2023/11/27 by Kai Liu, Liu, Kai, Deguang Han +1
Computer Science · Engineering · #Advanced Surface Polishing Techniques #FOS: Physical sciences #Formal Methods in Verification #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2311.16349
openalex publication_date 2023/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A twirling channel is a quantum channel induced by a continuous unitary representation π= ∑i⊕ miπi, where πi are inequivalent irreducible representations. Motivated by a recent work \citeTwirling on minimal mixed unitary rank of Φπ, we explore the connections of the independence number, zero error capacity, quantum codes, orthogonality index and phase retrievability of the quantum channel Φπ with the irreducible representation multiplicities mi, the irreducible representation dimensions dim Hπi. In particular we show that the independence number of Φπ is the sum of the multiplicities, the orthogonal index of Φπ is exactly the sum of those representation dimensions, and the zero-error capacity is equal to log (∑i=1dmi). We also present a lower bound for the phase retrievability in terms of the minimal length of phase retrievable frames for Cn.