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We study channel simulation under common randomness assistance in the finite-blocklength regime and identify the smooth channel max-information as a linear program one-shot converse on the minimal simulation cost for fixed error tolerance. We show that this one-shot converse can be achieved exactly using no-signaling-assisted codes, and approximately achieved using common randomness-assisted codes. Our one-shot converse thus takes on an analogous role to the celebrated meta-converse in the complementary problem of channel coding, and we find tight relations between these two bounds. We asymptotically expand our bounds on the simulation cost for discrete memoryless channels, leading to the second-order as well as the moderate deviation rate expansion, which can be expressed in terms of the channel capacity and channel dispersion known from noisy channel coding. Our bounds imply the well-known fact that the optimal asymptotic rate of one channel to simulate another under common randomness assistance is given by the ratio of their respective capacities. Additionally, our higher-order asymptotic expansion shows that this reversibility falls apart in the second order. Our techniques extend to discrete memoryless broadcast channels. In stark contrast to the elusive broadcast channel capacity problem, we show that the reverse problem of broadcast channel simulation under common randomness assistance allows for an efficiently computable single-letter characterization of the asymptotic rate region in terms of the broadcast channel's multipartite mutual information., Comment: 38 pages, 6 figures

The moderate deviation regime is concerned with the finite block length trade-off between communication cost and error for information processing tasks in the asymptotic regime, where the communication cost approaches a capacity-like quantity and the error vanishes at the same time. We find exact characterisations of these trade-offs for a variety of fully quantum communication tasks, including quantum source coding, quantum state splitting, entanglement-assisted quantum channel coding, and entanglement-assisted quantum channel simulation. The main technical tool we derive is a tight relation between the partially smoothed max-information and the hypothesis testing relative entropy. This allows us to obtain the expansion of the partially smoothed max-information for i.i.d. states in the moderate deviation regime., Comment: 32 pages

The capacity of noisy quantum channels characterizes the highest rate at which information can be reliably transmitted and it is therefore of practical as well as fundamental importance. Capacities of classical channels are computed using alternating optimization schemes, called Blahut-Arimoto algorithms. In this work, we generalize classical Blahut-Arimoto algorithms to the quantum setting. In particular, we give efficient iterative schemes to compute the capacity of channels with classical input and quantum output, the quantum capacity of less noisy channels, the thermodynamic capacity of quantum channels, as well as the entanglement-assisted capacity of quantum channels. We give rigorous a priori and a posteriori bounds on the estimation error by employing quantum entropy inequalities and demonstrate fast convergence of our algorithms in numerical experiments., Comment: v4: 22 pages, 4 figures, new title

A linear unsaturating magnetoresistance at high perpendicular magnetic fields, together with a quadratic positive magnetoresistance at low fields, has been seen in many different experimental materials, ranging from silver chalcogenides and thin films of InSb to topological materials like graphene and Dirac semimetals. In the literature, two very different theoretical approaches have been used to explain this classical magnetoresistance as a consequence of sample disorder. The phenomenological Random Resistor Network model constructs a grid of four-terminal resistors, each with a varying random resistance. The Effective Medium Theory model imagines a smoothly varying disorder potential that causes a continuous variation of the local conductivity. Here, we demonstrate numerically that both models belong to the same universality class and that a restricted class of the Random Resistor Network is actually equivalent to the Effective Medium Theory. Both models are also in good agreement with experiments on a diverse range of materials. Moreover, we show that in both cases, a single parameter, i.e. the ratio of the fluctuations in the carrier density to the average carrier density, completely determines the magnetoresistance profile., Comment: 6 pages, 5 figures

We theoretically investigate the transport and magnetotransport properties of three-dimensional Weyl semimetals. Using the RPA-Boltzmann transport scattering theory for electrons scattering off randomly distributed charged impurities, together with an effective medium theory to average over the resulting spatially inhomogeneous carrier density, we smoothly connect our results for the minimum conductivity near the Weyl point with known results for the conductivity at high carrier density. In the presence of a non-quantizing magnetic field, we predict that for both high and low carrier densities, Weyl semimetals show a transition from quadratic magnetoresistance (MR) at low magnetic fields to linear MR at high magnetic fields, and that the magnitude of the MR > 10 for realistic parameters. Our results are in quantitative agreement with recent unexpected experimental observations on the mixed-chalcogenide compound TlBiSSe., Comment: 5 pages, 5 figures

We describe the interaction of two two-level atoms in free space with propagating modes of the quantized electromagnetic field, using the time-dependent Heisenberg-Langevin method. For single- photon pulses, we consider the effect of the pulse's spatial and temporal profiles on the atomic excitation. In particular, we find the ideal shape for a pulse to put exactly one excitation in any desired state of the bi-atomic system. Furthermore, we analyze the differences in the atomic dynamics between the cases of Fock state pulses and coherent state pulses., Comment: 8 figures

We predict and demonstrate that a disorder induced carrier density inhomogeneity causes magnetoresistance (MR) in a two-dimensional electron system. Our experiments on graphene show a quadratic MR persisting far from the charge neutrality point. Effective medium calculations show that for charged impurity disorder, the low-field MR is a universal function of the ratio of carrier density to fluctuations in carrier density, a power-law when this ratio is large, in excellent agreement with experiment. The MR is generic and should occur in other materials with large carrier density inhomogeneity.