Vol.7
No.8
November 1, 2007
Research Articles:
Multipartite quantum
cryptographic protocols with noisy GHZ states (pp689715) PDF
K.
Chen and H.K. Lo
We propose a wide class of distillation schemes for
multipartite entangled states that are CSSstates. Our proposal
provides not only superior efficiency, but also new insights on the
connection between CSSstates and bipartite graph states. We then apply
our distillation schemes to the tripartite case for three cryptographic
tasksnamely, (a) conference key agreement, (b) quantum sharing of
classical secrets and (c) thirdman cryptography. Moreover, we construct
``prepareandmeasure'' protocols for the above three cryptographic
tasks which can be implemented with the generation of only a single
entangled pair at a time. This gives significant simplification over
previous experimental implementations which require two entangled pairs
generated simultaneously. We also study the yields of those protocols
and the threshold values of the fidelity above which the protocols can
function securely. Rather surprisingly, our protocols will function
securely even when the initial state does not violate the standard
Bellinequalities for GHZ states.
Asymmetric quantum teleclonging of multiqubit states (pp716729)
PDF
L.
Chen and Y.X. Chen
A scheme of 1$\rightarrow$2 optimal universal asymmetric
quantum telecloning for pure multiqubit states is proposed. We first
investigate the telecloning of arbitrary 2qubit states and then extend
it to the case of multiqubit system. We discuss the scheme in terms of
the quantum channels and fidelities of clones, as well as the
entanglement of states in the telecloning.
Quantumness, generalized spherical 2design, and symmetric
informationally complete POVM (pp730737)
PDF
I.H.
Kim
Fuchs and Sasaki defined the quantumness of a set of
quantum states in \cite{Quantumness}, which is related to the fidelity
loss in transmission of the quantum states through a classical channel.
In \cite{Fuchs}, Fuchs showed that in $d$dimensional Hilbert space,
minimum quantumness is $\frac{2}{d+1}$, and this can be achieved by all
rays in the space. He left an open problem, asking whether fewer than
$d^2$ states can achieve this bound. Recently, in a different context,
Scott introduced a concept of generalized $t$design in \cite{GenSphet},
which is a natural generalization of spherical $t$design. In this
paper, we show that the lower bound on the quantumness can be achieved
if and only if the states form a generalized 2design. As a corollary,
we show that this bound can be only achieved if the number of states are
larger or equal to $d^2$, answering the open problem. Furthermore, we
also show that the minimal set of such ensemble is Symmetric
Informationally Complete POVM(SICPOVM). This leads to an equivalence
relation between SICPOVM and minimal set of ensemble achieving minimal
quantumness.
Universal Mixing of Quantum Walk on Graphs
(pp738751) PDF
W.
Carlson, A. Ford, E. Harris, J. Rosen, C. Tamon, and K. Wrobel
We study the set of probability distributions visited by
a continuoustime quantum walk on graphs. An edgeweighted graph $G$ is
{\em universal mixing} if the instantaneous or average probability
distribution of the quantum walk on $G$ ranges over all probability
distributions on the vertices as the weights are varied over
nonnegative reals. The graph is {\em uniform} mixing if it visits the
uniform distribution. Our results include the following:
1) All weighted complete multipartite graphs are instantaneous universal
mixing. This is in contrast to the fact that no {\em unweighted}
complete multipartite graphs are uniform mixing (except for the
fourcycle $K_{2,2}$).
2) For all $n \ge 1$, the weighted claw $K_{1,n}$ is a minimally
connected instantaneous universal mixing graph. In fact, as a corollary,
the unweighted $K_{1,n}$ is instantaneous uniform mixing. This adds a
new family of uniform mixing graphs to a list that so far contains only
the hypercubes.
3) Any weighted graph is average almostuniform mixing unless its
spectral type is sublinear in the size of the graph. This provides a
nearly tight characterization for average uniform mixing on circulant
graphs.
4) No weighted graphs are average universal mixing. This shows that
weights do not help to achieve average universal mixing, unlike the
instantaneous case.
Our proofs exploit the spectra of the underlying weighted graphs and
path collapsing arguments.
For
distinguishing conjugate Hidden subgroups, the pretty good measurement
is as good as it gets (pp752765)
PDF
C.
Moore and A. Russell
Recently Bacon, Childs and van Dam showed that the
``pretty good measurement'' (PGM) is optimal for the Hidden Subgroup
Problem on the dihedral group $D_n$ in the case where the hidden
subgroup is chosen uniformly from the $n$ involutions. We show that, for
any group and any subgroup $H$, the PGM is the optimal oneregister
experiment in the case where the hidden subgroup is a uniformly random
conjugate of $H$. We go on to show that when $H$ forms a Gel'fand pair
with its parent group, the PGM is the optimal measurement for any number
of registers. In both cases we bound the probability that the optimal
measurement succeeds. This generalizes the case of the dihedral group,
and includes a number of other examples of interest.
Fully multiqubit entangled states (pp766774)
PDF
J.M.
Cai, Z.W. Zhou, and G.C. Guo
We investigate the properties of different levels of
entanglement in graph states which correspond to connected graphs.
Combining the operational definition of graph states and the postulates
of entanglement measures, we prove that in connected graph states of $N$
qubits there is no genuine $k$qubit entanglement, $2\leq k\leq N1$,
among every $k$ qubits. These results about connected graph states
naturally lead to the definition of fully multiqubit entangled states.
We also find that the connected graph states of four qubits is one but
not the only one class of fully fourqubit entangled states.
Macroscopic displaced thermal field as the entanglement catalyst (pp775781)
PDF
S.B.
Zheng
We show that entanglement of multiple atoms can arise via
resonant interaction with a displaced thermal field with a macroscopic
photonnumber. The cavity field acts as the catalyst, which is
disentangled with the atomic system after the operation. Remarkably, the
entanglement speed does not decrease as the average photonnumber of the
mixed thermal state increases. The atoms may evolve to a highly
entangled state even when the photonnumber of the cavity mode
approaches infinity.
Unambiguous unitary quantum channels (pp782798)
PDF
S.J.
Wu and X.M. Chen
Unambiguous unitary maps and unambiguous unitary quantum channels are
introduced and some of their properties are derived. These properties
ensures certain simple form for the measurements involved in realizing
an unambiguous unitary quantum channel. Error correction and unambiguous
error correction with nonzero probability are discussed in terms of
unambiguous unitary quantum channels. We not only rederive the
wellknown condition for a set of errors to
be correctable with certainty, but also obtain a necessary and
sufficient condition for the errors caused by a noisy channel to be
correctable with any nonzero probability. Dense coding with a partially
entangled state can also be viewed as an unambiguous unitary quantum
channel when all messages are required to be transmitted with equal
probability of success, the maximal achievable probability of success is
derived and the optimum protocol is also obtained.
Book Review:
On “An
introduction to quantum computing (authored by P. Kaye,
R. Laflamme and M. Mosca)” (pp799800)
PDF
G.J.
Milburn
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