Concavity of the Auxiliary Function for Classical-Quantum Channels

© 2016 IEEE. The auxiliary function of a classical channel appears in two fundamental quantities, the random coding exponent and the sphere-packing exponent, which yield upper and lower bounds on the error probability of decoding, respectively. A crucial property of the auxiliary function is its concavity, and this property consequently leads to several important results in finite blocklength analysis. In this paper, we prove that the auxiliary function of a classical-quantum channel also enjoys the same concavity property, extending an earlier partial result to its full generality. We also prove that the auxiliary function satisfies the data-processing inequality, among various other important properties. Furthermore, we show that the concavity property of the auxiliary function enables a geometric interpretation of the random coding exponent and the sphere-packing exponent of a classical-quantum channel. The key component in our proof is an important result from the theory of matrix geometric means

Characterizations of matrix and operator-valued Φ-entropies, and operator Efron-Stein inequalities

© 2016 The Author(s). We derive new characterizations of the matrix Φ-entropy functionals introduced in Chen & Tropp (Chen, Tropp 2014 Electron. J. Prob. 19, 1-30. (doi:10.1214/ejp.v19-2964)). These characterizations help us to better understand the properties of matrix Φ-entropies, and are a powerful tool for establishing matrix concentration inequalities for random matrices. Then, we propose an operator-valued generalization of matrix Φ-entropy functionals, and prove the subadditivity under Löwner partial ordering. Our results demonstrate that the subadditivity of operator-valued Φ-entropies is equivalent to the convexity. As an application, we derive the operator Efron-Stein inequality

Complete Mapping of Substrate Translocation Highlights the Role of LeuT N-terminal Segment in Regulating Transport Cycle

Neurotransmitter: sodium symporters (NSSs) regulate neuronal signal transmission by clearing excess neurotransmitters from the synapse, assisted by the co-transport of sodium ions. Extensive structural data have been collected in recent years for several members of the NSS family, which opened the way to structure-based studies for a mechanistic understanding of substrate transport. Leucine transporter (LeuT), a bacterial orthologue, has been broadly adopted as a prototype in these studies. This goal has been elusive, however, due to the complex interplay of global and local events as well as missing structural data on LeuT N-terminal segment. We provide here for the first time a comprehensive description of the molecular events leading to substrate/Na+ release to the postsynaptic cell, including the structure and dynamics of the N-terminal segment using a combination of molecular simulations. Substrate and Na+-release follows an influx of water molecules into the substrate/Na+-binding pocket accompanied by concerted rearrangements of transmembrane helices. A redistribution of salt bridges and cation-π interactions at the N-terminal segment prompts substrate release. Significantly, substrate release is followed by the closure of the intracellular gate and a global reconfiguration back to outward-facing state to resume the transport cycle. Two minimally hydrated intermediates, not structurally resolved to date, are identified: one, substrate-bound, stabilized during the passage from outward- to inward-facing state (holo-occluded), and another, substrate-free, along the reverse transition (apo-occluded)

Moderate deviation analysis for classical-quantum channels and quantum hypothesis testing

© 1963-2012 IEEE. In this paper, we study the tradeoffs between the error probabilities of classical-quantum channels and the blocklength n when the transmission rates approach the channel capacity at a rate lower than 1 {n} , a research topic known as moderate deviation analysis. We show that the optimal error probability vanishes under this rate convergence. Our main technical contributions are a tight quantum sphere-packing bound, obtained via Chaganty and Sethuraman's concentration inequality in strong large deviation theory, and asymptotic expansions of error-exponent functions. Moderate deviation analysis for quantum hypothesis testing is also established. The converse directly follows from our channel coding result, while the achievability relies on a martingale inequality

The learnability of unknown quantum measurements

© Rinton Press. In this work, we provide an elegant framework to analyze learning matrices in the Schatten class by taking advantage of a recently developed methodology—matrix concentration inequalities. We establish the fat-shattering dimension, Rademacher/Gaussian complexity, and the entropy number of learning bounded operators and trace class operators. By characterising the tasks of learning quantum states and two-outcome quantum measurements into learning matrices in the Schatten-1 and ∞ classes, our proposed approach directly solves the sample complexity problems of learning quantum states and quantum measurements. Our main result in the paper is that, for learning an unknown quantum measurement, the upper bound, given by the fat-shattering dimension, is linearly proportional to the dimension of the underlying Hilbert space. Learning an unknown quantum state becomes a dual problem to ours, and as a byproduct, we can recover Aaronson’s famous result [Proc. R. Soc. A 463, 3089–3144 (2007)] solely using a classical machine learning technique. In addition, other famous complexity measures like covering numbers and Rademacher/Gaussian complexities are derived explicitly under the same framework. We are able to connect measures of sample complexity with various areas in quantum information science, e.g. quantum state/measurement tomography, quantum state discrimination and quantum random access codes, which may be of independent interest. Lastly, with the assistance of general Bloch-sphere representation, we show that learning quantum measurements/states can be mathematically formulated as a neural network. Consequently, classical ML algorithms can be applied to efficiently accomplish the two quantum learning tasks

Quantum Sphere-Packing Bounds with Polynomial Prefactors

© 1963-2012 IEEE. We study lower bounds on the optimal error probability in classical coding over classical-quantum channels at rates below the capacity, commonly termed quantum sphere-packing bounds. Winter and Dalai have derived such bounds for classical-quantum channels; however, the exponents in their bounds only coincide when the channel is classical. In this paper, we show that these two exponents admit a variational representation and are related by the Golden-Thompson inequality, reaffirming that Dalai's expression is stronger in general classical-quantum channels. Second, we establish a finite blocklength sphere-packing bound for classical-quantum channels, which significantly improves Dalai's prefactor from the order of subexponential to polynomial. Furthermore, the gap between the obtained error exponent for constant composition codes and the best known classical random coding exponent vanishes in the order of $o(\log n / n)$ , indicating our sphere-packing bound is almost exact in the high rate regime. Finally, for a special class of symmetric classical-quantum channels, we can completely characterize its optimal error probability without the constant composition code assumption. The main technical contributions are two converse Hoeffding bounds for quantum hypothesis testing and the saddle-point properties of error exponent functions

Sphere-packing bound for symmetric classical-quantum channels

© 2017 IEEE. "To be considered for the 2017 IEEE Jack Keil Wolf ISIT Student Paper Award." We provide a sphere-packing lower bound for the optimal error probability in finite blocklengths when coding over a symmetric classical-quantum channel. Our result shows that the pre-factor can be significantly improved from the order of the subexponential to the polynomial, This established pre-factor is arguably optimal because it matches the best known random coding upper bound in the classical case. Our approaches rely on a sharp concentration inequality in strong large deviation theory and crucial properties of the error-exponent function

Exponential decay of matrix Φ-entropies on Markov semigroups with applications to dynamical evolutions of quantum ensembles

In this work, we extend the theory of quantum Markov processes on a single quantum state to a broader theory that covers Markovian evolution of an ensemble of quantum states, which generalizes Lindblad's formulation of quantum dynamical semigroups. Our results establish the equivalence between an exponential decrease of the matrix Φ-entropies and the Φ-Sobolev inequalities, which allows us to characterize the dynamical evolution of a quantum ensemble to its equilibrium. In particular, we study the convergence rates of two special semigroups, namely, the depolarizing channel and the phase-damping channel. In the former, since there exists a unique equilibrium state, we show that the matrix Φ-entropy of the resulting quantum ensemble decays exponentially as time goes on. Consequently, we obtain a stronger notion of monotonicity of the Holevo quantity-the Holevo quantity of the quantum ensemble decays exponentially in time and the convergence rate is determined by the modified log-Sobolev inequalities. However, in the latter, the matrix Φ-entropy of the quantum ensemble that undergoes the phase-damping Markovian evolution generally will not decay exponentially. There is no classical analogy for these different equilibrium situations. Finally, we also study a statistical mixing of Markov semigroups on matrix-valued functions. We can explicitly calculate the convergence rate of a Markovian jump process defined on Boolean hypercubes and provide upper bounds to the mixing time. Published by AIP Publishing

A γA-Crystallin Mouse Mutant Secc with Small Eye, Cataract and Closed Eyelid

published_or_final_versio

Fourier domain mode locking laser based on two-pump optical parametric amplification

We present a Fourier domain mode locked (FDML) laser scanning from 1540 to 1570 using two-pump optical parametric amplifier (OPA) as the gain medium. The sweep rate of 39.683 kHz is achieved. © 2010 IEEE.published_or_final_versionThe IEEE Photonics Society Summer Topical Meetings, Playa del Carmen, Mexico, 19-21 July 2010. In Proceedings of PHOSST, 2010, p. 186-18