The invalidity of a strong capacity for a quantum channel with memory

Abstract

The strong capacity of a particular channel can be interpreted as a sharp limit on the amount of information which can be transmitted reliably over that channel. To evaluate the strong capacity of a particular channel one must prove both the direct part of the channel coding theorem and the strong converse for the channel. Here we consider the strong converse theorem for the periodic quantum channel and show some rather surprising results. We first show that the strong converse does not hold in general for this channel and therefore the channel does not have a strong capacity. Instead, we find that there is a scale of capacities corresponding to error probabilities between integer multiples of the inverse of the periodicity of the channel. A similar scale also exists for the random channel.

7 pages, double column. Comments welcome. Repeated equation removed and one reference added

References in corpus (3)

• Coding Theorem and Strong Converse for Quantum Channels
• Coding Theorem for a Class of Quantum Channels with Long-Term Memory
• The classical capacity of quantum channels with memory

Cited by in corpus (8)

• Fundamental bound on the reliability of quantum information transmission
• On the strong converses for the quantum channel capacity theorems
• Entanglement Cost of Quantum Channels
• "Pretty strong" converse for the quantum capacity of degradable channels
• Quantum Side Information: Uncertainty Relations, Extractors, Channel Simulations
• One-shot Capacity bounds on the Simultaneous Transmission of Classical and Quantum Information
• A strong converse for the quantum state merging protocol
• The strong converse theorem for the product-state capacity of quantum channels with ergodic Markovian memory