Minimal Entropy of States Emerging from Noisy Quantum Channels

Details Minimal Entropy of States Emerging from Noisy Quantum Channels Minimal Entropy of States Emerging from Noisy Quantum Channels

1999-11-17

arxiv.org/abs/quant-ph/9911079v3

IEEE Trans. Info. Theory, 47, 192-209 (2001)

Physics

Quantum Physics

LATEX file; 44 pages, 7 figures; references added, typos corrected; extended discussion of additivity for minimal entropy vs c

Scientific paper

In this paper, we consider the minimal entropy of qubit states transmitted through two uses of a noisy quantum channel, which is modeled by the action of a completely positive trace-preserving (or stochastic) map. We provide strong support for the conjecture that this minimal entropy is additive, namely that the minimum entropy can be achieved when product states are transmitted. Explicitly, we prove that for a tensor product of two unital stochastic maps on qubit states, using an entanglement that involves only states which emerge with minimal entropy cannot decrease the entropy below the minimum achievable using product states. We give a separate argument, based on the geometry of the image of the set of density matrices under stochastic maps, which suggests that the minimal entropy conjecture holds for non-unital as well as for unital maps. We also show that the maximal norm of the output states is multiplicative for most product maps on $n$-qubit states, including all those for which at least one map is unital. For the class of {\it unital} channels on ${\bf C}^2$, we show that additivity of minimal entropy implies that the Holevo capacity of the channel is {\it additive} over two inputs, achievable with orthogonal states, and equal to the Shannon capacity. This implies that superadditivity of the capacity is possible only for non-unital channels.

Affiliated with

Also associated with

No associations

Rating

Minimal Entropy of States Emerging from Noisy Quantum Channels does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Minimal Entropy of States Emerging from Noisy Quantum Channels, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Minimal Entropy of States Emerging from Noisy Quantum Channels will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-239303