Vol.7
No.1&2
January 1, 2007
Review:
An introduction to
entanglement measures (pp001051) PDF
M.B. Plenio
and S. Virmani
We review the theory of entanglement measures,
concentrating mostly on the finite dimensional twoparty case. Topics
covered include: singlecopy and asymptotic entanglement manipulation;
the entanglement of formation; the entanglement cost; the distillable
entanglement; the relative entropic measures; the squashed entanglement;
lognegativity; the robustness monotones; the greatest crossnorm;
uniqueness and extremality theorems. Infinite dimensional systems and
multiparty settings will be discussed briefly.
Research Articles:
Modeling ion trap
thermal noise decoherence (pp052072) PDF
D.
Leibrandt, B. Yurke, and R. Slusher
We present a detailed analysis of ion heating caused by
thermal fluctuation noise in ion traps. The results of the analysis are
used to estimate thermal noise ion heating rates for a variety of trap
electrode configurations and materials, including recent scalable
multiplexed planar ion trap proposals based on silicon VLSI technology.
We find that minimizing thermal noise ion heating places severe
constraints on the design and materials used for ion traps.
Timeshift attack in
practical quantum cryptosystems (pp073082) PDF
B. Qi,
C.H.
F.
Fung, H.K. Lo,
and F.X. Ma
Recently, a new type of attack, which exploits the
efficiency mismatch of two single photon detectors (SPD) in a quantum
key distribution (QKD) system, has been proposed. In this paper, we
propose another ``timeshift'' attack that exploits the same
imperfection. In our attack, Eve shifts the arrival time of either the
signal pulse or the synchronization pulse or both between Alice and Bob.
In particular, in a QKD system where Bob employs timemultiplexing
technique to detect both bit "0'' and bit "1'' with the same SPD, Eve,
in some circumstances, could acquire full information on the final key
without introducing any error. In addition, we prove that if Alice and
Bob are unaware of our attack, the final key they share is insecure. We
emphasize that our attack is simple and feasible with current
technology. Finally, we discuss some counter measures against our and
earlier attacks.
Hidden symmetry
detection on a quantum computer (pp083092) PDF
R.
Schutzhold and W.G. Unruh
The fastest quantum algorithms (for the solution of
classical computational tasks) known so far are basically variations of
the hidden subgroup problem with {$f(U[x])=f(x)$}. Following a
discussion regarding which tasks might be solved efficiently by quantum
computers, it will be demonstrated by means of a simple example, that
the detection of more general hidden (twopoint) symmetries {$V\{f(x),f(U[x])\}=0$}
by a quantum algorithm can also admit an exponential speedup. E.g., one
member of this class of symmetries {$V\{f(x),f(U[x])\}=0$} is discrete
selfsimilarity (or discrete scale invariance).
Quantum walks on
directed graphs (pp093102) PDF
A. Montanaro
We consider the definition of quantum walks on directed
graphs. Call a directed graph reversible if, for each pair of
vertices $(v_i, v_j)$, if $v_i$ is connected to $v_j$ then there is a
path from $v_j$ to $v_i$. We show that reversibility is a necessary and
sufficient condition for a directed graph to allow the notion of a
discretetime quantum walk, and discuss some implications of this
condition. We present a method for defining a "partially quantum'' walk
on directed graphs that are not reversible.
Invertible quantum
operations and perfect encryption of quantum states (pp103110) PDF
A. Nayak and P. Sen
In this note, we characterize the form of an invertible
quantum operation, i.e., a completely positive trace preserving linear
transformation (a CPTP map) whose inverse is also a CPTP map. The
precise form of such maps becomes important in contexts such as
selftesting and encryption. We show that these maps correspond to
applying a unitary transformation to the state along with an ancilla
initialized to a fixed state, which may be mixed. The characterization
of invertible quantum operations implies that oneway schemes for
encrypting quantum states using a classical key may be slightly more
general than the "private quantum channels'' studied by Ambainis, Mosca,
Tapp and de Wolf {AmbainisMTW00}. Nonetheless, we show that their
results, most notably a lower bound of 2n bits of key to encrypt
n quantum bits, extend in a straightforward manner to the general
case.
Multiplayer quantum
minority game with decoherence (pp111126) PDF
A.P. Flitney and
L.L.C. Hollenberg
A quantum version of the Minority game for an arbitrary
number of agents is considered. It is known that when the number of
agents is odd, quantizing the game produces no advantage to the players,
but for an even number of agents new Nash equilibria appear that have no
classical analogue and have improved payoffs. We study the effect on the
Nash equilibrium payoff of various forms of decoherence. As the number
of players increases the multipartite GHZ state becomes increasingly
fragile, as indicated by the smaller error probability required to
reduce the Nash equilibrium payoff to the classical level.
Feedback control for
communication with nonorthogonal states (pp127138)
PDF
K. Jacobs
Communicating classical information with a quantum system
involves the receiver making a measurement on the system so as to
distinguish as well as possible the alphabet of states used by the
sender. We consider the situation in which this measurement takes an
appreciable time. In this case the measurement must be described by a
continuous measurement process. We consider a continuous implementation
of the optimal measurement for distinguishing between two nonorthogonal
states, and show that feedback control can be used during this
measurement to increase the rate at which the information regarding the
initial preparation is obtained. We show that while the maximum
obtainable increase is modest, the effect is purely quantum mechanical
in the sense that the enhancement is only possible when the initial
states are nonorthogonal. We find further that the enhancement in the
rate of information gain is achieved at the expense of reducing the
total information which the measurement can extract in the longtime
limit.
Faulttolerant quantum
computation for local leakage faults (pp139156) PDF
P. Aliferis and B.M.
Terhal
We provide a rigorous analysis of faulttolerant quantum
computation in the presence of local leakage faults. We show that one
can systematically deal with leakage by using appropriate
leakagereduction units such as quantum teleportation. The leakage noise
is described microscopically, by Hamiltonian couplings, and the noise is
treated coherently, similar to general nonMarkovian noise analyzed in
Refs. \cite{Terhal04} and \cite{Aliferis05b}. We describe ways to limit
the use of leakagereduction units while keeping the quantum circuits
faulttolerant and we also discuss how leakage reduction by
teleportation is naturally achieved in measurementbased computation.
An anomaly of
nonlocality (pp157170) PDF
A.A. Methot and V. Scarani
Ever since the work of Bell, it has been known that
entangled quantum states can produce nonlocal correlations between the
outcomes of separate measurements. However, for almost forty years, it
has been assumed that the most nonlocal states would be the maximally
entangled ones. Surprisingly it is not the case: nonmaximally entangled
states are generally more nonlocal than maximally entangled states for
all the measures of nonlocality proposed to date: Bell inequalities,
the KullbackLeibler distance, entanglement simulation with
communication or with nonlocal boxes, the detection loophole and
efficiency of cryptography. In fact, one can even find simple examples
in low dimensions, confirming that it is not an artefact of a
specifically constructed Hilbert space or topology. This anomaly shows
that entanglement and nonlocality are not only different concepts, but
also truly different resources. We review the present knowledge on this
anomaly, point out that Hardy's theorem has the same feature, and
discuss the perspectives opened by these discoveries.
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