Vol.9
No.11&12
November 1, 2009
Research Articles:
Demonstration of
a scalable, multiplexed ion trap for quantum information processing
(pp09010919)
D.R.
Leibrandt, J. Labaziewicz, R.J. Clark, I.L. Chuang, R.J. Epstein,
C. Ospelkaus, J.H. Wesenberg, J.H. Bollinger, D. Leibfried, D. Wineland,
D.
Stick, J. Stick, C. Monroe, C.S. Pai, Y. Low, R. Frahm, and R.E.
Slusher
A scalable, multiplexed ion trap for quantum information processing is
fabricated and tested. The trap design and fabrication process are
optimized for scalability to small trap size and large numbers of
interconnected traps, and for integration of control electronics and
optics. Multiple traps with similar designs are tested with
$^{111}$Cd$^+$, $^{25}$Mg$^+$, and $^{88}$Sr$^{+}$ ions at room
temperature and with $^{88}$Sr$^+$ at 6 K, with respective ion lifetimes
of 90 s, 300 $\pm$ 30 s, 56 $\pm$ 6 s, and 4.5 $\pm$ 1.1 hours. The
motional heating rate for $^{25}$Mg$^{+}$ at room temperature and a trap
frequency of 1.6 MHz is measured to be 7 $\pm$ 3 quanta per millisecond.
For $^{88}$Sr$^{+}$ at 6 K and 540 kHz the heating rate is measured to
be 220 $\pm$ 30 quanta per second.
Highfidelity quantum
control using ion crystals in a Penning trap
(pp09200949)
M.J.
Biercuk, H. Uys, A.P. VanDevender, N. Shiga, W.M. Itano,
and J.J.
Bollinger
We provide an introduction to the use of ion crystals in a Penning trap
for experiments in quantum information. Macroscopic Penning traps allow
for the containment of a few to a few million atomic ions whose internal
states may be used in quantum information experiments. Ions are laser
Doppler cooled, and the mutual Coulomb repulsion of the ions leads to
the formation of crystalline arrays. The structure and dimensionality of
the resulting ion crystals may be tuned using a combination of control
laser beams and external potentials. We discuss the use of
twodimensional $^{9}$Be$^{+}$ ion crystals for experimental tests of
quantum control techniques. Our primary qubit is the 124 GHz
groundstate electron spin flip transition, which we drive using
microwaves. An ion crystal represents a spatial ensemble of qubits, but
the effects of inhomogeneities across a typical crystal are small, and
as such we treat the ensemble as a single effective spin. We are able to
initialize the qubits in a simple state and perform a projective
measurement on the system. We demonstrate full control of the qubit
Bloch vector, performing arbitrary highfidelity rotations
($\tau_{\pi}\sim$200 $\mu$s). Randomized Benchmarking demonstrates an
error per gate (a Paulirandomized $\pi/2$ and $\pi$ pulse pair) of
$8\pm1\times10^{4}$. Ramsey interferometry and spinlocking
measurements are used to elucidate the limits of qubit coherence in the
system, yielding a typical freeinduction decay coherence time of
$T_{2}\sim$2 ms, and a limiting $T_{1\rho}\sim$688 ms. These
experimental specifications make ion crystals in a Penning trap ideal
candidates for novel experiments in quantum control. As such, we briefly
describe recent efforts aimed at studying the errorsuppressing
capabilities of dynamical decoupling pulse sequences, demonstrating an
ability to extend qubit coherence and suppress phase errors. We conclude
with a discussion of future avenues for experimental exploration,
including the use of additional nuclearspinflip transitions for
effective multiqubit protocols, and the potential for Coulomb crystals
to form a useful testbed for studies of largescale entanglement.
Deterministic quantum
distribution of a dary key
(pp09500962)
A.
Eusebi and S. Mancini
We present an extension to a dary alphabet of a recently proposed
deterministic quantum key distribution protocol. It relies on the use of
mutually unbiased bases in prime power dimension d, for which we provide
an explicit expression. Then, by considering a powerful individual
attack, we show that the security of the protocol is maximal for d=3.
Robust cryptography in
the noisyquantumstorage model
(pp09630996)
C.
Schaffner, B. Terhal, and S. Wehner
It was shown that cryptographic primitives can be implemented based on
the assumption that quantum storage of qubits is noisy. In this work we
analyze a protocol for the universal task of oblivious transfer that can
be implemented using quantumkeydistribution (QKD) hardware in the
practical setting where honest participants are unable to perform
noisefree operations. We derive tradeoffs between the amount of
storage noise, the amount of noise in the operations performed by the
honest participants and the security of oblivious transfer which are
greatly improved compared to the results in \cite{prl:noisy}. As an
example, we show that for the case of depolarizing noise in storage we
can obtain secure oblivious transfer as long as the quantum biterror
rate of the channel does not exceed 11% and the noise on the channel is
strictly less than the quantum storage noise. This is optimal for the
protocol considered. Finally, we show that our analysis easily carries
over to quantum protocols for secure identification.
Locally undetermined
states, generalized Schmidt decomposition, and application in
distributed computing
(pp09971012)
Y.
Feng, R. Duan, and M. Ying
Multipartite quantum states that cannot be uniquely determined by their
reduced states of all proper subsets of the parties exhibit some inherit
`highorder' correlation. This paper elaborates this issue by giving
necessary and sufficient conditions for a pure multipartite state to be
locally undetermined, and moreover, characterizing precisely all the
pure states sharing the same set of reduced states with it.
Interestingly, local determinability of pure states is closely related
to a generalized notion of Schmidt decomposition. Furthermore, we find
that locally undetermined states have some applications to the
wellknown consensus problem in distributed computing. To be specific,
given some physically separated agents, when communication between them,
either classical or quantum, is unreliable, then there exists a totally
correct and completely faulttolerant protocol for them to reach a
consensus if and only if they share a priori a locally undetermined
quantum state.
On global effects
caused by locally noneffective unitary operations
(pp10131029)
S.
Gharibian, H. Kampermann, and D. Bruss
Given a bipartite quantum state $\rho$ with subsystems $A$ and $B$ of
arbitrary dimensions, we study the entanglement detecting capabilities
of locally noneffective, or cyclic, unitary operations [Fu, Europhys.
Lett., vol. 75]. Local cyclic unitaries have the special property that
they leave their target subsystem invariant. We investigate the distance
between $\rho$ and the global state after local application of such
unitaries as a possible indicator of entanglement. To this end, we
derive and discuss closed formulae for the maximal such distance
achievable for three cases of interest: (pseudo)pure quantum states,
Werner states, and twoqubit states. What makes this criterion
interesting, as we show here, is that it surprisingly displays behavior
similar to recent anomalies observed for nonlocality measures in higher
dimensions, as well as demonstrates an equivalence to the CHSH
inequality for certain classes of twoqubit states. Yet, despite these
similarities, the criterion is not itself a nonlocality measure. We
also consider entanglement detection in bound entangled states.
Quantum universality by
state distillation
(pp10301052)
B.W.
Reichardt
Quantum universality can be achieved using classically controlled
stabilizer operations and repeated preparation of certain ancilla
states. Which ancilla states suffice for universality? This ``magic
states distillation" question is closely related to quantum fault
tolerance. Lower bounds on the noise tolerable on the ancilla help give
lower bounds on the tolerable noise rate threshold for faulttolerant
computation. Upper bounds show the limits of threshold upperbound
arguments based on the GottesmanKnill theorem. We extend the range of
singlequbit mixed states that are known to give universality, by using
a simple paritychecking operation. For applications to proving
threshold lower bounds, certain practical stability characteristics are
often required, and we also show a stable distillation procedure.}{No
distillation upper bounds are known beyond those given by the
GottesmanKnill theorem. One might ask whether distillation upper bounds
reduce to upper bounds for singlequbit ancilla states. For multiqubit
pure states and previously considered twoqubit ancilla states, the
answer is yes. However, we exhibit twoqubit mixed states that are not
mixtures of stabilizer states, but for which every postselected
stabilizer reduction from two qubits to one outputs a mixture of
stabilizer states. Distilling such states would require true multiqubit
state distillation methods.
Fast amplification of
QMA
(pp10531068)
D.
Nagaj, P. Wocjan, and Y. Zhang
Given a verifier circuit for a problem in QMA, we show how to
exponentially amplify the gap between its acceptance probabilities in
the `yes' and `no' cases, with a method that is quadratically faster
than the procedure given by Marriott and Watrous. Our construction is
natively quantum, based on the analogy of a product of two reflections
and a quantum walk. Second, in some special cases we show how to amplify
the acceptance probability for good witnesses to 1, making a step
towards the proof that QMA with onesided error QMA_1 is equal to QMA.
Finally, we simplify the filterstate method to search for QMA witnesses
by Poulin and Wocjan.
Some properties of
partial fidelities
(pp10691080)
A.E.
Rastegin
Basic
properties of Uhlmann's partial fidelities are discussed. Statistical
interpretation in terms of POVM measurements is established.
Multiplicativity properties are considered. The relationship between
partial fidelities and partitioned trace distances is derived. As it is
shown, the partial fidelities cannot decrease under unistochastic
quantum operations. Thus, the partial fidelities have good properties in
the sense of their use as distinguishability measures.
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