2,635 research outputs found
Apply current exponential de Finetti theorem to realistic quantum key distribution
In the realistic quantum key distribution (QKD), Alice and Bob respectively
get a quantum state from an unknown channel, whose dimension may be unknown.
However, while discussing the security, sometime we need to know exact
dimension, since current exponential de Finetti theorem, crucial to the
information-theoretical security proof, is deeply related with the dimension
and can only be applied to finite dimensional case. Here we address this
problem in detail. We show that if POVM elements corresponding to Alice and
Bob's measured results can be well described in a finite dimensional subspace
with sufficiently small error, then dimensions of Alice and Bob's states can be
almost regarded as finite. Since the security is well defined by the smooth
entropy, which is continuous with the density matrix, the small error of state
actually means small change of security. Then the security of
unknown-dimensional system can be solved. Finally we prove that for heterodyne
detection continuous variable QKD and differential phase shift QKD, the
collective attack is optimal under the infinite key size case.Comment: 11 pages, 2 figures, detailed version, applications adde
Fast Low-rank Representation based Spatial Pyramid Matching for Image Classification
Spatial Pyramid Matching (SPM) and its variants have achieved a lot of
success in image classification. The main difference among them is their
encoding schemes. For example, ScSPM incorporates Sparse Code (SC) instead of
Vector Quantization (VQ) into the framework of SPM. Although the methods
achieve a higher recognition rate than the traditional SPM, they consume more
time to encode the local descriptors extracted from the image. In this paper,
we propose using Low Rank Representation (LRR) to encode the descriptors under
the framework of SPM. Different from SC, LRR considers the group effect among
data points instead of sparsity. Benefiting from this property, the proposed
method (i.e., LrrSPM) can offer a better performance. To further improve the
generalizability and robustness, we reformulate the rank-minimization problem
as a truncated projection problem. Extensive experimental studies show that
LrrSPM is more efficient than its counterparts (e.g., ScSPM) while achieving
competitive recognition rates on nine image data sets.Comment: accepted into knowledge based systems, 201
Security proof of differential phase shift quantum key distribution in the noiseless case
Differential phase shift quantum key distribution systems have a high
potential for achieving high speed key generation. However, its unconditional
security proof is still missing, even though it has been proposed for many
years. Here, we prove its security against collective attacks with a weak
coherent light source in the noiseless case (i.e. no bit error). The only
assumptions are that quantum theory is correct, the devices are perfect and
trusted and the key size is infinite. Our proof works on threshold detectors.
We compute the lower bound of the secret key generation rate using the
information-theoretical security proof method. Our final result shows that the
lower bound of the secret key generation rate per pulse is linearly
proportional to the channel transmission probability if Bob's detection counts
obey the binomial distribution.Comment: Published version, 13 pages, 4 figures, minor changes, references
added, acknowledgement adde
Applicability of the Friedberg-Lee-Zhao method
Friedberg, Lee and Zhao proposed a method for effectively evaluating the
eigenenergies and eigen wavefunctions of quantum systems. In this work, we
study several special cases to investigate applicability of the method.
Concretely, we calculate the ground-state eigenenergy of the Hellmann potential
as well as the Cornell potential, and also evaluate the energies of the systems
where linear term is added to the Coulomb and harmonic oscillator potentials as
a perturbation. The results obtained in this method have a surprising agreement
with the traditional method or the numerical results. Since the results in this
method have obvious analyticity compared to that in other methods, and because
of the simplicity for calculations this method can be applied to solving the
Schr\"{o}dinger equation and provides us better understanding of the physical
essence of the concerned systems. But meanwhile applications of the FLZ method
are restricted at present, especially for certain potential forms, but due to
its obvious advantages, it should be further developed.Comment: 14 pages,no figure
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