Quantum-Channel Matrix Optimization for Holevo Bound Enhancement

TL;DR

The paper addresses maximizing the Holevo bound for a fixed input ensemble by optimizing a CPTP quantum channel. It introduces a projected gradient ascent algorithm that updates Kraus operators with a CPTP-preserving projection and derives closed-form gradients for $\partial C/\partial H_k$. A detailed complexity analysis shows linear scaling in the number of input states $P$ and Kraus operators $K$, and cubic scaling in dimensions $N$ and $M$. Simulations demonstrate that channel optimization yields higher Holevo bounds than input-ensemble optimization, validating its practical benefits for programmable quantum communications.

Abstract

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.

Figures (4)

• Figure 1: Quantum communication system model.
• Figure 2: The convergence curves of the proposed AG algorithm with $N=3, M=4, K=5$.
• Figure 3: Comparison of Holevo bound across different schemes under varying input and output dimensions $N = M$.
• Figure 4: Comparison of Holevo bound across different schemes under varying number of Kraus operators $K$ with $N = M = 4$.