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ACM International Symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Networks and Mobile Computing (MobiHoc)

Quantum-Inspired Semantic Communication Capacity Analysis based on von Neumann Entropy

Zhu Han, Dusit Tao Niyato

Published Oct 30, 2026• 0 citations
Publisher

Abstract

Semantic communication aims to transmit the task-relevant uncertainty that remains after common knowledge has been taken into account. However, the semantic communication capacity and rate distortion analysis have not been well investigated theoretically. Inspired by quantum entanglement across a black-hole horizon, this paper develops a quantum-inspired framework, where we present a von Neumann entropy bridge between new information and existing common knowledge. Conditioned on the existing common knowledge and the new information, we show that the corresponding von Neumann entropy is continuous and nondecreasing. To give this von Neumann entropy a practical interpretation, we define an auxiliary classical spectral-mode source, whose conditional probabilities are the eigenvalues of the reduced state. Then the resulting semantic capacity and tradeoff are discussed between the fully new information (the Shannon capacity case) and fully common knowledge (no new information) limits. Furthermore, we derive a conditional rate-distortion function, a source-channel feasibility condition, and a task-specific semantic-sample throughput over a cost-constrained discrete memoryless channel. A binary example illustrates the effects of common knowledge, semantic distinguishability, distortion tolerance, and the physical channel capacity.

DOI
10.1145/3842721.3856773

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Semantic communication aims to transmit the task-relevant uncertainty that remains after common knowledge has been taken into account. However, the semantic communication capacity and rate distortion analysis have not been well investigated theoretically. Inspired by quantum entanglement across a black-hole horizon, this paper develops a quantum-inspired framework, where we present a von Neumann entropy bridge between new information and existing common knowledge. Conditioned on the existing common knowledge and the new information, we show that the corresponding von Neumann entropy is continuous and nondecreasing. To give this von Neumann entropy a practical interpretation, we define an auxiliary classical spectral-mode source, whose conditional probabilities are the eigenvalues of the reduced state. Then the resulting semantic capacity and tradeoff are discussed between the fully new information (the Shannon capacity case) and fully common knowledge (no new information) limits. Furthermore, we derive a conditional rate-distortion function, a source-channel feasibility condition, and a task-specific semantic-sample throughput over a cost-constrained discrete memoryless channel. A binary example illustrates the effects of common knowledge, semantic distinguishability, distortion tolerance, and the physical channel capacity.
We discuss the capacity of quantum channels for information transmission and storage. Quantum channels have dual uses: they can be used to transmit known quantum states which code for classical information, and they can be used in a purely quantum manner, for transmitting or storing quantum entanglement. We propose here a definition of the von Neumann capacity of quantum channels, which is a quantum-mechanical extension of the Shannon capacity and reverts to it in the classical limit. As such, the von Neumann capacity assumes the role of a classical or quantum capacity depending on the usage of the channel. In analogy to the classical construction, this capacity is defined as the maximum von Neumann mutual entropy processed by the channel, a measure which reduces to the capacity for classical information transmission through quantum channels (the ``Kholevo capacity'') when known quantum states are sent. The quantum mutual entropy fulfills all basic requirements for a measure of information, and observes quantum data-processing inequalities. We also derive a quantum Fano inequality relating the quantum loss of the channel to the fidelity of the quantum code. The quantities introduced are calculated explicitly for the quantum depolarizing channel. The von Neumann capacity is interpreted within the context of superdense coding, and an extended Hamming bound is derived that is consistent with that capacity.
We consider the transmission of classical information over a quantum channel. The channel is defined by an ``alphabet'' of quantum states, e.g., certain photon polarizations, together with a specified set of probabilities with which these states must be sent. If the receiver is restricted to making separate measurements on the received ``letter'' states, then the Kholevo theorem implies that the amount of information transmitted per letter cannot be greater than the von Neumann entropy H of the letter ensemble. In fact the actual amount of transmitted information will usually be significantly less than H. We show, however, that if the sender uses a block coding scheme consisting of a choice of code words that respects the a priori probabilities of the letter states, and the receiver distinguishes whole words rather than individual letters, then the information transmitted per letter can be made arbitrarily close to H and never exceeds H. This provides a precise information-theoretic interpretation of von Neumann entropy in quantum mechanics. We apply this result to ``superdense'' coding, and we consider its extension to noisy channels. \textcopyright{} 1996 The American Physical Society.
A central question in classical information theory is that of source compression, which is the task where Alice receives a sample from a known probability distribution and needs to transmit it to the receiver Bob with small error. This problem has a one-shot solution due to Huffman, in which the messages are of variable length and the expected length of the messages matches the asymptotic and i.i.d. compression rate of the Shannon entropy of the source. In this work, we consider a quantum extension of above task, where Alice receives a sample from a known probability distribution and needs to transmit a part of a pure quantum state (that is associated to the sample) to Bob. We allow entanglement assistance in the protocol, so that the communication is possible through classical messages, for example using quantum teleportation. The classical messages can have a variable length and the goal is to minimize their expected length. We provide a characterization of the expected communication cost of this task, by giving a lower bound that is near optimal up to some additive factors. A special case of above task, and the quantum analogue of the source compression problem, is when Alice needs to transmit the whole of her pure quantum state. Here we show that there is no one-shot interactive scheme which matches the asymptotic and i.i.d. compression rate of the von Neumann entropy of the average quantum state. This is a relatively rare case in quantum information theory where the cost of a quantum task is significantly different from its classical analogue. Further, we also exhibit similar results for the fully quantum task of quantum state redistribution, employing some different techniques. We show implications for the one-shot version of the problem of quantum channel simulation.
A central question in the classical information theory is that of source compression, which is the task where Alice receives a sample from a known probability distribution and needs to transmit it to the receiver Bob with small error. This problem has a one-shot solution due to Huffman, in which the messages are of variable length and the expected length of the messages matches the asymptotic and independent identically distributed (i.i.d.) compression rate of the Shannon entropy of the source. In this paper, we consider a quantum extension of above task, where Alice receives a sample from a known probability distribution and needs to transmit a part of a pure quantum state (that is associated with the sample) to Bob. We allow entanglement assistance in the protocol, so that the communication is possible through classical messages, for example using quantum teleportation. The classical messages can have a variable length, and the goal is to minimize their expected length. We provide a characterization of the expected communication cost of this task, by giving a lower bound that is near optimal up to some additive factors. A special case of above task, and the quantum analogue of the source compression problem, is when Alice needs to transmit the whole of her pure quantum state. Here, we show that there is no one-shot interactive scheme which matches the asymptotic and i.i.d. compression rate of the von Neumann entropy of the average quantum state. This is a relatively rare case in the quantum information theory where the cost of a quantum task is significantly different from its classical analogue. Furthermore, we also exhibit similar results for the fully quantum task of quantum state redistribution, employing some different techniques. We show implications for the one-shot version of the problem of quantum channel simulation.
Semantic communication is a new paradigm for information transmission that integrates the essential meaning (semantics) of the message into the communication process. However, like in classic wireless communications, the open nature of wireless channels poses security risks for semantic communications. In this paper, we characterize information-theoretic limits for the secure transmission of a semantic source over a wiretap channel. Under separate secrecy and distortion constrains for semantics and observed data, we present general inner and outer bounds on the rate-distortion-equivocation region. We also reduce the general region to the case of Gaussian source and Gaussian wiretap channel and provide numerical evaluations.
We propose a framework to variationally obtain detectable capacity bounds for quantum channels. The proposal of this framework is motivated by the difficulty of estimating the von Neumann entropy of an unknown quantum state. Instead of estimating the von Neumann entropy at the channel output, we propose to estimate the state purity---which can be measured by a single measurement setting---followed by bounding the von Neumann entropy from above and below. This procedure leads to new upper and lower bounds on various communication rates of quantum channels for some fixed input states. Then, by utilizing the variational method to find optimal input states we obtain lower bounds on (i) the quantum capacity of arbitrary channels, (ii) the entanglement-assisted classical capacity of arbitrary channels, and (iii) the classical capacity of covariant channels. Corresponding to these lower bounds, we also obtain upper bounds on (i) NNN-shot coherent information, (ii) the entanglement-assisted classical capacity, and (iii) the NNN-shot Holevo capacity of arbitrary quantum channels. All these bounds can be estimated by a single measurement setting without needing a full process tomography or any further a priori knowledge, e.g., preferred basis of the channel.