We introduce a minimax approach for characterizing the capacities of fully quantum arbitrarily varying channels (FQAVCs) under different shared resource models. In contrast to previous methods, our technique avoids de Finetti-type reductions, providing a more streamlined proof without dependency on the dimension of the jamming system. Consequently, we show that the entanglement-assisted and shared-randomness-assisted capacities of FQAVCs match those of the corresponding compound channels, even in the presence of general quantum adversaries.

We study the problem of quantum channel discrimination between two channels with an adversary input party (a.k.a. a jammer). This setup interpolates between the best-case channel discrimination as studied by (Wang & Wilde, 2019) and the worst-case channel discrimination as studied by (Fang, Fawzi, & Fawzi, 2025), thereby generalizing both frameworks. To address this problem, we introduce the notion of minimax channel divergence and establish several of its key mathematical properties. We prove the Stein's lemma in this new setting, showing that the optimal type-II error exponent in the asymptotic regime under parallel strategies is characterized by the regularized minimax channel divergence.

We determine the exact error and strong converse exponents of shared randomness-assisted channel simulation in worst case total-variation distance. Namely, we find that these exponents can be written as simple optimizations over the R´enyi channel mutual information. Strikingly, and in stark contrast to channel coding, there are no critical rates, allowing a tight characterization for arbitrary rates below and above the simulation capacity. We derive our results by asymptotically expanding the meta-converse for channel simulation [Caoet al., IEEE Trans. Inf. Theory (2024)], which corresponds to nonsignaling assisted codes. We prove this to be asymptotically tight by employing the approximation algorithms from [Bertaet al., Proc. IEEE ISIT (2024)], which show how to round any non-signaling assisted strategy to a strategy that only uses shared randomness. Notably, this implies that any additional quantum entanglement-assistance does not change the error or the strong converse exponents.

We determine the exact error and strong converse exponents of shared randomness-assisted channel simulation in worst case total-variation distance. Namely, we find that these exponents can be written as simple optimizations over the Rényi channel mutual information. Strikingly, and in stark contrast to channel coding, there are no critical rates, allowing a tight characterization for arbitrary rates below and above the simulation capacity.

Characterizing the minimal communication needed for quantum channel simulation is a fundamental task in the quantum information theory. In this paper, we show that, in fidelity, the quantum channel simulation can be directly achieved via quantum state splitting without using a technique known as the de Finetti reduction, and thus provide a pair of tighter one-shot bounds. This opens up new potentials for higher-order analysis. Using the bounds, we also recover the quantum reverse Shannon theorem in a much simpler way.

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.

We study the problem of random-assisted simulation of discrete broadcast channel in one-shot and i.i.d. setups. We derive one-shot inner and outer bounds of the set of attainable message-size pairs for simulating WYZ|Xwithin some total variation distance (TVD) tolerance of ϵ. The inner bounds are based on the bipartite convex split lemma. Whereas the outer bounds are based on the properties of the multi-partite max information. Using these bounds, we establish a single-letter expression of the simulation region of a broadcast channel.

The quadratic decaying property of the information rate function states that, given a fixed conditional distribution$p_{ \mathsf {Y}| \mathsf {X}}$, the mutual information between the (finite) discrete random variables$\mathsf {X}$and$\mathsf {Y}$decreases at least quadratically in the Euclidean distance as$p_{\mathsf {X}}$moves away from the capacity-achieving input distributions. It is a property of the information rate function that is particularly useful in the study of higher order asymptotics and finite blocklength information theory, where it was already implicitly used by Strassen (1962) and later, more explicitly, by Polyanskiy–Poor–Verdú (2010). However, the proofs outlined in both works contain gaps that are nontrivial to close. This comment provides an alternative, complete proof of this property.

We study the problem of one-shot channel simulation of DMCs with unlimited shared randomness. For any fixed tolerance measured in total variational distance, we propose an achievability bound and a converse bound on the size of the code to simulate the channel. The achievability bound utilizes the convex split lemma, whereas the converse bound is the result of the relationships between smoothed max-divergences and the max-mutual information. The achievability proof does not rely on a "universal state" (compared with some previous related works), and provides a tighter bound. Using the two bounds, we also provide an alternative proof to the reverse Shannon theorem.

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.

We are interested in classical communication over a quantum channel with memory, in particular, we are interested in quantum-auxiliary-channel-based upper and lower bounds on the information rate. Toward improving these bounds, we propose efficient algorithms for optimizing the auxiliary channel. From a practical perspective, the lower bounds are of significant interest because they represent mismatched information rates, i.e., information rates that are achievable by a communication system where the decoder is matched to the auxiliary channel, instead of the original channel. 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.

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 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 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.

Some of the most interesting quantities associated with a factor graph are its marginals and its partition sum. For factor graphs 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 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 kernel functions. 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.