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arXiv:2507.18259 · IEEE Information Theory Workshop (ITW)

Data Transmission over a Bosonic Arbitrarily Varying Quantum Channel

Janis Nötzel, Florian Seitz

Published Sep 29, 2025• 1 citation
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Abstract

Arbitrarily varying channels offer a powerful framework for analyzing the robustness of quantum communication systems, especially for classical-quantum models, where the analysis displays strengths or weaknesses of specific signal constellations under generic attacks. In this work, we provide a coding theorem for a large class of practically relevant arbitrarily varying channel models. Namely, we give an explicit capacity formula for the lossy bosonic channel subject to semi-classical attacks, where an adversary injects semi-classical states into the transmission line. Mathematically, this is modeled via a beam-splitter setup, with transmitter and jammer controlling different input ports and the receiver observing one output port. We show how a recently conjectured new quantum entropy power inequality relates to our capacity formula.

DOI
10.1109/itw62417.2025.11240401

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Arbitrarily varying channels offer a powerful framework for analyzing the robustness of quantum communication systems, especially for classical-quantum models, where the analysis displays strengths or weaknesses of specific signal constellations under generic attacks. In this work, we provide a coding theorem for a large class of practically relevant arbitrarily varying channel models. Namely, we give an explicit capacity formula for the lossy bosonic channel subject to semi-classical attacks, where an adversary injects semi-classical states into the transmission line. Mathematically, this is modeled via a beam-splitter setup, with transmitter and jammer controlling different input ports and the receiver observing one output port. We show how a recently conjectured new quantum entropy power inequality relates to our capacity formula.
Compound channels model situations where a sender and receiver both have only partial information about the stationary channel they are transmitting over. They can be used to analyse the robustness of a communication system. With this work we provide a coding theorem for a class of practically relevant quantum compound channel models, where we consider the system uncertainty as due to a stationary but unknown jamming signal. Namely, we give an explicit formula for the case of the lossy Bosonic channel in the presence of a semi-classical attack utilizing the injection of coherent states into the transmission line. Mathematically, this is modelled by letting transmitter and jammer access the two different ports of a beam-splitter, and the receiver observe one of the output ports. While the transmitter can modulate their input, the jammer must transmit a constant (but unknown) sequence of states. We conjecture a new quantum entropy power inequality and show its relation to the capacity under study.
In this paper, a new model for arbitrarily varying classical-quantum channels is proposed. In this model, a jammer has side information. The communication scenario in which a jammer can select only classical inputs as a jamming sequence is considered in the first part of the paper. This situation corresponds to the standard model of arbitrarily varying classical-quantum channels. Two scenarios are considered. In the first scenario, the jammer knows the channel input, while in the second scenario the jammer knows both the channel input and the message. The transmitter and receiver share a secret random key with a vanishing key rate. The capacity for both average and maximum error criteria for both scenarios is determined in this paper. A strong converse is also proved. It is shown that all these corresponding capacities are equal, which means that additionally revealing the message to the jammer does not change the capacity. The communication scenario with a fully quantum jammer is considered in the second part of the paper. A single letter characterization for the capacity with secret random key as assistance for both average and maximum error criteria is derived in the paper.
We consider a model of communication via a fully quantum jammer channel with quantum jammer, quantum sender and quantum receiver, which we dub quantum arbitrarily varying channel (QAVC). Restricting to finite dimensional user and jammer systems, we show, using permutation symmetry and a de Finetti reduction, how the random coding capacity (classical and quantum) of the QAVC is reduced to the capacity of a naturally associated compound channel, which is obtained by restricting the jammer to i.i.d. input states. Furthermore, we demonstrate that the shared randomness required is at most logarithmic in the block length, via a quantum version of the “elimination of of correlation” using a random matrix tail bound. This implies a dichotomy theorem: either the classical capacity of the QAVC is zero, and then also the quantum capacity is zero, or each capacity equals its random coding variant.
We investigate entanglement transmission over an unknown channel in the presence of a third party (called the adversary), which is enabled to choose the channel from a given set of memoryless but non-stationary channels without informing the legitimate sender and receiver about the particular choice that he made. This channel model is called an arbitrarily varying quantum channel (AVQC). We derive a quantum version of Ahlswede's dichotomy for classical arbitrarily varying channels. This includes a regularized formula for the common randomness-assisted capacity for entanglement transmission of an AVQC. Quite surprisingly and in contrast to the classical analog of the problem involving the maximal and average error probability, we find that the capacity for entanglement transmission of an AVQC always equals its strong subspace transmission capacity. These results are accompanied by different notions of symmetrizability (zero-capacity conditions) as well as by conditions for an AVQC to have a capacity described by a single-letter formula. In the final part of the paper the capacity of the erasure-AVQC is computed and some light shed on the connection between AVQCs and zero-error capacities. Additionally, we show by entirely elementary and operational arguments motivated by the theory of AVQCs that the quantum, classical, and entanglement-assisted zero-error capacities of quantum channels are generically zero and are discontinuous at every positivity point.
In this paper we propose a new model for arbitrarily varying classical-quantum channels. In this model a jammer has side information. We consider two scenarios. In the first scenario the jammer knows the channel input, while in the second scenario the jammer knows both the channel input and the message. The transmitter and receiver share a secret random key with a vanishing key rate. We determine the capacity for both average and maximum error criteria. We prove that additionally revealing the message to the jammer does not change the capacity.
We derive universal codes for simultaneous transmission of classical messages and entanglement through quantum channels, possibly under the attack of a malignant third party. These codes are robust to different kinds of channel uncertainties. To construct such universal codes, we invoke and generalize the properties of random codes for classical and quantum message transmission through quantum channels. We show these codes to be optimal by giving a multi-letter characterization of regions corresponding to capacity of compound quantum channels for simultaneously transmitting and generating entanglement with classical messages. In addition, we give dichotomy statements in which we characterize the capacity of arbitrarily varying quantum channels for simultaneous transmission of classical messages and entanglement. These include cases where the malignant jammer present in the arbitrarily varying channel model is classical (chooses channel states of the product form) and fully quantum (is capable of general attacks not necessarily of the product form).