Vol.9
No.9&10
September 1, 2009
Review Article:
Topological cluster state quantum computing
(pp07210738)
A.G.
Fowler and K. Goyal
The quantum computing scheme described by Raussendorf et.
al (2007), when
viewed as a cluster state computation, features a 3D cluster state,
novel adjustable strength error correction capable of correcting general
errors through the correction of Z errors only, a threshold error rate
approaching 1% and low overhead arbitrarily longrange logical gates. In
this work, we review the scheme in detail framing the discussion solely
in terms of the required 3D cluster state and its stabilizers.
Research Articles:
Properties of local quantum operations with shared entanglement
(pp07390764)
G.
Gutoski
Multiparty local quantum operations with shared quantum entanglement or
shared classical randomness are studied. The following facts are
established:
* There is a ball of local operations with shared randomness lying
within the space spanned by the nosignaling operations and centred at
the completely noisy channel.
* The existence of the ball of local operations with shared randomness
is employed to prove that the weak membership problem for local
operations with shared entanglement is strongly NPhard.
* Local operations with shared entanglement are characterized in terms
of linear functionals that are "completely'' positive on a certain cone
K of separable Hermitian operators, under a natural notion of complete
positivity appropriate to that cone. Local operations with shared
randomness (but not entanglement) are also characterized in terms of
linear functionals that are merely positive on that same cone K.
* Existing characterizations of nosignaling operations are generalized
to the multiparty setting and recast in terms of the ChoiJamio\l
kowski representation for quantum superoperators.
It is noted that the standard nonlocal box is an example of a
nosignaling operation that is separable, yet cannot be implemented by
local operations with shared entanglement.
Security of quantum secret sharing with twoparticle entanglement
against individual attacks
(pp07650772)
S.J. Qin, F. Gao,
Q.Y. Wen, and F.C. Zhu
Security is the most important criterion to evaluate cryptography
protocols. We investigate the security of one important quantum secret
sharing protocol (KKI protocol). By discriminating two mixed states, we
derive the optimal relationship between the induced error rate (QBER)
and the maximal amount of information gained by a dishonest participant.
For a specific amount of eavesdropper's knowledge on the shared secret
that we consider, the disturbance on the quantum state in terms of QBER
is actually larger for the hybrid protocol than the KKI protocol.
Therefore, the hybrid protocol appears to be better able to detect
eavesdroppers than the KKI protocol. For this reason, we do not see any
reason to employ the KKI protocol against individual attacks.
Exact universality from any entangling gate without inverses
(pp07730777)
A.W. Harrow
This note proves that arbitrary local gates together with any entangling
bipartite gate V are universal. Previously this was known only when
access to both V and V^\dag was given, or when approximate universality
was demanded.
SLOCC classification for nine families of fourqubits
(pp07780800)
D.F. Li,
X.R. Li, H.T. Huang, and X.X. Li
In 2000, D\"{u}r, Vidal and Cirac indicated that there are infinitely
many SLOCC classes for four qubits. Later, Verstraete, Dehaene, and
Verschelde proposed nine families of states corresponding to nine
different ways of entangling four qubits. And then in 2007 Lamata et al.
reported that there are eight true SLOCC entanglement classes of four
qubits up to permutations of the qubits. In this paper, we investigate
SLOCC classification of the nine families proposed by Verstraete,
Dehaene and Verschelde, and distinguish 49 true SLOCC entanglement
classes from them.
Relaxed uncertainty relations and information processing
(pp08010832)
G. Ver
Steeg and S. Wehner
We consider a range of "theories'' that violate the uncertainty relation
for anticommuting observables derived. We first show that Tsirelson's
bound for the CHSH inequality can be derived from this uncertainty
relation, and that relaxing this relation allows for nonlocal
correlations that are stronger than what can be obtained in quantum
mechanics. We continue to construct a hierarchy of related nonsignaling
theories, and show that on one hand they admit superstrong random access
encodings and exponential savings for a particular communication
problem, while on the other hand it becomes much harder in these
theories to learn a state. We show that the existence of these effects
stems from the absence of certain constraints on the expectation values
of commuting measurements from our nonsignaling theories that
are present in quantum theory.
Eigenpath traversal by phase randomization
(pp08330855)
S.
Boixo, E. Knill, and R. Somma
A computation in adiabatic quantum computing is implemented by
traversing a path of nondegenerate eigenstates of a continuous family of
Hamiltonians. We introduce a method that traverses a discretized form of
the path: At each step we apply the instantaneous Hamiltonian for a
random time. The resulting decoherence approximates a projective
measurement onto the desired eigenstate, achieving a version of the
quantum Zeno effect. If negative evolution times can be implemented with
constant overhead, then the average absolute evolution time required by
our method is $\cO(L^{2} /\Delta)$ for constant error probability, where
$L$ is the length of the path of eigenstates and $\Delta$ is the minimum
spectral gap of the Hamiltonian. The dependence of the cost on
$\Delta$ is optimal. Making explicit the dependence on the path length
is useful for cases where $L$ is much less than the general bound. The
complexity of our method has a logarithmic improvement over previous
algorithms of this type. The same cost applies to the discretetime
case, where a family of unitary operators is given and each unitary and
its inverse can be used. Restriction to positive evolution times incurs
an error that decreases exponentially with the cost. Applications of
this method to unstructured search and quantum sampling are considered.
In particular, we discuss the quantum simulated annealing algorithm for
solving combinatorial optimization problems. This algorithm provides a
quadratic speedup in the gap of the stochastic matrix over its
classical counterpart implemented via Markov chain Monte Carlo.
Complete characterization of mixing time for the continuous quantum walk
on
the hypercube with Markovian decoherence model
(pp08560878)
M.
Drezgich, A.P. Hines, M. Sarovar, and S. Sastry
The ndimensional hypercube quantum random walk (QRW) is a particularily
appealing example of a quantum walk because it has a natural
implementation on a register on n qubits. However, any real
implementation will encounter decoherence effects due to interactions
with uncontrollable degrees of freedom. We present a complete
characterization of the mixing properties of the hypercube QRW under a
physically relevant Markovian decoherence model. In the local
decoherence model considered the nonunitary dynamics are modeled as a
sum of projections on individual qubits to an arbitrary direction on the
Bloch sphere. We prove that there is always classical (asymptotic)
mixing in this model and specify the conditions under which
instantaneous mixing always exists. And we show that the latter
mixing property, as well as the classical mixing time, depend heavily on
the exact environmental interaction and its strength. Therefore,
algorithmic applications of the QRW on the hypercube, if they intend to
employ mixing properties, need to consider both the walk dynamics and
the precise decoherence model.
New
approach to quantum key distribution via quantum encryption
(pp08790898)
A. Fahmi
Recently, Zhang, Li and Guo (ZLG) suggested a new approach to quantum
key distribution by using a shared Bell state which acts as quantum key
in order to encode and decode classical information. Subsequently,
others extended ZLG protocol to ddimensional systems and to quantum
secret sharing based on reusable GHZ states. However, Gao et al. have
shown that if Eve employs a special strategy to attack, these protocols
become insecure. Afterwards, they repair ZLG protocol so that their
eavesdropping strategy becomes inefficient. In this paper, we
investigate the security of ZLG quantum key distribution protocol and
show that it is not secure against Eve's attacks and with probability of
one half she gets all of the keys without being detected by the two
parties. In this eavesdropping strategy, Eve transforms the previously
shared Bell state between Alice and Bob to two Bell states among herself
and the parties. Moreover, we briefly show that ZLG's repairing by Gao
et al's is not efficient against of our attack and Eve can choose an
appropriate rotation angle and measurement bases which help her to do
eavesdropping. Afterwards, we discuss generalization of ZLG protocol to
ddimensional systems and show that with probability 1/d, Eve gets all
of keys. We show that quantum secret sharing based on reusable GHZ
states is also not secure and with probability one half, Eve gets all of
keys. We repair them by going to higher dimensional shared EPR or GHZ
states. Finally, we compare ZLG protocol with ours and show that the ZLG
protocol and its extensions are less robust against the channel noise
with respect to ours.
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