30 research outputs found
Efficient Computations of Encodings for Quantum Error Correction
We show how, given any set of generators of the stabilizer of a quantum code,
an efficient gate array that computes the codewords can be constructed. For an
n-qubit code whose stabilizer has d generators, the resulting gate array
consists of O(n d) operations, and converts k-qubit data (where k = n - d) into
n-qubit codewords.Comment: 16 pages, REVTeX, 3 figures within the tex
Effect of an inhomogeneous external magnetic field on a quantum dot quantum computer
We calculate the effect of an inhomogeneous magnetic field, which is
invariably present in an experimental environment, on the exchange energy of a
double quantum dot artificial molecule, projected to be used as a 2-qubit
quantum gate in the proposed quantum dot quantum computer. We use two different
theoretical methods to calculate the Hilbert space structure in the presence of
the inhomogeneous field: the Heitler-London method which is carried out
analytically and the molecular orbital method which is done computationally.
Within these approximations we show that the exchange energy J changes slowly
when the coupled dots are subject to a magnetic field with a wide range of
inhomogeneity, suggesting swap operations can be performed in such an
environment as long as quantum error correction is applied to account for the
Zeeman term. We also point out the quantum interference nature of this slow
variation in exchange.Comment: 12 pages, 4 figures embedded in tex
Separability in 2xN composite quantum systems
We analyze the separability properties of density operators supported on
\C^2\otimes \C^N whose partial transposes are positive operators. We show
that if the rank of equals N then it is separable, and that bound
entangled states have rank larger than N. We also give a separability criterion
for a generic density operator such that the sum of its rank and the one of its
partial transpose does not exceed 3N. If it exceeds this number we show that
one can subtract product vectors until decreasing it to 3N, while keeping the
positivity of and its partial transpose. This automatically gives us a
sufficient criterion for separability for general density operators. We also
prove that all density operators that remain invariant after partial
transposition with respect to the first system are separable.Comment: Extended version of quant-ph/9903012 with new results. 11 page
Information and entropy in quantum Brownian motion: Thermodynamic entropy versus von Neumann entropy
We compare the thermodynamic entropy of a quantum Brownian oscillator derived
from the partition function of the subsystem with the von Neumann entropy of
its reduced density matrix. At low temperatures we find deviations between
these two entropies which are due to the fact that the Brownian particle and
its environment are entangled. We give an explanation for these findings and
point out that these deviations become important in cases where statements
about the information capacity of the subsystem are associated with
thermodynamic properties, as it is the case for the Landauer principle.Comment: 8 pages, 7 figure
Achievable rates for the Gaussian quantum channel
We study the properties of quantum stabilizer codes that embed a
finite-dimensional protected code space in an infinite-dimensional Hilbert
space. The stabilizer group of such a code is associated with a symplectically
integral lattice in the phase space of 2N canonical variables. From the
existence of symplectically integral lattices with suitable properties, we
infer a lower bound on the quantum capacity of the Gaussian quantum channel
that matches the one-shot coherent information optimized over Gaussian input
states.Comment: 12 pages, 4 eps figures, REVTe
Maximizing the entanglement of two mixed qubits
Two-qubit states occupy a large and relatively unexplored Hilbert space. Such
states can be succinctly characterized by their degree of entanglement and
purity. In this letter we investigate entangled mixed states and present a
class of states that have the maximum amount of entanglement for a given linear
entropy.Comment: 4 pages, 3 figure
Quantum computing with mixed states
We discuss a model for quantum computing with initially mixed states.
Although such a computer is known to be less powerful than a quantum computer
operating with pure (entangled) states, it may efficiently solve some problems
for which no efficient classical algorithms are known. We suggest a new
implementation of quantum computation with initially mixed states in which an
algorithm realization is achieved by means of optimal basis independent
transformations of qubits.Comment: 2 figures, 52 reference
Implementation of a Deutsch-like quantum algorithm utilizing entanglement at the two-qubit level, on an NMR quantum information processor
We describe the experimental implementation of a recently proposed quantum
algorithm involving quantum entanglement at the level of two qubits using NMR.
The algorithm solves a generalisation of the Deutsch problem and distinguishes
between even and odd functions using fewer function calls than is possible
classically. The manipulation of entangled states of the two qubits is
essential here, unlike the Deutsch-Jozsa algorithm and the Grover's search
algorithm for two bits.Comment: 4 pages, two eps figure
Generation of atom-photon entangled states in atomic Bose-Einstein condensate via electromagnetically induced transparency
In this paper, we present a method to generate continuous-variable-type
entangled states between photons and atoms in atomic Bose-Einstein condensate
(BEC). The proposed method involves an atomic BEC with three internal states, a
weak quantized probe laser and a strong classical coupling laser, which form a
three-level Lambda-shaped BEC system. We consider a situation where the BEC is
in electromagnetically induced transparency (EIT) with the coupling laser being
much stronger than the probe laser. In this case, the upper and intermediate
levels are unpopulated, so that their adiabatic elimination enables an
effective two-mode model involving only the atomic field at the lowest internal
level and the quantized probe laser field. Atom-photon quantum entanglement is
created through laser-atom and inter-atomic interactions, and two-photon
detuning. We show how to generate atom-photon entangled coherent states and
entangled states between photon (atom) coherent states and atom-(photon-)
macroscopic quantum superposition (MQS) states, and between photon-MQS and
atom-MQS states.Comment: 9 pages, 1 figur
Grover search with pairs of trapped ions
The desired interference required for quantum computing may be modified by
the wave function oscillations for the implementation of quantum
algorithms[Phys.Rev.Lett.84(2000)1615]. To diminish such detrimental effect, we
propose a scheme with trapped ion-pairs being qubits and apply the scheme to
the Grover search. It can be found that our scheme can not only carry out a
full Grover search, but also meet the requirement for the scalable hot-ion
quantum computing. Moreover, the ion-pair qubits in our scheme are more robust
against the decoherence and the dissipation caused by the environment than
single-particle qubits proposed before.Comment: RevTe