Vol.6 No.7
November 1, 2006
Research Articles:
On the security
of $\alpha\eta$: response to 'some attacks on quantumbased
cryptographic protocols' (pp561582)
H.P.
Yuen, R. Nair, E. Corndorf, G.S. Kanter, and P. Kumar
Lo and Ko have developed some attacks on the cryptosystem
called $\alpha \eta$}, claiming that these attacks undermine the
security of $\alpha\eta$ for both direct encryption and key generation.
In this paper, we show that their arguments fail in many different ways.
In particular, the first attack in [1] requires channel loss or length
of knownplaintext that is exponential in the key length and is
unrealistic even for moderate key lengths. The second attack is a Grover
search attack based on `asymptotic orthogonality' and was not analyzed
quantitatively in [1]. We explain why it is not logically possible to
"pull back'' an argument valid only at $n=\infty$ into a limit
statement, let alone one valid for a finite number of transmissions n.
We illustrate this by a `proof' using a similar asymptotic orthogonality
argument that coherentstate BB84 is insecure for any value of
loss. Even if a limit statement is true, this attack is a priori
irrelevant as it requires an indefinitely large amount of
knownplaintext, resources and processing. We also explain why the
attacks in [1] on $\alpha\eta$ as a keygeneration system are based on
misinterpretations of [2]. Some misunderstandings in [1] regarding
certain issues in cryptography and optical communications are also
pointed out. Short of providing a security proof for $\alpha\eta$, we
provide a description of relevant results in standard cryptography and
in the design of $\alpha\eta$ to put the above issues in the proper
framework and to elucidate some security features of this new approach
to quantum cryptography.
Characterization
of several kinds of
quantum analogues of
relative entropy (pp583596)
M. Hayashi
Quantum relative entropy $D(\rho\\sigma)\defeq\Tr \rho
(\log \rho \log \sigma)$ plays an important role in quantum information
and related fields. However, there are many quantum analogues of
relative entropy. In this paper, we characterize these analogues from
information geometrical viewpoint. We also consider the naturalness of
quantum relative entropy among these analogues.
Characterizations
of symmetric monotone metrics on the state space of quantum systems (pp597605)
F. Hansen
The quantum Fisher information is a Riemannian metric,
defined on the state space of a quantum system, which is symmetric and
decreasing under stochastic mappings. Contrary to the classical case
such a metric is not unique. We complete the characterization, initiated
by Morozova, Chentsov and Petz, of these metrics by providing a closed
and tractable formula for the set of MorozovaChentsov functions. In
addition, we provide a continuously increasing bridge between the
smallest and largest symmetric monotone metrics.
Quantum advantage
without entanglement (pp606615)
D. Kenigsberg, A. Mor, and
G. Ratsaby
We study the advantage of purestate quantum computation
without entanglement over classical computation. For the DeutschJozsa
algorithm we present the \emph{maximal} subproblem that can be solved
without entanglement, and show that the algorithm still has an advantage
over the classical ones. We further show that this subproblem is of
greater significance, by proving that it contains all the Boolean
functions whose quantum phaseoracle is nonentangling. For Simon's and
Grover's algorithms we provide simple proofs that no nontrivial
subproblems can be solved by these algorithms without entanglement.
Robustness of
Shor's algorithm (pp616629)
S.J. Devitt, A.G. Fowler,
and L.C.L. Hollenberg
Shor's factorisation algorithm is a combination of
classical pre and postprocessing and a quantum period finding (QPF)
subroutine which allows an exponential speed up over classical factoring
algorithms. We consider the stability of this subroutine when exposed to
a discrete error model that acts to perturb the computational trajectory
of a quantum computer. Through detailed state vector simulations of an
appropriate quantum circuit, we show that the error locations within the
circuit itself heavily influences the probability of success of the QPF
subroutine. The results also indicate that the naive estimate of
required component precision is too conservative.
Entanglement and
its role in Shor's algorithm (pp630640)
V.M.
Kendon and W.J. Munro
Entanglement has been termed a critical resource for
quantum information processing and is thought to be the reason that
certain quantum algorithms, such as Shor's factoring algorithm, can
achieve exponentially better performance than their classical
counterparts. The nature of this resource is still not fully understood:
here we use numerical simulation to investigate how entanglement between
register qubits varies as Shor's algorithm is run on a quantum computer.
The shifting patterns in the entanglement are found to relate to the
choice of basis for the quantum Fourier transform.
Teleportation via multiqubit channels (pp641670)
J.
Links, J.P. Barjaktarevic, G.J. Milburn, and R.H. Mckenzie
We investigate the problem of teleporting an unknown
qubit state to a recipient via a channel of $2{\mathcal L}$ qubits. In
this procedure a protocol is employed whereby ${\mathcal L}$ Bell state
measurements are made and information based on these measurements is
sent via a classical channel to the recipient. Upon receiving this
information the recipient determines a local gate which is used to
recover the original state. We find that the $2^{2\mathcal
L}$dimensional Hilbert space of states available for the channel admits
a decomposition into four subspaces. Every state within a given subspace
is a perfect channel, and each sequence of Bell measurements projects
$2{\mathcal L}$ qubits of the system into one of the four subspaces. As
a result, only two bits of classical information need be sent to the
recipient for them to determine the gate. We note some connections
between these four subspaces and ground states of manybody Hamiltonian
systems, and discuss the implications of these results towards
understanding entanglement in multiqubit systems.
Authors Index (Vol6, 2006)
(pp671672)
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