83 research outputs found
Resource cost results for one-way entanglement distillation and state merging of compound and arbitrarily varying quantum sources
We consider one-way quantum state merging and entanglement distillation under
compound and arbitrarily varying source models. Regarding quantum compound
sources, where the source is memoryless, but the source state an unknown member
of a certain set of density matrices, we continue investigations begun in the
work of Bjelakovi\'c et. al. [Universal quantum state merging, J. Math. Phys.
54, 032204 (2013)] and determine the classical as well as entanglement cost of
state merging. We further investigate quantum state merging and entanglement
distillation protocols for arbitrarily varying quantum sources (AVQS). In the
AVQS model, the source state is assumed to vary in an arbitrary manner for each
source output due to environmental fluctuations or adversarial manipulation. We
determine the one-way entanglement distillation capacity for AVQS, where we
invoke the famous robustification and elimination techniques introduced by R.
Ahlswede. Regarding quantum state merging for AVQS we show by example, that the
robustification and elimination based approach generally leads to suboptimal
entanglement as well as classical communication rates.Comment: Improved presentation. Close to the published version. Results
unchanged. 25 pages, 0 figure
Joint exceedances of random products
We analyze the joint extremal behavior of random products of the form
for non-negative, independent
regularly varying random variables and general coefficients
. Products of this form appear for example if one
observes a linear time series with gamma type innovations at points in
time. We combine arguments of linear optimization and a generalized concept of
regular variation on cones to show that the asymptotic behavior of joint
exceedance probabilities of these products is determined by the solution of a
linear program related to the matrix
Conditional Extreme Value Models: Fallacies and Pitfalls
Conditional extreme value models have been introduced by Heffernan and
Resnick (2007) to describe the asymptotic behavior of a random vector as one
specific component becomes extreme. Obviously, this class of models is related
to classical multivariate extreme value theory which describes the behavior of
a random vector as its norm (and therefore at least one of its components)
becomes extreme. However, it turns out that this relationship is rather subtle
and sometimes contrary to intuition. We clarify the differences between the two
approaches with the help of several illuminative (counter)examples.
Furthermore, we discuss marginal standardization, which is a useful tool in
classical multivariate extreme value theory but, as we point out, much less
straightforward and sometimes even obscuring in conditional extreme value
models. Finally, we indicate how, in some situations, a more comprehensive
characterization of the asymptotic behavior can be obtained if the conditions
of conditional extreme value models are relaxed so that the limit is no longer
unique.Comment: 22 page
Resource Cost Results for Entanglement Distillation and State Merging under Source Uncertainties
We introduce one-way LOCC protocols for quantum state merging for compound
sources, which have asymptotically optimal entanglement as well as classical
communication resource costs. For the arbitrarily varying quantum source (AVQS)
model, we determine the one-way entanglement distillation capacity, where we
utilize the robustification and elimination techniques, well-known from
classical as well as quantum channel coding under assumption of arbitrarily
varying noise. Investigating quantum state merging for AVQS, we demonstrate by
example, that the usual robustification procedure leads to suboptimal resource
costs in this case.Comment: 5 pages, 0 figures. Accepted for presentation at the IEEE ISIT 2014
Honolulu. This is a conference version of arXiv:1401.606
Simultaneous transmission of classical and quantum information under channel uncertainty and jamming attacks
We derive universal codes for simultaneous transmission of classical messages
and entanglement through quantum channels, possibly under attack of a malignant
third party. These codes are robust to different kinds of channel uncertainty.
To construct such universal codes, we invoke and generalize properties of
random codes for classical and quantum message transmission through quantum
channels. We show these codes to be optimal by giving a multi-letter
characterization of regions corresponding to the capacity of compound quantum
channels for simultaneously transmitting and generating entanglement with
classical messages. Also, we give dichotomy statements in which we characterize
the capacity of arbitrarily varying quantum channels for simultaneous
transmission of classical messages and entanglement. These include cases where
the malignant jammer present in the arbitrarily varying channel model is
classical (chooses channel states of product form) and fully quantum (is
capable of general attacks not necessarily of product form)
Entanglement-assisted classical capacities of compound and arbitrarily varying quantum channels
We consider classical message transmission under entanglement assistance for
compound memoryless and arbitrarily varying quantum channels. In both cases, we
prove general coding theorems together with corresponding weak converse bounds.
In this way, we obtain single-letter characterizations of the
entanglement-assisted classical capacities for both channel models. Moreover,
we show that the entanglement-assisted classical capacity does exhibit no
strong converse property for some compound quantum channels for the average as
well as the maximal error criterion. A strong converse to the
entanglement-assisted classical capacities does hold for each arbitrarily
varying quantum channel.Comment: Minor corrections, results unchanged, presentation updated, 21 pages,
0 figures, accepted for publication in Quant. Inf. Pro
Randomness cost of symmetric twirling
We study random unitary channels which reproduce the action of the twirling
channel corresponding to the representation of the symmetric groupon an n-fold
tensor product. We derive upper andlower bounds on the randomness cost of
implementing such a map which depend exponentially on the number of systems.
Consequently, symmetrictwirling can be regarded as a reasonable Shannon
theoretic protocol. On the other hand, such protocols are disqualified by their
resource-inefficiency in situations where randomness is a costly resource.Comment: 8 pages, 2 figure
Universal superposition codes: capacity regions of compound quantum broadcast channel with confidential messages
We derive universal codes for transmission of broadcast and confidential
messages over classical-quantum-quantum and fully quantum channels. These codes
are robust to channel uncertainties considered in the compound model. To
construct these codes we generalize random codes for transmission of public
messages, to derive a universal superposition coding for the compound quantum
broadcast channel. As an application, we give a multi-letter characterization
of regions corresponding to the capacity of the compound quantum broadcast
channel for transmitting broadcast and confidential messages simultaneously.
This is done for two types of broadcast messages, one called public and the
other common
Arbitrarily varying and compound classical-quantum channels and a note on quantum zero-error capacities
We consider compound as well as arbitrarily varying classical-quantum channel
models. For classical-quantum compound channels, we give an elementary proof of
the direct part of the coding theorem. A weak converse under average error
criterion to this statement is also established. We use this result together
with the robustification and elimination technique developed by Ahlswede in
order to give an alternative proof of the direct part of the coding theorem for
a finite classical-quantum arbitrarily varying channels with the criterion of
success being average error probability. Moreover we provide a proof of the
strong converse to the random coding capacity in this setting.The notion of
symmetrizability for the maximal error probability is defined and it is shown
to be both necessary and sufficient for the capacity for message transmission
with maximal error probability criterion to equal zero. Finally, it is shown
that the connection between zero-error capacity and certain arbitrarily varying
channels is, just like in the case of quantum channels, only partially valid
for classical-quantum channels.Comment: 37 pages, 0 figures. Accepted for publication in the LNCS Volume in
Memory of Rudolf Ahlswede. Includes a section on certain differences between
classical and classical-quantum channels regarding their zero-error
capacitie
On a minimum distance procedure for threshold selection in tail analysis
Power-law distributions have been widely observed in different areas of
scientific research. Practical estimation issues include how to select a
threshold above which observations follow a power-law distribution and then how
to estimate the power-law tail index. A minimum distance selection procedure
(MDSP) is proposed in Clauset et al. (2009) and has been widely adopted in
practice, especially in the analyses of social networks. However, theoretical
justifications for this selection procedure remain scant. In this paper, we
study the asymptotic behavior of the selected threshold and the corresponding
power-law index given by the MDSP. We find that the MDSP tends to choose too
high a threshold level and leads to Hill estimates with large variances and
root mean squared errors for simulated data with Pareto-like tails
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