Vol.2 No.5 August 15, 2002 (print:
September 15,
2002)
Researches:
Geometry and product states
(pp333347)
R.B.
Lockhart, M.J. Steiner, and K. Gerlach
As separable states are a convex combination of product
states, the geometry of the manifold of product states, $\Sigma$, is
studied. Prior results by Sanpera, Vidal and Tarrach are extended.
Furthermore, it is proven that states in the set tangent to $\Sigma$ at
the maximally mixed state are separable; the set normal contains, among
others, all extended GHZ states. A canonical decomposition is given. A
surprising result is that for the case of two particles, the closest
product state to the maximally entangled state is the maximally mixed
state. An algorithm is provided to find the closest product state.
Purification of twoqubit mixed states
(pp348354)
E. Jan\'e
We find the necessary and sufficient condition under
which two twoqubit mixed states can be purified into a pure maximally
entangled state by local operations and classical communication. The
optimal protocol for such transformation is obtained. This result leads
to a necessary and sufficient condition for the exact purification of
$n$ copies of a twoqubit state.
The
quantum monty hall problem
(pp355366)
G.M.
D'Ariano, R.D. Gill, M. Keyl, B. Kummerer, H. Maassen, and R.F. Werner
We consider a quantum version of a wellknown statistical
decision problem, whose solution is, at first sight, counterintuitive
to many. In the quantum version a continuum of possible choices (rather
than a finite set) has to be considered. It can be phrased as a two
person game between a player P and a quiz master Q. Then P always has a
strategy at least as good as in the classical case, while Q's best
strategy results in a game having the same value as the classical game.
We investigate the consequences of Q storing his information in
classical or quantum ways. It turns out that Q's optimal strategy is to
use a completely entangled quantum notepad, on which to encode his prior
information.
Teleportation and
dense coding via a multiparticle quantum channel of the GHZclass (pp367378)
V.N.
Gorbachev, A.I. Zhiliba A.I. Trubilko, and A.A. Rodichkina
A set of protocols
for teleportation and dense coding schemes based on a multiparticle
quantum channel, represented by the $N$particle entangled states of the
GHZ class, is introduced. Using a found representation for the GHZ
states, it was shown that for dense coding schemes enhancement of the
classical capacity of the channel due from entanglement is $N/N1$.
Within the context of our schemes it becomes clear that there is no
oneto one correspondence between teleportation and dense coding schemes
in comparison when the EPR channel is exploited. A set of schemes, for
which two additional operations as entanglement and disentanglement are
permitted, is considered. On quantum
oneway permutations
(pp379398)
E. Kashefi,
H. Nishimura and V. Vedral
We discuss the
question of the existence of quantum oneway permutations. First, we
consider the question: if a state is difficult to prepare, is the
reflection operator about that state difficult to construct? By
revisiting Grover's algorithm, we present the relationship between this
question and the existence of quantum oneway permutations. Next, we
prove the equivalence between inverting a permutation and that of
constructing polynomial size quantum networks for reflection operators
about a class of quantum states. We will consider both the worst case
and the average case complexity scenarios for this problem. Moreover, we
compare our method to Grover's algorithm and discuss possible
applications of our results.
Speedup
and entanglement in quantum Searching
(pp399409)
S.L.
Braunstein and A.K. Pati
We
investigate the issue of speedup and the necessity of entanglement in
Grover's quantum search algorithm. We find that in a pure state
implementation of Grover's algorithm entanglement is present even though
the initial and target states are product states. In pseudopure state
implementations, the separability of the states involved defines an
entanglement boundary in terms of a bound on the purity parameter. Using
this bound we investigate the necessity of entanglement in quantum
searching for these pseudopure state implementations. If every active
molecule involved in the ensemble is `charged for' then in existing
machines speedup without entanglement is not possible.
Book Review:
On "A
New Kind of Science" by Stephen Wolfram
(pp410423)
S.
Aaronson
Erratum
(p424)
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