2023/08/30 by Yeow Meng Chee, Hoang Ta, Chee, Yeow Meng +3 · 1 citation
Computer Science · #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.2308.15884
openalex publication_date 2023/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Determining the optimal fidelity for the transmission of quantum information over noisy quantum channels is one of the central problems in quantum information theory. Recently, [Berta-Borderi-Fawzi-Scholz, Mathematical Programming, 2021] introduced an asymptotically converging semidefinite programming hierarchy of outer bounds for this quantity. However, the size of the semidefinite programs (SDPs) grows exponentially with respect to the level of the hierarchy, thus making their computation unscalable. In this work, by exploiting the symmetries in the SDP, we show that, for a fixed output dimension of the quantum channel, we can compute the SDP in time polynomial with respect to the level of the hierarchy and input dimension. As a direct consequence of our result, the optimal fidelity can be approximated with an accuracy of ε in poly(1/ε, input dimension) time.