Vol.3 No.5
September 1,
2003
Researches:
Squeezing quantum information through
a classical channel: measuring the “quantumness” of a set of quantum
states
(pp377404)
C.A. Fuchs and M. Sasaki
In this paper we propose a general method to quantify how
``quantum'' a set of quantum states is. The idea is to gauge the
quantumness of the set by the worstcase difficulty of transmitting the
states through a purely classical communication channel. Potential
applications of this notion arise in quantum cryptography, where one
might like to use an alphabet of states that promises to be the most
sensitive to quantum eavesdropping, and in laboratory demonstrations of
quantum teleportation, where it is necessary to check that quantum
entanglement has actually been used in the protocol.
Entanglement cost of generalised
measurements
(pp405422)
R. Jozsa, M. Koashi, N. Linden, S.
Popescu, S. Presnell, D. Shepherd and A. Winter
Bipartite entanglement is one of the fundamental
quantifiable resources of quantum information theory. We propose a new
application of this resource to the theory of quantum measurements.
According to Naimark's theorem any rank 1 generalised measurement (POVM)
M may be represented as a von Neumann measurement in an extended (tensor
product) space of the system plus ancilla. By considering a suitable
average of the entanglements of these measurement directions and
minimising over all Naimark extensions, we define a notion of
entanglement cost E_{\min}(M) of M. We give a constructive means of
characterising all Naimark extensions of a given POVM. We identify
various classes of POVMs with zero and nonzero cost and explicitly
characterise all POVMs in 2 dimensions having zero cost. We prove a
constant upper bound on the entanglement cost of any POVM in any
dimension. Hence the asymptotic entanglement cost (i.e. the large n
limit of the cost of n applications of M, divided by n) is zero for all
POVMs. The trine measurement is defined by three rank 1 elements, with
directions symmetrically placed around a great circle on the Bloch
sphere. We give an analytic expression for its entanglement cost.
Defining a normalised cost of any $d$dimensional POVM by E_{\min}
(M)/\log_2 d, we show (using a combination of analytic and numerical
techniques) that the trine measurement is more costly than any other
POVM with d>2, or with d=2 and ancilla dimension 2. This strongly
suggests that the trine measurement is the most costly of all POVMs.
Quantum communication protocols using
the vacuum
(pp423430)
S.J. van Enk and T. Rudolph
We speculate what quantum information protocols can be
implemented between two accelerating observers using the vacuum. Whether
it is in principle possible or not to implement a protocol depends on
whether the aim is to end up with classical information or quantum
information. Thus, unconditionally secure coin flipping seems possible
but not teleportation.
Logical network implementation for
graph codes and cluster states
(pp431449)
D. Schlingemann
In a previous paper a
straight forward construction method for quantum error correcting codes,
based on graphs, has been presented. These graph codes are directly
related to cluster states which have been introduced by Briegel and
Raussendorf. We show that the preparation of a cluster state as well as
the coding operation for a graph code, can be implemented by a logical
network by only using one type of twoqubit gate, e.g. CNOT or
controlled Phase, and one type of onequbit gate, e.g. the Hadamard
transform. Concerning the qubit case each vertex corresponds to an
Hadamard gate and each edge corresponds to a controlled not gate.
Tutorial:
Fabrication of micromagnetic traps for cold neutral atoms (pp450464)
B. Lev
Many proposals for
quantum information processing require precise control over the motion
of neutral atoms, as in the manipulation of coherent matter waves or the
confinement and localization of individual atoms. Patterns of
micronsized wires, fabricated lithographically on a flat substrate, can
conveniently produce large magneticfield gradients and curvatures to
trap cold atoms and to facilitate the production of BoseEinstein
condensates. The intent of this paper is to provide the researcher who
has access to a standard cleanroom enough information to design and
fabricate such devices.
Book Review:
On “A shortcut through time” by G.
Johnson, and “The quest for the quantum computer” by J. Brown
(pp465467)
N.D. Mermin
Editorial
Notes:
(pp468468)
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