Vol.11
No.11&12, November 1, 2011
Research Articles:
Complexity of commuting Hamiltonians on a square lattice of qubits
(pp09010912)
Norbert Schuch
We consider the computational complexity of Hamiltonians which are sums
of commuting terms acting on plaquettes in a square lattice of qubits,
and we show that deciding whether the ground state minimizes the energy
of each local term individually is in the complexity class NP. That is,
if the ground states has this property, this can be proven using a
classical certificate which can be efficiently verified on a classical
computer. Different to previous results on commuting Hamiltonians, our
certificate proves the existence of such a state without giving
instructions on how to prepare it.
Passively selferrorrejecting qubit transmission over a
collectivenoise channel
(pp09130924)
FuGuo Deng,
XiHan Li, and HongYu Zhou
We propose a passively selferrorrejecting singlequbit transmission
scheme for an arbitrary polarization state of a single qubit over a
collectivenoise channel, without resorting to additional qubits and
entanglement. By splitting a single qubit into some wavepackets with
some MachZehnder interferometers, we can obtain an uncorrupted state
with a success probability approaching 100% via postselection in
different time bins, independent of the parameters of collective noise.
It is simpler and more flexible than the schemes utilizing decoherencefree
subspace and those with additional qubits. One can directly apply this
scheme to almost all quantum communication protocols based on single
photons or entangled photon systems against a collective noise.
Low temperature dynamics of netral atoms for quantum logic
(pp09250936)
FangYu Hong,
Yang Xiang, Z.Y. Zhu, and W.H. Tang
We study from the point of view of quantum logic the properties of the
collective oscillations of two Rydberg atoms in two harmonic traps. The
difference in the frequency of two normal modes of motion expands with
the difference in the mass of the two atoms. The probability of
excitation of the motional quanta due to the strong dipoledipole
interaction can be made to be sufficiently small. Based on the normal
modes of motion we present a scheme for quantum state transfer which is
useful for quantum information process and for precision spectroscopy of
atoms that lack suitable transitions for efficient laser cooling,
internal state preparation, and detection.
Security of quantum key distribution with statedependent
imperfections
(pp09370947)
HongWei Li,
ZhenQiang Yin, Shuang Wang, WanSu Bao, GuangCan Guo, and ZhengFu Han
In practical quantum key distribution system, the state preparation and
measurement have statedependent imperfections comparing with the ideal
BB84 protocol. If the statedependent imperfection can not be regarded
as an unitary transformation, it should not be considered as part of
quantum channel noise introduced by the eavesdropper, the commonly used
secret key rate formula GLLP can not be applied correspondingly. In this
paper, the unconditional security of quantum key distribution with
statedependent imperfections will be analyzed by estimating upper bound
of the phase error rate in the quantum channel and the imperfect
measurement. Interestingly, since Eve can not control all phase error in
the quantum key distribution system, the final secret key
rate under constant quantum bit error rate can be improved comparing
with the perfect quantum key distribution protocol.
Bound on genuine multipartite correlations from the principle of
information causality
(pp09480956)
Yang Xiang and
Wei Ren
Quantum mechanics is not the unique nosignaling theory which is endowed
with strongerthanclassical correlations, and there exists a broad
class of nosignaling theories allowing even strongerthanquantum
correlations. The principle of information causality has been suggested
to distinguish quantum theory from these nonphysical theories, together
with an elegant informationtheoretic proof of the quantum bound of
twoparticle correlations. In this work, we extend this to genuine
$N$particle correlations that cannot be reduced to mixtures of states
in which a smaller number of particles are entangled. We first express
Svetlichny's inequality in terms of multipartite nosignaling boxes,
then prove that the strongest genuine multipartite correlations lead to
the maximal violation of information causality. The maximal genuine
multipartite correlations under the constraint of information causality
is found to be equal to the quantum mechanical bound. This result
consolidates information causality as a physical principle defining the
possible correlations allowed by nature, and provides intriguing
insights into the limits of genuine multipartite correlations in quantum
theory.
Relativity of mixed entangled states
(pp09570967)
Shahpoor
Moradi
We obtain the necessary and sufficient separability and distillability
conditions of mixtures of a maximally entangled state and the completely
separable state in relativistic setting. In an inertial frame we study
the entanglement under Wigner rotations induced by Lorentz
transformations. We also investigate the mixed state entanglement of
scalar and Dirac fields as seen by two relatively accelerated observers.
For scalar field we show that in infinite acceleration limit the state
has no longer distillable entanglement. For dirac field the entanglement
in the infinite acceleration limit is finite. In both cases we show that
there are states that will change from entangled into separable for a
certain value of velocity or acceleration. We conclude that
distillability is a relative concept, depending on the frame in which it
is observed.
Security analysis of the timecoding quantum key distribution
protocols
(pp09680987)
Thierry
Debuisschert and Simon Fossier
We report the security analysis of timecoding quantum key distribution
protocols. The protocols make use of coherent singlephoton pulses. The
key is encoded in the photon timedetection. The use of coherent
superposition of states allows to detect eavesdropping of the key. We
give a mathematical model of a first protocol from which we derive a
second, simpler, protocol. We derive the security analysis of both
protocols and find that the secure rates can be similar to those
obtained with the BB84 protocol. We then calculate the secure distance
for those protocols over standard fibre links. When using lownoise
superconducting single photon detectors, secure distances over 200 km
can be foreseen. Finally, we analyse the consequences of photonnumber
splitting attacks when faint pulses are used instead of single photon
pulses. A decoy states technique can be used to prevent such attacks.
Polarizationentanglement purification and concentration using
crossKerr nonlinearity
(pp09881002)
Chuan Wang,
Yong Zhang, and GuangSheng Jin
We present an entanglement purification protocol and an entanglement
concentration protocol in this paper, resorting to crossKerr
nonlinearities and interference of two coherent beams. Our purification
protocol can be used to purify photon pairs not only from an ideal
entangled source but also from a parametric downconversion source by
the measurement on the interference of two coherent beams without giant
crossKerr media. Our quantum nondemolition detection can also used to
concentrate photon pairs in less entangled pure states efficiently. Our
protocols are more flexibilities in distinguishing the phases of the
coherent states during homodyne detection.
Universal quantum computation and leakage reduction in the 3Qubit
decoherence free subsystem
(pp10031018)
Bryan H. Fong
and Stephen M. Wandzura
We describe exchangeonly universal quantum computation and leakage
reduction in the 3qubit decoherence free subsystem (DFS). We discuss
the angular momentum structure of the DFS, the proper forms for the DFS
CNOT and leakage reduction operators in the total angular momentum
basis, and new exchangeonly pulse sequences for the CNOT and leakage
reduction operators. Our new DFS CNOT sequence requires 22 pulses in 13
time steps. The DFS leakage reduction sequence, the first explicit
leakage reduction sequence of its kind, requires 30 pulses in 20 time
steps. Although the search for sequences was performed numerically using
a genetic algorithm, the solutions presented here are exact, with
closedform expressions.
A note about a partial nogo theorem for quantum PCP (pp10191027)
Itai Arad
This is not a disproof of the quantum PCP conjecture! In this note we
use perturbation on the commuting Hamiltonian problem on a graph, based
on results by Bravyi and Vyalyi, to provide a very partial nogo theorem
for quantum PCP. Specifically, we derive an upper bound on how large
the promise gap can be for the quantum PCP still to hold, as a function
of the noncommuteness of the system. As the system becomes more and
more commuting, the maximal promise gap shrinks. We view these results
as possibly a preliminary step towards disproving the quantum PCP
conjecture posed in \cite{ref:Aha09}. A different way to view these
results is actually as indications
that a critical point exists, beyond which quantum PCP indeed holds; in
any case, we hope that these results will lead to progress on this
important open problem.
Local extrema of entropy functions under tensor products (pp10281044)
Shmuel
Friedland, Gilad Gour, and Aidan Roy
We show that under a certain condition of local commutativity the
minimum vonNeumann entropy output of a quantum channel is locally
additive. We also show that local minima of the 2norm entropy functions
are closed under tensor products if one of the subspaces has dimension
2.
Nondemolition Adiabatic Measurement of the Phase Qubit State (pp10451065)
G.P. Berman,
A.A. Chumaka,b, D.I. Kameneva, D. Kinionc, and V.I. Tsifrinovichd
An adiabatic method for a singleshot
nondemolition measurement of the phase qubit is suggested. The qubit is
inductively coupled to a lowfrequency resonator, which in turn is
connected with a classical measurement device (phase meter). The
resonator drives adiabatic oscillations of the supercurrent in the qubit
loop. The back reaction of the qubit loop on the resonator depends on
the qubit state. Measuring the phase shift of the resonator’s
oscillations one can determine the state of the qubit. Numerical
computations with available experimental parameters show that the phase
difference between the two qubit states increases at a rate of 0.0044
rad/ns with the fidelity of about 0.9989 and the measurement time of
about 100 ns. The fidelity of the measurement is estimated taking into
consideration possible quantum transitions inside and outside the qubit
manifold. An increase of the phase difference is possible but it is
linked to a reduction of the fidelity. The requirements for the
reproducibility of the qubit and resonator parameters are formulated.
back to QIC online Front page
