The capacity of the quantum depolarizing channel

2002/04/30 by Christopher King, C. King, King, C. · 10 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0204172

25 pages, no figures; error in earlier version corrected; discussion of qubit depolarizing channel added

openalex publication_date 2002/04/30 · arxiv created 2002/05/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The information carrying capacity of the d-dimensional depolarizing channel is computed. It is shown that this capacity can be achieved by encoding messages as products of pure states belonging to an orthonormal basis of the state space, and using measurements which are products of projections onto this same orthonormal basis. In other words, neither entangled signal states nor entangled measurements give any advantage for information capacity. The result follows from an additivity theorem for the capacity of the product of the depolarizing channel with an arbitrary channel. We establish the Amosov-Holevo-Werner p-norm conjecture for this product channel for all p >= 1, and deduce from this the additivity of the minimal entropy and of the Holevo quantity.

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