Quantum communication holds the potential to revolutionize information transmission by enabling secure data exchange that exceeds the limits of classical systems. One of the key performance metrics in quantum information theory, namely the Holevo bound, quantifies the amount of classical information that can be transmitted reliably over a quantum channel. However, computing and optimizing the Holevo bound remains a challenging task due to its dependence on both the quantum input ensemble and the quantum channel. In order to maximize the Holevo bound, we propose a unified projected gradient ascent algorithm to optimize the quantum channel given a fixed input ensemble. We provide a detailed complexity analysis for the proposed algorithm. Simulation results demonstrate that the proposed quantum channel optimization yields higher Holevo bounds than input ensemble optimization.
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6 pages, 4 figures, accepted by 2026 IEEE International Conference on Communications (ICC)
Quantum communication holds the potential to revolutionize information transmission by enabling secure data exchange that exceeds the limits of classical systems. One of the key performance metrics in quantum information theory, namely the Holevo bound, quantifies the amount of classical information that can be transmitted reliably over a quantum channel. However, computing and optimizing the Holevo bound remains a challenging task due to its dependence on both the quantum input ensemble and the quantum channel. In order to maximize the Holevo bound, we propose a unified projected gradient ascent algorithm to optimize the quantum channel given a fixed input ensemble. We provide a detailed complexity analysis for the proposed algorithm. Simulation results demonstrate that the proposed quantum channel optimization yields higher Holevo bounds than input ensemble optimization.
Computing the classical capacity of a noisy quantum channel is crucial for understanding the limits of communication over quantum channels. However, its evaluation remains challenging due to the difficulty of computing the Holevo capacity and the even greater difficulty of regularization. In this work, we formulate the computation of the Holevo capacity as an optimization problem on a product manifold constructed from probability distributions and their corresponding pure input states for a quantum channel. A Riemannian gradient descent algorithm is proposed to solve the problem, providing lower bounds on the classical capacity of general quantum channels and outperforming existing methods in numerical experiments in both efficiency and scale.
The processing of quantum information is limited by fundamental physical constraints on how information can be encoded, transmitted, and extracted. In particular, the nonorthogonality of quantum states limits their distinguishability, and thermodynamic constraints, including the energetic cost of state preparation and quantum operations, further restrict the viability of realistic information protocols. This work explores the impact of such constraints on the preparation, evolution, and readout of quantum information. We demonstrate that preparing the system for encoding and measurement affects the distinguishability and purity of the resulting ensemble of states. Furthermore, we analyze a noisy communication channel and propose an optimal protocol for encoding and decoding the transmitted information. For this realistic protocol, we show that the maximum probability of successfully retrieving the information is equal to the maximum correlation that can be achieved between the system and the register. The protocol uses only Gibbs states as free resources, ensuring minimal thermodynamic cost. Based on this, we provide a thermodynamic interpretation of the Holevo information, which quantifies the capacity of the transmitted information and establishes a fundamental limit on its retrieval in thermodynamically constrained scenarios.
Due to its complexity, resource allocation in complex communication networks has been always designed with great deal of approximations and restrictions. With the availability of quantum computing, quantum optimization and quantum search algorithms, we are able to overcome these limitations significantly and come up with more precise and efficient “quantum era” algorithms. The main objective of this paper is to provide the future network designers with a new optimization framework for resource (capacity and secrete key rate) allocation in quantum networks. The analysis is general to include: the classical capacityC, for transmitting classical information; the quantum capacityQ, for reliably transmitting intact quantum states; the two-way classical-assisted quantum capacityQ2, for transmitting quantum states with the help of a two-way classical side channel; and the entanglement-assisted classical capacityCE, which we define as the classical capacity of a quantum channel enabled by prior shared entanglement between two nodes. Once the optimization framework is introduced the rest of the paper discusses the optimization constraints, by surveying some examples of the relevant work on achievable network resources (capacity and secrete key rate) and relaxation of the optimization constraints by increasing these parameters using the quantum coding schemes. These constraints are an integral part of the optimization algorithms and full understanding of their nature and limits is essential for system optimization. The achievable secret key rates/capacity of quantum channels are limited, so our optimization framework for resource allocation enables maximization of the overall resources allocated to all users, or maximization of the number of users accessing the network, or minimization of the number of hopes on the routes or maximization of remaining resources in the most critical node in the network. The optimization problems have combinatorial form, and the most efficient execution of these algorithms can be achieved by using quantum search algorithms like Grover’s algorithm or quantum approximative optimization algorithms (QAOA) which are extensively discussed in the paper.Regarding the scope of the technology survey in Section VIII we summarize the coverage of our targeted survey and the coverage of other relevant works.
What can be transmitted with a fixed photon supply? An optical source that supplies exactly K photons across n modes poses a concrete communication problem: how many messages can it transmit at a chosen error probability, and which input states make the best use of those photons? This paper gives directly evaluable coding bounds for pure loss and identifies the exact optimal input ensembles for identical noisy Gaussian channels. The results allow researchers to assess finite optical blocks, quantify the information cost of fixing the photon supply, and determine when entanglement between separately constrained blocks can be dispensed with. Every message is supported on the same exact K-photon sector. Within that sector, encoding may use arbitrary mixed states and entanglement among modes, and the receiver may perform a joint measurement. Communication is unassisted. All logarithms below are natural; information is measured in nats. Finite-message bounds and the optimal third-order rate For n ≥ 2 identical pure-loss channels of transmissivity 0 < η < 1 and K ≥ 1, the number L of surviving photons has the same binomial distribution for every encoded state. Define pℓ=(ℓK)ηℓ(1−η)K−ℓ,dn,ℓ=(ℓn+ℓ−1). If ps*(M;n,K) is the best average success probability for M equiprobable messages, then ∑ℓ=0Kpℓ[1−dn,ℓM−1]+≤ps∗(M;n,K)≤∑ℓ=0Kpℓmin{1,Mdn,ℓ}. Here [x]+ = max{x,0}. The lower bound provides an achievable guarantee; the upper bound limits every admissible code. Evaluating both sums brackets the performance at a specified photon supply and block length. Their proof has a simple physical interpretation: surviving photons determine the available output dimension, while one collective-mode codebook works across all possible survivor counts. For fixed E > 0, fixed error tolerance 0 < ε < 1, Kn = ⌊nE⌋ and en = Kn/n, the bounds determine the largest message count through third order: logM∗(n,Kn,ε)=ng(ηen)+nη(1−η)enh(ηen)ΦN−1(ε)−21logn+O(1). Here g(x) = (x+1)log(x+1) − x log x, h(x) = log(1+1/x), and ΦN is the standard normal distribution function. This fixes both the fluctuation scale and the optimal −½ log n correction. The finite bounds also yield the exact decay exponent of success above capacity and a matching error exponent on a specified interval below capacity. Which inputs are optimal under Gaussian noise? For n identical nonidentity gauge-covariant Gaussian channels, with thermal photon means transformed as r ↦ ar+b, a > 0 and b ≥ max{0,a−1}, the paper determines the exact fixed-photon Holevo optimum and every ensemble attaining it. Each optimal letter places all K photons in one collective mode: ∣K,u⟩=K!(∑j=1nujaj†)K∣0⟩,∑j∣uj∣2=1. An ensemble is optimal precisely when almost all its letters have this form and its average is uniform on the K-photon sector. A finite weighted optimal ensemble exists. These collective modes may themselves extend across, and be entangled among, physical optical modes. Thus the characterization identifies the structure to optimize without imposing a Gaussian-input restriction. The central proof step combines different loss histories that end in the same output photon sector. A common ordering of the comparison eigenstates allows the separate majorization bounds to be combined. For pure loss, a quantitative rigidity estimate further converts a small Holevo deficit into closeness to collective-mode number states. Resource cost and communication across blocks At fixed positive photon density and fixed nonidentity Gaussian noise, requiring an exact photon supply incurs a Holevo penalty of ½ log n plus an explicitly determined constant, relative to the usual mean-energy value. The paper separates this cost into photon-count uncertainty and the mismatch from a thermal output distribution. For separately constrained blocks of quantum-limited loss, quantum-limited amplification or entanglement-breaking Gaussian noise, the one-block Holevo values add exactly. Every optimal letter is a product of blockwise collective-mode number states, and the repeated-block unassisted classical capacity equals the one-block Holevo value. The low-rate reliability interval outside the matching range and repeated-block additivity for intermediate Gaussian noise remain open.
Optimal convex approximation of quantum channels based on α-affinity
Determining the minimal distance between a target channel and a convex hull of predefined set of implementable channels is a fundamental problem in quantum resource theory, and provides key guidance for experimental implementations. In this work, we develop a unified analytical framework for optimal convex approximation of quantum channels based on the quantum α-affinity measure. We construct a channel distance metric induced by the α-affinity and the ChoiJamiolkowski isomorphism, which satisfies the required properties of a well-defined channel distance. Subsequently, we present an optimization framework for the convex approximation of quantum channels, and derive analytical solutions for the optimal convex approximation of single-qubit unitary channels over both the SU(2)-covariant and Pauli channel families, obtaining closed-form expressions for the optimal parameters and the minimal approximation distance. This framework is further applied to the amplitude-damping channel, yielding the explicit form of its optimal approximation and the associated minimal α-affinity distance. In contrast to conventional approaches based on the diamond norm, our framework provides a systematic and analytically tractable approach to quantum channel approximation under realistic constraints.
Quantum information storage presents a significant challenge due to the need for precise control and efficient manipulation of quantum states. Traditional optimization algorithms often struggle to effectively address the complex constraints inherent in this field. This paper proposes a novel high-order matrix optimization algorithm designed to address these challenges, aiming to dramatically improve the efficiency of quantum information storage. The algorithm leverages the inherent properties of high-order matrices to efficiently navigate the space of possible quantum state configurations, offering a pathway towards enhanced storage density and reduced error rates. The core mechanism involves a sophisticated matrix manipulation strategy, coupled with predictive modeling based on calculated efficiency, offering a promising approach to optimizing quantum information storage. The proposed algorithm demonstrates significant improvements in computational efficiency compared to existing methods, and the resulting predictions offer insights into the potential for enhanced storage capabilities.