Estimating the Information Rate of a Channel with Classical Input and Output and a Quantum State (Extended Version)

We consider the problem of transmitting classical information over a time-invariant channel with memory. A popular class of time-invariant channels with memory are finite-state-machine channels, where a \emph{classical} state evolves over time and governs the relationship between the classical input and the classical output of the channel. For such channels, various techniques have been developed for estimating and bounding the information rate. In this paper we consider a class of time-invariant channels where a \emph{quantum} state evolves over time and governs the relationship between the classical input and the classical output of the channel. We propose algorithms for estimating and bounding the information rate of such channels. In particular, we discuss suitable graphical models for doing the relevant computations.Comment: This is an extended version of a paper that appears in Proc. 2017 IEEE International Symposium on Information Theory, Aachen, Germany, June 201

Bounding and Estimating the Classical Information Rate of Quantum Channels with Memory

We consider the scenario of classical communication over a finite-dimensional quantum channel with memory using a separable-state input ensemble and local output measurements. We propose algorithms for estimating the information rate of such communication setups, along with algorithms for bounding the information rate based on so-called auxiliary channels. Some of the algorithms are extensions of their counterparts for (classical) finite-state-machine channels. Notably, we discuss suitable graphical models for doing the relevant computations. Moreover, the auxiliary channels are learned in a data-driven approach; i.e., only input/output sequences of the true channel are needed, but not the channel model of the true channel.Comment: This work has been submitted to the IEEE Transactions on Information Theory for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Factor Graphs for Quantum Information Processing

[...] In this thesis, we are interested in generalizing factor graphs and the relevant methods toward describing quantum systems. Two generalizations of classical graphical models are investigated, namely double-edge factor graphs (DeFGs) and quantum factor graphs (QFGs). Conventionally, a factor in a factor graph represents a nonnegative real-valued local functions. Two different approaches to generalize factors in classical factor graphs yield DeFGs and QFGs, respectively. We proposed/re-proposed and analyzed generalized versions of belief-propagation algorithms for DeFGs/QFGs. As a particular application of the DeFGs, we investigate the information rate and their upper/lower bounds of classical communications over quantum channels with memory. In this study, we also propose a data-driven method for optimizing the upper/lower bounds on information rate.Comment: This is the finial version of the thesis of Michael X. Cao submitted in April 2021 in partial fulfillment of the requirements for the degree of doctor of philosophy in information engineering at the Chinese university of Hong Kon

Security Against Collective Attacks of a Modified BB84 QKD Protocol with Information only in One Basis

The Quantum Key Distribution (QKD) protocol BB84 has been proven secure against several important types of attacks: the collective attacks and the joint attacks. Here we analyze the security of a modified BB84 protocol, for which information is sent only in the z basis while testing is done in both the z and the x bases, against collective attacks. The proof follows the framework of a previous paper (Boyer, Gelles, and Mor, 2009), but it avoids the classical information-theoretical analysis that caused problems with composability. We show that this modified BB84 protocol is as secure against collective attacks as the original BB84 protocol, and that it requires more bits for testing.Comment: 6 pages; 1 figur

Quantum logarithmic Sobolev inequalities and rapid mixing

A family of logarithmic Sobolev inequalities on finite dimensional quantum state spaces is introduced. The framework of non-commutative \bL_p-spaces is reviewed and the relationship between quantum logarithmic Sobolev inequalities and the hypercontractivity of quantum semigroups is discussed. This relationship is central for the derivation of lower bounds for the logarithmic Sobolev (LS) constants. Essential results for the family of inequalities are proved, and we show an upper bound to the generalized LS constant in terms of the spectral gap of the generator of the semigroup. These inequalities provide a framework for the derivation of improved bounds on the convergence time of quantum dynamical semigroups, when the LS constant and the spectral gap are of the same order. Convergence bounds on finite dimensional state spaces are particularly relevant for the field of quantum information theory. We provide a number of examples, where improved bounds on the mixing time of several semigroups are obtained; including the depolarizing semigroup and quantum expanders.Comment: Updated manuscript, 30 pages, no figure

Device independent quantum key distribution secure against coherent attacks with memoryless measurement devices

Device independent quantum key distribution aims to provide a higher degree of security than traditional QKD schemes by reducing the number of assumptions that need to be made about the physical devices used. The previous proof of security by Pironio et al. applies only to collective attacks where the state is identical and independent and the measurement devices operate identically for each trial in the protocol. We extend this result to a more general class of attacks where the state is arbitrary and the measurement devices have no memory. We accomplish this by a reduction of arbitrary adversary strategies to qubit strategies and a proof of security for qubit strategies based on the previous proof by Pironio et al. and techniques adapted from Renner.Comment: 13 pages. Expanded main proofs with more detail, miscellaneous edits for clarit

Fundamental And Practical Problems of QKD Security - the Actual and the Perceived Situation

It is widely believed that quantum key distribution (QKD) has been proved unconditionally secure for realistic models applicable to various current experimental schemes. Here we summarize briefly why this is not the case, from both the viewpoints of fundamental quantitative security and applicable models of security analysis, with some morals drawn.Comment: This paper is being revised. It will appear later. 14 pages, 2 figure