Vol.6 No.4&5
July 1, 2006
Research Articles:
Electrode Configurations for fast
separation of trapped ions
(pp289325)
J.P.Home and A.M.Steane
We study the problem of designing electrode structures
that allow pairs of ions to be brought together and separated rapidly in
an array of linear Paul traps. We show that it is desirable for the
electrode structure to produce a d.c. octupole moment with an a.c.
radial quadrupole. For the case where electrical breakdown limits the
voltages that can be applied, we show that the octupole is more
demanding than the quadrupole when the characteristic distance scale of
the structure is larger than 1 to 10 microns (for typical materials). We
present a variety of approaches and optimizations of structures
consisting of one to three layers of electrodes. The threelayer
structures allow the fastest operation at given distance \rho from the
trap centres to the nearest electrode surface, but when the total
thickness w of the structure is constrained, leading to w < \rho,
then twolayer structures may be preferable.
Implementation of continuous variable
quantum cryptography in optical fibres using a go&return configuration
(pp326335)
M. Legré, H. Zbinden, and N. Gisin
We demonstrate an implementation of quantum key
distribution with continuous variables based on a go&return
configuration over distances up to 14km. This configuration leads to
selfcompensation of polarisation and phase fluctuations. We observe a
high degree of stability of our setup over many hours.
Quantum information processing with
hyperentangled photon states
(pp336350)
S. P. Walborn, M. P. Almeida, P. H.
Souto Ribeiro, and C. H. Monken
We discuss quantum information processing with
hyperentangled photon states  states entangled in multiple degrees of
freedom. Using an additional entangled degree of freedom as an ancilla
space, it has been shown that it is possible to perform efficient
Bellstate measurements. We briefly review these results and present a
novel deterministic quantum key distribution protocol based on
Bellstate measurements of hyperentangled photons. In addition, we
propose a scheme for a probabilistic controllednot gate which operates
with a 50% success probability. We also show that despite its
probabilistic nature, the controllednot gate can be used for an
efficient, nonlocal demonstration of the Deutsch algorithm using two
separate photons.
A logarithmicdepth quantum carrylookahead
adder
(pp351369)
T.G. Draper, S.A. Kutin, E.M. Rains, and
K.M. Svore
We present an efficient addition circuit, borrowing
techniques from classical carrylookahead arithmetic. Our quantum carrylookahead
(\QCLA) adder accepts two nbit numbers and adds them in O(\log
n) depth using O(n) ancillary qubits. We present both inplace
and outofplace versions, as well as versions that add modulo 2^n
and modulo 2^n  1. Previously, the lineardepth ripplecarry
addition circuit has been the method of choice. Our work reduces the
cost of addition dramatically with only a slight increase in the number
of required qubits. The \QCLA\ adder can be used within current modular
multiplication circuits to reduce substantially the runtime of Shor's
algorithm.
Mixing of quantum walk on circulant
bunkbeds
(pp370381)
P. Lo, S. Rajaram, D. Schepens, D.
Sullivan, C. Tamon, and J. Ward
This paper gives new observations on the mixing dynamics
of a continuoustime quantum walk on circulants and their bunkbeds.
These bunkbeds are defined through two standard graph operators: the
join G + H and the Cartesian product G \cprod H of graphs
G and H. Our results include the following: (i) The
quantum walk is average uniform mixing on circulants with bounded
eigenvalue multiplicity; this extends a known fact about the cycles
C_{n}. (ii) Explicit analysis of the probability distribution
of the quantum walk on the join of circulants; this explains why
complete multipartite graphs are not average uniform mixing, using the
fact K_{n} = K_{1} + K_{n1} and K_{n,\ldots,n} = \overline{K}_{n}
+ \ldots + \overline{K}_{n}. (iii) The quantum walk on the
Cartesian product of a $m$vertex path P_{m} and a circulant G,
namely, P_{m} \cprod G, is average uniform mixing if G is;
this highlights a difference between circulants and the hypercubes
Q_{n} = P_{2} \cprod Q_{n1}. Our proofs employ purely elementary
arguments based on the spectra of the graphs.
Operator quantum error correction
(pp382399)
D.W. Kribs, R. Laflamme, D. Poulin, and
M. Lesosky
This paper is an expanded and more detailed version of
the work \cite{KLP04} in which the Operator Quantum Error Correction
formalism was introduced. This is a new scheme for the error correction
of quantum operations that incorporates the known techniques  i.e.
the standard error correction model, the method of decoherencefree
subspaces, and the noiseless subsystem method  as special cases, and
relies on a generalized mathematical framework for noiseless subsystems
that applies to arbitrary quantum operations. We also discuss a number
of examples and introduce the notion of "unitarily noiseless
subsystems''.
The geometry and topology of
entanglement: Conifold, Segre variety, and Hopf fibration
(pp400409)
H. Heydari
We establish relations between conifold, Segre variety,
Hopf fibration, and separable sets of pure twoqubit states. Moreover,
we investigate the geometry and topology of separable sets of pure
multiqubit states based on the complex multiprojective Segre variety
and higher order Hopf fibration. We show that the Segre variety and Hopf
fibration give a unified geometrical and topological picture of multiqubit
states. We also construct entanglement monotones for multiqubit states.
Generalized asymmetric quantum
cloning machines
(pp410435)
S. Iblisdir, A. Acin, and N. Gisin
We study machines that take N identical replicas
of a pure qudit state as input and output a set of M_A clones of
a given fidelity and another set of M_B clones of another
fidelity. The tradeoff between these two fidelities is investigated,
and numerous examples of optimal N \to M_A+M_B cloning machines
are exhibited using a generic method. A generalisation to more than two
sets of clones is also discussed. Finally, an optical implementation of
some such machines is proposed. This paper is an extended version of
Phys. Rev. A 72, 042328 (2005).
Efficient circuits for
exactuniversal computation with qudits
(pp436454)
G.K. Brennen, S.S. Bullock, and D.P.
O'Leary
This paper concerns the efficient implementation of
quantum circuits for qudits. We show that controlled twoqudit gates can
be implemented without ancillas and prove that the gate library
containing arbitrary local unitaries and one twoqudit gate, $\CINC$, is
exactuniversal. A recent paper [S.Bullock, D.O'Leary, and G.K. Brennen,
Phys. Rev. Lett. 94, 230502 (2005)] describes quantum
circuits for qudits which require O(d^n) twoqudit gates for
state synthesis and O(d^{2n}) twoqudit gates for unitary
synthesis, matching the respective lower bound complexities. In this
work, we present the statesynthesis circuit in much greater detail and
prove that it is correct. Also, the (n2)/(d2) ancillas
required in the original algorithm may be removed without changing the
asymptotics. Further, we present a new algorithm for unitary synthesis,
inspired by the QR matrix decomposition, which is also
asymptotically optimal.
Concurrence and Schwarz inequality
(pp455460)
H. Heydari and G. Björk
We show that generalized concurrence is closely related
to, and can be derived from, the Schwarz inequality. This connection
places concurrence in a geometrical and functionalanalytical setting.
Communication complexity of remote
state preparation with entanglement
(pp461464)
R Jain
We consider the problem of remote state preparation
recently studied in several papers. We study the communication
complexity of this problem, in the presence of entanglement and in the
scenario of single use of the channel.
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