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

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

2011-08-22

arxiv.org/abs/1108.4282v2

Phys. Rev. A, vol. 84, 042318, (2011)

Physics

Quantum Physics

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

Scientific paper

10.1103/PhysRevA.84.042318

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.

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