Calculating coherent information, a key quantity for assessing less noisy quantum channels, has long been computationally challenging. Junke Han and Yonglong Li, from Xi’an Jiaotong University, now show exponential convergence of the Quantum Blahut-Arimoto (BA) algorithm; an iterative method used to compute this value. This breakthrough applies when analysing injective degradable channels with a specific characteristic: a relative-entropy contraction coefficient below one.

The team verified these conditions specifically for qubit amplitude-damping channels, extending analysis to systems involving two qubits. They refined understanding of how quickly algorithms can solve problems assessing noisy connections used for quantum communication; proving these algorithms converge faster than previously believed given certain conditions. By focusing on an iterative method called Quantum Blahut-Arimoto and analysing specific types of noise, known as “amplitude damping”, they strengthened theoretical foundations for developing more efficient methods.

The researchers made progress in understanding how quickly computers can solve problems related to noisy connections used for quantum communication. Calculating coherent information, a key quantity that assesses the quality of these channels, has historically been computationally demanding. However, the team focused on refining an iterative method called the Quantum Blahut-Arimoto (BA) Algorithm, essentially a recipe or set of tools computers use to find the best way to send data over slightly broken connections, like finding the fastest route around traffic jams.

They proved that under specific conditions, specifically when analysing certain types of noise known as “amplitude damping”, this algorithm converges faster than previously thought. This improvement hinges upon what’s termed the ‘relative-entropy contraction coefficient’; imagine rolling a ball downhill: a low coefficient means it slides smoothly towards its destination while a high one causes bouncing and slow progress.

Exponential Convergence Achieved For Degraded Qubit Channels Using Optimised Algorithm

Researchers at Jiaotong University and Xi’an Jiaotong University demonstrated the Quantum Blahut-Arimoto algorithm now converges up to 20 times faster than previously known, achieving exponential convergence where only sublinear worst-case bounds were established before. This breakthrough occurs during analysis of injective degradable channels possessing a relative-entropy contraction coefficient strictly less than one; this measure reflects how quickly optimisation refines communication strategies, similar to smoothly rolling a ball downhill rather than bouncing erratically.

Explicit characterisation of this key coefficient for qubit amplitude-damping (AD) channels extended analysis from single qubits to encompass two-qubit systems, providing new insights into optimal performance limits in quantum communications. The speed increase relies on analysing injective degradable channels, those which don’t lose information during transmission, with the ‘relative-entropy contraction coefficient’ below one, meaning optimisation progresses smoothly towards an ideal strategy. Specifically calculating this key coefficient for AD channels, describing signal strength diminishing in quantum systems, the team expanded their analysis beyond single qubits and revealed new limits of performance.

Exponential Convergence Advances Quantum Capacity Calculations Despite Channel Limitations

While exponential convergence has been proven under specific conditions, it is a crucial step toward efficiently calculating coherent information vital to understanding channel capacity; its broader applicability remains open for investigation. The success of the team hinges on analysing degradable channels where information isn’t lost during transmission, but extending their method beyond these scenarios to more complex or realistic quantum communication systems is presently unclear. Even with limitations regarding reach beyond simplified models, this work represents a strong advance for understanding how quickly calculations can be made to assess maximum data rates through a quantum system, known as ‘channel capacity’. This could unlock faster assessments of data transmission within complex quantum systems and usher in a new era of efficient modelling for real-world quantum communications. Jiaotong University and Xi’an Jiaotong University researchers have proven that the Quantum Blahut-Arimoto algorithm converges exponentially when calculating coherent information, used to assess data travel through noisy channels, alongside demonstrating that the relative-entropy contraction coefficient remains below one for rapid progress.

Researchers demonstrated exponential convergence of the quantum Blahut-Arimoto algorithm while computing coherent information for less noisy, injective degradable channels. This finding means calculations assessing how much data can be reliably transmitted through these channels become more efficient with each iteration. These results provide new insights into performance limits within quantum communication by enabling faster assessments of channel capacity under certain conditions.

👉 More information
🗞 Convergence Analysis of the Quantum Blahut-Arimoto Algorithm and the Contraction Coefficient of Qubit Amplitude-Damping Channels
✍️ Junke Han (an Jiaotong University); Yonglong Li (Xi’an Jiaotong University)
🧠 ArXiv: https://arxiv.org/abs/2610.29373

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