66,207 research outputs found

### Well-posedness and blowup of the geophysical boundary layer problem

Under the assumption that the initial velocity and outflow velocity are
analytic in the horizontal variable, the local well-posedness of the
geophysical boundary layer problem is obtained by using energy method in the
weighted Chemin-Lerner spaces. Moreover, when the initial velocity and outflow
velocity satisfy certain condition on a transversal plane, it is proved that
the $W^{1,\infty}-$norm of any smooth solution decaying exponentially in the
normal variable to the geophysical boundary layer problem blows up in a finite
time

### An efficient implementation of the decoy-state measurement-device-independent quantum key distribution with heralded single-photon sources

We study the decoy-state measurement-device-independent quantum key
distribution using heralded single-photon sources. This has the advantage that
the observed error rate in X basis is in higher order and not so large. We
calculate the key rate and transmission distance for two cases: one using only
triggered events, and the other using both triggered and non-triggered events.
We compare the key rates of various protocols and find that our new scheme
using triggered and non-triggered events can give higher key rate and longer
secure distance. Moreover, we also show the different behavior of our scheme
when using different heralded single-photon sources, i.e., in poisson or
thermal distribution. We demonstrate that the former can generate a relatively
higher secure key rate than the latter, and can thus work more efficiently in
practical quantum key distributions.Comment: 15 pages, 4 figure

### A review on the decoy-state method for practical quantum key distribution

We present a review on the historic development of the decoy state method,
including the background, principles, methods, results and development. We also
clarify some delicate concepts. Given an imperfect source and a very lossy
channel, the photon-number-splitting (PNS) attack can make the quantum key
distribution (QKD) in practice totally insecure. Given the result of ILM-GLLP,
one knows how to distill the secure final key if he knows the fraction of
tagged bits. The purpose of decoy state method is to do a tight verification of
the the fraction of tagged bits. The main idea of decoy-state method is
changing the intensities of source light and one can verify the fraction of
tagged bits of certain intensity by watching the the counting rates of pulses
of different intensities. Since the counting rates are small quantities, the
effect of statistical fluctuation is very important. It has been shown that
3-state decoy-state method in practice can work even with the fluctuations and
other errors.Comment: 17 page

### Graphs induced by iterated function systems

For an iterated function system (IFS) of simillitidues, we define two graphs
on the representing symbolic space. We show that if the self-similar set $K$
has positive Lebesgue measure or the IFS satisfies the weak separation
condition, then the graphs are hyperbolic, moreover the hyperbolic boundaries
are homeomorphic to the self-similar sets

### On the role of coherent attacks in a type of strategic problem related to quantum key distribution

We consider a strategic problem of the Evesdropping to quantum key
distribution. Evesdropper hopes to obtain the maxium information given the
disturbance to the qubits is often For this strategy, the optimized individual
attack have been extensively constructed under various conditions. However, it
seems a difficult task in the case of coherent attack, i.e., Eve may treat a
number of intercepted qubits collectively, including the collective unitary
transformations and the measurements. It was conjectured by Cirac and Gisin
that no coherent attack can be more powerful for this strategy for BB84
protocol. In this paper we give a general conclusion on the role of coherent
attacks for the strategy of maxmizing the information given the disturbance.
Suppose in a quantum key distribution(QKD) protocol, all the transmitted bits
from Alice are independent and only the individual disturbances to each qubits
are examined by Alice and Bob. For this type of protocols(so far almost all QKD
protocols belong to this type), in principle no coherent attack is more
powerful than the product of optimized individual attack to each individual
qubits. All coherent attacks to the above QKD protocols can be disregarded for
the strategy above.Comment: This is identical to quant-ph/0110073. The the title of the old
version is inappropriate. What I have proven is the Cirac-Gisin conjecture in
Phys. Lett. A229, 1(1997). The actual conclusion is that coherent attack can
be ignored for the strategy of maximizing Eve's total information given
disturbance. But this does not mean coherent attack can be ignored in QK

### Perfect random number generator is unnecessary for secure quantum key distribution

Game G: Clare passes a string s which is either from perfect random number
generator R0 or from good imperfect number generator R1, with equal
probability. Alice's information about whether it is from R0 or R1 is bounded
by small value h. Alice use s as the input random numbers for QKD protocol with
Bob. Suppose Eve may have very small information about the final key if s is
from R0 and Eve has large information if s is from R1, then after the protocol,
Alice announce the final key, Eve's information about whether s is from R0 or
R1 is unreasonablly large, i.e., breaks the known bound, h. Explicit formulas
are given in the article.Comment: The proof is VERY simpl

### Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain

We revisit the problem of linear regression under a differential privacy
constraint. By consolidating existing pieces in the literature, we clarify the
correct dependence of the feature, label and coefficient domains in the
optimization error and estimation error, hence revealing the delicate price of
differential privacy in statistical estimation and statistical learning.
Moreover, we propose simple modifications of two existing DP algorithms: (a)
posterior sampling, (b) sufficient statistics perturbation, and show that they
can be upgraded into **adaptive** algorithms that are able to exploit
data-dependent quantities and behave nearly optimally **for every instance**.
Extensive experiments are conducted on both simulated data and real data, which
conclude that both AdaOPS and AdaSSP outperform the existing techniques on
nearly all 36 data sets that we test on.Comment: Uncertainty in Artificial Intelligence (UAI-2018), Monterey, C

### A practically feasible entanglement assisted quantum key distribution protocol

We give an entanglement assisted scheme for quantum key distribution.
The scheme requires the maximally entangled 2-qubit state but does not
require any quantum storage. The scheme is unconditionally secure under
whatever Eve's attack.
Given the symmetric noisy channel with uncorrelated noise, our scheme can
tolerate the bit error rate up to
26% in the 4-state case and 30% in the
6-state respectively, respectively. These values are higher than those of all
currently known two-level-state schemes without using a quantum storage.Comment: 13 pages, 3 figure

### On quantum key distribution in decoherence-free subspace

We propose easy implementable protocols for robust quantum key distribution
with the collective dephasing channel or collective rotating channel.
In these protocols, Bob only takes passive photon detection to measure the
polarization qubits in the random bases. The source for the protocol with
collective rotating channel is made by type 2 spontaneous parametric down
conversion with random unitary rotation and phase shifter, no quantum
disentangler is required.
A simple proof for unconditionally security is shown.Comment: 5 pages, 3 figur

### Criteria for unconditional entanglement purification

We show that the fidelity result of advantage distillation (Bennett et al,
Phys. Rev. Lett., 76, 722(1996)) is not only for the product state of raw
pairs, it is actually correct with whatever form of state of raw pairs. We then
give a general theorem for unconditional entanglement purification. This
theorem lists the conditions on which the fidelity result of a purification
protocol keeps unchanged from product form of raw-pair state and arbitrary form
of raw-pair state. Using this theorem, we find that all existing purification
puricfication can work for arbitrary initial state of raw pairs.Comment: The motivation and the title are change

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