Double-Edge Factor Graphs: Definition, Properties, and Examples

Some of the most interesting quantities associated with a factor graph are its marginals and its partition sum. For factor graphs \emph{without cycles} and moderate message update complexities, the sum-product algorithm (SPA) can be used to efficiently compute these quantities exactly. Moreover, for various classes of factor graphs \emph{with cycles}, the SPA has been successfully applied to efficiently compute good approximations to these quantities. Note that in the case of factor graphs with cycles, the local functions are usually non-negative real-valued functions. In this paper we introduce a class of factor graphs, called double-edge factor graphs (DE-FGs), which allow local functions to be complex-valued and only require them, in some suitable sense, to be positive semi-definite. We discuss various properties of the SPA when running it on DE-FGs and we show promising numerical results for various example DE-FGs, some of which have connections to quantum information processing.Comment: Submitte

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

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

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

Calcium release through P2X4 activates calmodulin to promote endolysosomal membrane fusion

Intra-endolysosomal Ca(2+) release is required for endolysosomal membrane fusion with intracellular organelles. However, the molecular mechanisms for intra-endolysosomal Ca(2+) release and the downstream Ca(2+) targets involved in the fusion remain elusive. Previously, we demonstrated that endolysosomal P2X4 forms channels activated by luminal adenosine triphosphate in a pH-dependent manner. In this paper, we show that overexpression of P2X4, as well as increasing endolysosomal P2X4 activity by alkalinization of endolysosome lumen, promoted vacuole enlargement in cells and endolysosome fusion in a cell-free assay. These effects were prevented by inhibiting P2X4, expressing a dominant-negative P2X4 mutant, and disrupting the P2X4 gene. We further show that P2X4 and calmodulin (CaM) form a complex at endolysosomal membrane where P2X4 activation recruits CaM to promote fusion and vacuolation in a Ca(2+)-dependent fashion. Moreover, P2X4 activation-triggered fusion and vacuolation were suppressed by inhibiting CaM. Our data thus suggest a new molecular mechanism for endolysosomal membrane fusion involving P2X4-mediated endolysosomal Ca(2+) release and subsequent CaM activation

Exceptional electronic transport and quantum oscillations in thin bismuth crystals grown inside van der Waals materials

Confining materials to two-dimensional forms changes the behavior of electrons and enables new devices. However, most materials are challenging to produce as uniform thin crystals. Here, we present a new synthesis approach where crystals are grown in a nanoscale mold defined by atomically-flat van der Waals (vdW) materials. By heating and compressing bismuth in a vdW mold made of hexagonal boron nitride (hBN), we grow ultraflat bismuth crystals less than 10 nanometers thick. Due to quantum confinement, the bismuth bulk states are gapped, isolating intrinsic Rashba surface states for transport studies. The vdW-molded bismuth shows exceptional electronic transport, enabling the observation of Shubnikov-de Haas quantum oscillations originating from the (111) surface state Landau levels, which have eluded previous studies. By measuring the gate-dependent magnetoresistance, we observe multi-carrier quantum oscillations and Landau level splitting, with features originating from both the top and bottom surfaces. Our vdW-mold growth technique establishes a platform for electronic studies and control of bismuth's Rashba surface states and topological boundary modes. Beyond bismuth, the vdW-molding approach provides a low-cost way to synthesize ultrathin crystals and directly integrate them into a vdW heterostructure