424 research outputs found
Context Tree Selection: A Unifying View
The present paper investigates non-asymptotic properties of two popular
procedures of context tree (or Variable Length Markov Chains) estimation:
Rissanen's algorithm Context and the Penalized Maximum Likelihood criterion.
First showing how they are related, we prove finite horizon bounds for the
probability of over- and under-estimation. Concerning overestimation, no
boundedness or loss-of-memory conditions are required: the proof relies on new
deviation inequalities for empirical probabilities of independent interest. The
underestimation properties rely on loss-of-memory and separation conditions of
the process.
These results improve and generalize the bounds obtained previously. Context
tree models have been introduced by Rissanen as a parsimonious generalization
of Markov models. Since then, they have been widely used in applied probability
and statistics
Deformed Statistics Kullback-Leibler Divergence Minimization within a Scaled Bregman Framework
The generalized Kullback-Leibler divergence (K-Ld) in Tsallis statistics
[constrained by the additive duality of generalized statistics (dual
generalized K-Ld)] is here reconciled with the theory of Bregman divergences
for expectations defined by normal averages, within a measure-theoretic
framework. Specifically, it is demonstrated that the dual generalized K-Ld is a
scaled Bregman divergence. The Pythagorean theorem is derived from the minimum
discrimination information-principle using the dual generalized K-Ld as the
measure of uncertainty, with constraints defined by normal averages. The
minimization of the dual generalized K-Ld, with normal averages constraints, is
shown to exhibit distinctly unique features.Comment: 16 pages. Iterative corrections and expansion
Equivalence between two-qubit entanglement and secure key distribution
We study the problem of secret key distillation from bipartite states in the
scenario where Alice and Bob can only perform measurements at the single-copy
level and classically process the obtained outcomes. Even with these
limitations, secret bits can be asymptotically distilled by the honest parties
from any two-qubit entangled state, under any individual attack. Our results
point out a complete equivalence between two-qubit entanglement and secure key
distribution: a key can be established through a one-qubit channel if and only
if it allows to distribute entanglement. These results can be generalized to
higher dimension for all those states that are one-copy distillable.Comment: 5 pages, REVTEX. Accepted version + added appendix. Proof of the main
result and discussion improved, conclusions unchange
Strong Secrecy for Multiple Access Channels
We show strongly secret achievable rate regions for two different wiretap
multiple-access channel coding problems. In the first problem, each encoder has
a private message and both together have a common message to transmit. The
encoders have entropy-limited access to common randomness. If no common
randomness is available, then the achievable region derived here does not allow
for the secret transmission of a common message. The second coding problem
assumes that the encoders do not have a common message nor access to common
randomness. However, they may have a conferencing link over which they may
iteratively exchange rate-limited information. This can be used to form a
common message and common randomness to reduce the second coding problem to the
first one. We give the example of a channel where the achievable region equals
zero without conferencing or common randomness and where conferencing
establishes the possibility of secret message transmission. Both coding
problems describe practically relevant networks which need to be secured
against eavesdropping attacks.Comment: 55 page
Classical no-cloning theorem under Liouville dynamics by non-Csisz\'ar f-divergence
The Csisz\'ar f-divergence, which is a class of information distances, is
known to offer a useful tool for analysing the classical counterpart of the
cloning operations that are quantum mechanically impossible for the factorized
and marginality classical probability distributions under Liouville dynamics.
We show that a class of information distances that does not belong to this
divergence class also allows for the formulation of a classical analogue of the
quantum no-cloning theorem. We address a family of nonlinear Liouville-like
equations, and generic distances, to obtain constraints on the corresponding
functional forms, associated with the formulation of classical analogue of the
no-cloning principle.Comment: 6 pages, revised, published versio
The Bregman chord divergence
Distances are fundamental primitives whose choice significantly impacts the
performances of algorithms in machine learning and signal processing. However
selecting the most appropriate distance for a given task is an endeavor.
Instead of testing one by one the entries of an ever-expanding dictionary of
{\em ad hoc} distances, one rather prefers to consider parametric classes of
distances that are exhaustively characterized by axioms derived from first
principles. Bregman divergences are such a class. However fine-tuning a Bregman
divergence is delicate since it requires to smoothly adjust a functional
generator. In this work, we propose an extension of Bregman divergences called
the Bregman chord divergences. This new class of distances does not require
gradient calculations, uses two scalar parameters that can be easily tailored
in applications, and generalizes asymptotically Bregman divergences.Comment: 10 page
Photon-Number-Splitting versus Cloning Attacks in Practical Implementations of the Bennett-Brassard 1984 protocol for Quantum Cryptography
In practical quantum cryptography, the source sometimes produces multi-photon
pulses, thus enabling the eavesdropper Eve to perform the powerful
photon-number-splitting (PNS) attack. Recently, it was shown by Curty and
Lutkenhaus [Phys. Rev. A 69, 042321 (2004)] that the PNS attack is not always
the optimal attack when two photons are present: if errors are present in the
correlations Alice-Bob and if Eve cannot modify Bob's detection efficiency, Eve
gains a larger amount of information using another attack based on a 2->3
cloning machine. In this work, we extend this analysis to all distances
Alice-Bob. We identify a new incoherent 2->3 cloning attack which performs
better than those described before. Using it, we confirm that, in the presence
of errors, Eve's better strategy uses 2->3 cloning attacks instead of the PNS.
However, this improvement is very small for the implementations of the
Bennett-Brassard 1984 (BB84) protocol. Thus, the existence of these new attacks
is conceptually interesting but basically does not change the value of the
security parameters of BB84. The main results are valid both for Poissonian and
sub-Poissonian sources.Comment: 11 pages, 5 figures; "intuitive" formula (31) adde
Exponential lower bound on the highest fidelity achievable by quantum error-correcting codes
On a class of memoryless quantum channels which includes the depolarizing
channel, the highest fidelity of quantum error-correcting codes of length n and
rate R is proven to be lower bounded by 1-exp[-nE(R)+o(n)] for some function
E(R). The E(R) is positive below some threshold R', which implies R' is a lower
bound on the quantum capacity.Comment: Ver.4. In vers.1--3, I claimed Theorem 1 for general quantum
channels. Now I claim this only for a slight generalization of depolarizing
channel in this paper because Lemma 2 in vers.1--3 was wrong; the original
general statement is proved in quant-ph/0112103. Ver.5. Text sectionalized.
Appeared in PRA. The PRA article is typographically slightly crude: The LaTeX
symbol star, used as superscripts, was capriciously replaced by the asterisk
in several places after my proof readin
Distributions attaining secret key at a rate of the conditional mutual information
© International Association for Cryptologic Research 2015. In this paper we consider the problem of extracting secret key from an eavesdropped source pXY Z at a rate given by the conditional mutual information. We investigate this question under three different scenarios: (i) Alice (X) and Bob (Y) are unable to communicate but share common randomness with the eavesdropper Eve (Z), (ii) Alice and Bob are allowed one-way public communication, and (iii) Alice and Bob are allowed two-way public communication. Distributions having a key rate of the conditional mutual information are precisely those in which a âhelpingâ Eve offers Alice and Bob no greater advantage for obtaining secret key than a fully adversarial one. For each of the above scenarios, strong necessary conditions are derived on the structure of distributions attaining a secret key rate of I(X: Y |Z). In obtaining our results, we completely solve the problem of secret key distillation under scenario (i) and identify H(S|Z) to be the optimal key rate using shared randomness, where S is the GĂ cs-Körner Common Information. We thus provide an operational interpretation of the conditional GĂ cs- Körner Common Information. Additionally, we introduce simple example distributions in which the rate I(X: Y |Z) is achievable if and only if two-way communication is allowed
Practical Evaluation of Security for Quantum Key Distribution
Many papers proved the security of quantum key distribution (QKD) system, in
the asymptotic framework. The degree of the security has not been discussed in
the finite coding-length framework, sufficiently. However, to guarantee any
implemented QKD system requires, it is needed to evaluate a protocol with a
finite coding-length. For this purpose, we derive a tight upper bound of the
eavesdropper's information. This bound is better than existing bounds. We also
obtain the exponential rate of the eavesdropper's information. Further, we
approximate our bound by using the normal distribution.Comment: The manuscript has been modfie
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