17,191 research outputs found
On privacy amplification, lossy compression, and their duality to channel coding
We examine the task of privacy amplification from information-theoretic and
coding-theoretic points of view. In the former, we give a one-shot
characterization of the optimal rate of privacy amplification against classical
adversaries in terms of the optimal type-II error in asymmetric hypothesis
testing. This formulation can be easily computed to give finite-blocklength
bounds and turns out to be equivalent to smooth min-entropy bounds by Renner
and Wolf [Asiacrypt 2005] and Watanabe and Hayashi [ISIT 2013], as well as a
bound in terms of the divergence by Yang, Schaefer, and Poor
[arXiv:1706.03866 [cs.IT]]. In the latter, we show that protocols for privacy
amplification based on linear codes can be easily repurposed for channel
simulation. Combined with known relations between channel simulation and lossy
source coding, this implies that privacy amplification can be understood as a
basic primitive for both channel simulation and lossy compression. Applied to
symmetric channels or lossy compression settings, our construction leads to
proto- cols of optimal rate in the asymptotic i.i.d. limit. Finally, appealing
to the notion of channel duality recently detailed by us in [IEEE Trans. Info.
Theory 64, 577 (2018)], we show that linear error-correcting codes for
symmetric channels with quantum output can be transformed into linear lossy
source coding schemes for classical variables arising from the dual channel.
This explains a "curious duality" in these problems for the (self-dual) erasure
channel observed by Martinian and Yedidia [Allerton 2003; arXiv:cs/0408008] and
partly anticipates recent results on optimal lossy compression by polar and
low-density generator matrix codes.Comment: v3: updated to include equivalence of the converse bound with smooth
entropy formulations. v2: updated to include comparison with the one-shot
bounds of arXiv:1706.03866. v1: 11 pages, 4 figure
Asymmetric Protocols for Scalable High-Rate Measurement-Device-Independent Quantum Key Distribution Networks
Measurement-device-independent quantum key distribution (MDI-QKD) can
eliminate detector side channels and prevent all attacks on detectors. The
future of MDI-QKD is a quantum network that provides service to many users over
untrusted relay nodes. In a real quantum network, the losses of various
channels are different and users are added and deleted over time. To adapt to
these features, we propose a type of protocols that allow users to
independently choose their optimal intensity settings to compensate for
different channel losses. Such protocol enables a scalable high-rate MDI-QKD
network that can easily be applied for channels of different losses and allows
users to be dynamically added/deleted at any time without affecting the
performance of existing users.Comment: Changed the title to better represent the generality of our method,
and added more discussions on its application to alternative protocols (in
Sec. II, the new Table II, and Appendix E with new Fig. 9). Added more
conceptual explanations in Sec. II on the difference between X and Z bases in
MDI-QKD. Added additional discussions on security of the scheme in Sec. II
and Appendix
Weighted Norms of Ambiguity Functions and Wigner Distributions
In this article new bounds on weighted p-norms of ambiguity functions and
Wigner functions are derived. Such norms occur frequently in several areas of
physics and engineering. In pulse optimization for Weyl--Heisenberg signaling
in wide-sense stationary uncorrelated scattering channels for example it is a
key step to find the optimal waveforms for a given scattering statistics which
is a problem also well known in radar and sonar waveform optimizations. The
same situation arises in quantum information processing and optical
communication when optimizing pure quantum states for communicating in bosonic
quantum channels, i.e. find optimal channel input states maximizing the pure
state channel fidelity. Due to the non-convex nature of this problem the
optimum and the maximizers itself are in general difficult find, numerically
and analytically. Therefore upper bounds on the achievable performance are
important which will be provided by this contribution. Based on a result due to
E. Lieb, the main theorem states a new upper bound which is independent of the
waveforms and becomes tight only for Gaussian weights and waveforms. A
discussion of this particular important case, which tighten recent results on
Gaussian quantum fidelity and coherent states, will be given. Another bound is
presented for the case where scattering is determined only by some arbitrary
region in phase space.Comment: 5 twocolumn pages,2 figures, accepted for 2006 IEEE International
Symposium on Information Theory, typos corrected, some additional cites,
legend in Fig.2 correcte
Entropy Production of Doubly Stochastic Quantum Channels
We study the entropy increase of quantum systems evolving under primitive,
doubly stochastic Markovian noise and thus converging to the maximally mixed
state. This entropy increase can be quantified by a logarithmic-Sobolev
constant of the Liouvillian generating the noise. We prove a universal lower
bound on this constant that stays invariant under taking tensor-powers. Our
methods involve a new comparison method to relate logarithmic-Sobolev constants
of different Liouvillians and a technique to compute logarithmic-Sobolev
inequalities of Liouvillians with eigenvectors forming a projective
representation of a finite abelian group. Our bounds improve upon similar
results established before and as an application we prove an upper bound on
continuous-time quantum capacities. In the last part of this work we study
entropy production estimates of discrete-time doubly-stochastic quantum
channels by extending the framework of discrete-time logarithmic-Sobolev
inequalities to the quantum case.Comment: 24 page
Random quantum channels II: Entanglement of random subspaces, Renyi entropy estimates and additivity problems
In this paper we obtain new bounds for the minimum output entropies of random
quantum channels. These bounds rely on random matrix techniques arising from
free probability theory. We then revisit the counterexamples developed by
Hayden and Winter to get violations of the additivity equalities for minimum
output R\'enyi entropies. We show that random channels obtained by randomly
coupling the input to a qubit violate the additivity of the -R\'enyi
entropy. For some sequences of random quantum channels, we compute almost
surely the limit of their Schatten norms.Comment: 3 figures added, minor typos correcte
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