Vol.5 No.3
May 15,
2005
Research and
Review Articles:
Cryptanalysis of a
Practical Quantum Key Distribution with PolarizationEntangled
Photons (pp181186)
Th. Beth, J. MullerQuade and R. Steinwandt
Recently, a quantum key exchange protocol has been
described\cite{PFLM04}, which served as basis for securing an actual
bank transaction by means of quantum cryptography \cite{ZVS04}. The
authentication scheme used to this aim has been proposed by Peev et al.
\cite{PML04}. Here we show, that this authentication is insecure in the
sense that an attacker can provoke a situation where initiator and
responder of a key exchange end up with different keys. Moreover, it may
happen that an attacker can decrypt a part of the plaintext protected
with the derived encryption key.
Commutative version
of the local Hamiltonian problem and common eigenspace problem
(pp187215)
S. Bravyi and M. Vyalyi
We study the complexity of a problem Common Eigenspace
 verifying consistency of eigenvalue equations for composite quantum
systems. The input of the problem is a family of pairwise commuting
Hermitian operators H_1,\ldots,H_r on a Hilbert space (\CC^d)^{\otimes
n} and a string of real numbers \lambda=(\lambda_1,\ldots,\lambda_r).
The problem is to determine whether the common eigenspace specified by
equalities H_a\psi\ra=\lambda_a\psi\ra, a=1,\ldots,r has a positive
dimension. We consider two cases: (i) all operators H_a are klocal;
(ii) all operators H_a are factorized. It can be easily shown that both
problems belong to the class \QMA  quantum analogue of \NP, and that
some \NPcomplete problems can be reduced to either (i) or (ii). A
nontrivial question is whether the problems (i) or (ii) belong to \NP?
We show that the answer is positive for some special values of k and d.
Also we prove that the problem (ii) can be reduced to its special case,
such that all operators H_a are factorized projectors and all
\lambda_a=0.
Lagrangian
representation for fermionic linear optics
(pp216238)
S. Bravyi
Notions of a Gaussian state and a Gaussian linear map are
generalized to the case of anticommuting (Grassmann) variables.
Conditions under which a Gaussian map is trace preserving and (or)
completely positive are formulated. For any Gaussian map an explicit
formula relating correlation matrices of input and output states is
presented. This formalism allows to develop the Lagrangian
representation for fermionic linear optics (FLO). It covers both unitary
operations and the singlemode projectors associated with FLO
measurements. Using the Lagrangian representation we reduce a classical
simulation of FLO to a computation of Gaussian integrals over Grassmann
variables. Explicit formulas describing evolution of a quantum state
under FLO operations are put forward.
Communicating
continuous quantum variables between different Lorentz frames (pp239246)
P. Kok, T.C. Ralph and G.J. Milburn
We show how to communicate Heisenberglimited
continuous (quantum) variables between Alice and Bob in the case where
they occupy two inertial reference frames that differ by an unknown
Lorentz boost. There are two effects that need to be overcome: the
Doppler shift and the absence of synchronized clocks. Furthermore, we
show how Alice and Bob can share Dopplerinvariant entanglement, and we
demonstrate that the protocol is robust under photon loss.
Deterministic Local
Conversion of Incomparable States by Collective LOCC
(pp247257)
I. Chattopadhyay
and D. Sarkar
Incomparability of pure bipartite entangled
states under deterministic LOCC is a very strange phenomena. We find two
possible ways of getting our desired pure entangled state which is
incomparable with the given input state, by collective LOCC with
certainty. The first one is by providing some pure entanglement through
the lower dimensional maximallyentangled states or using further less
amount of entanglement and the next one is by collective operation on
two pairs which are individually incomparable. It is quite surprising
that we are able to achieve maximally entangled states of any Schmidt
rank from a finite number of 2x2 pure entangled states only by
deterministic LOCC. We provide general theory for the case of 3x3 system
of incomparable states by the above processes where incomparability
seems to be the most hardest one.
Classical and
quantum fingerprinting with shared randomness and onesided error
(pp258271)
R.T. Horn, A.J. Scott, J.
Walgate, R. Cleve, A.I. Lvovsky and B.C. Sanders
Within the simultaneous message passing model of
communication complexity, under a publiccoin assumption, we derive the
minimum achievable worstcase error probability of a classical
fingerprinting protocol with onesided error. We then present
entanglementassisted quantum fingerprinting protocols attaining
worstcase error probabilities that breach this bound.
Webcorner updates
(pp272272)
P. Kok
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