by a theorem of Brudno. In this paper, we prove a quantum
version of this theorem, connecting the von Neumann entropy rate and two
notions of quantum Kolmogorov complexity, both based on the shortest qubit
descriptions of qubit strings that, run by a universal quantum Turing machine,
reproduce them as outputs.Comment: 26 pages, no figures. Reference to publication added: published in
the Communications in Mathematical Physics
(http://www.springerlink.com/content/1432-0916/
Limits to error correction in quantum chaos
We study the correction of errors that have accumulated in an entangled state
of spins as a result of unknown local variations in the Zeeman energy (B) and
spin-spin interaction energy (J). A non-degenerate code with error rate kappa
can recover the original state with high fidelity within a time kappa^1/2 /
max(B,J) -- independent of the number of encoded qubits. Whether the
Hamiltonian is chaotic or not does not affect this time scale, but it does
affect the complexity of the error-correcting code.Comment: 4 pages including 1 figur
Cross-regulation of viral kinases with cyclin A secures shutoff of host DNA synthesis
Herpesviruses encode conserved protein kinases (CHPKs) to stimulate phosphorylation-sensitive processes during infection. How CHPKs bind to cellular factors and how this impacts their regulatory functions is poorly understood. Here, we use quantitative proteomics to determine cellular interaction partners of human herpesvirus (HHV) CHPKs. We find that CHPKs can target key regulators of transcription and replication. The interaction with Cyclin A and associated factors is identified as a signature of β-herpesvirus kinases. Cyclin A is recruited via RXL motifs that overlap with nuclear localization signals (NLS) in the non-catalytic N termini. This architecture is conserved in HHV6, HHV7 and rodent cytomegaloviruses. Cyclin A binding competes with NLS function, enabling dynamic changes in CHPK localization and substrate phosphorylation. The cytomegalovirus kinase M97 sequesters Cyclin A in the cytosol, which is essential for viral inhibition of cellular replication. Our data highlight a fine-tuned and physiologically important interplay between a cellular cyclin and viral kinases
Variations on a theme of Heisenberg, Pauli and Weyl
The parentage between Weyl pairs, generalized Pauli group and unitary group
is investigated in detail. We start from an abstract definition of the
Heisenberg-Weyl group on the field R and then switch to the discrete
Heisenberg-Weyl group or generalized Pauli group on a finite ring Z_d. The main
characteristics of the latter group, an abstract group of order d**3 noted P_d,
are given (conjugacy classes and irreducible representation classes or
equivalently Lie algebra of dimension d**3 associated with P_d). Leaving the
abstract sector, a set of Weyl pairs in dimension d is derived from a polar
decomposition of SU(2) closely connected to angular momentum theory. Then, a
realization of the generalized Pauli group P_d and the construction of
generalized Pauli matrices in dimension d are revisited in terms of Weyl pairs.
Finally, the Lie algebra of the unitary group U(d) is obtained as a subalgebra
of the Lie algebra associated with P_d. This leads to a development of the Lie
algebra of U(d) in a basis consisting of d**2 generalized Pauli matrices. In
the case where d is a power of a prime integer, the Lie algebra of SU(d) can be
decomposed into d-1 Cartan subalgebras.Comment: Dedicated to the memory of Mosh\'e Flato on the occasion of the tenth
anniversary of his deat
Quantum walks: a comprehensive review
Quantum walks, the quantum mechanical counterpart of classical random walks,
is an advanced tool for building quantum algorithms that has been recently
shown to constitute a universal model of quantum computation. Quantum walks is
now a solid field of research of quantum computation full of exciting open
problems for physicists, computer scientists, mathematicians and engineers.
In this paper we review theoretical advances on the foundations of both
discrete- and continuous-time quantum walks, together with the role that
randomness plays in quantum walks, the connections between the mathematical
models of coined discrete quantum walks and continuous quantum walks, the
quantumness of quantum walks, a summary of papers published on discrete quantum
walks and entanglement as well as a succinct review of experimental proposals
and realizations of discrete-time quantum walks. Furthermore, we have reviewed
several algorithms based on both discrete- and continuous-time quantum walks as
well as a most important result: the computational universality of both
continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing
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