# Additivity for unital qubit channels

@article{King2001AdditivityFU, title={Additivity for unital qubit channels}, author={Christopher King}, journal={Journal of Mathematical Physics}, year={2001}, volume={43}, pages={4641-4653} }

Additivity of the Holevo capacity is proved for product channels, under the condition that one of the channels is a unital qubit channel, with the other completely arbitrary. As a byproduct this proves that the Holevo bound is the classical information capacity of such qubit channels, and provides an explicit formula for this classical capacity. Additivity of minimal entropy and multiplicativity of p-norms are also proved under the same assumptions. The proof relies on a new bound for the p…

## 171 Citations

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- Mathematics, Computer ScienceQuantum Inf. Comput.
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An example is given of a qubit quantum channel which requires four inputs to maximize the Holevo capacity and a conjecture about the concavity of output entropy as a function of entanglement parameters is supported.

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A conjecture arising naturally in the investigation of additivity of classical information capacity of quantum channels states that the maximal purity of outputs from a quantum channel, as measured…

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- Mathematics, MedicinePhysical review letters
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It is shown that a strong converse holds for a large class of channels, including all unital qubit channels, the d-dimensional depolarizing channel and the Werner-Holevo channel, which justifies the interpretation of the classical capacity as a sharp threshold for information transmission.

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- 2004

We introduce a condition for memoryless quantum channels which, when satisfied guarantees the multiplicativity of the maximal lp-norm with p a fixed integer. By applying the condition to qubit…

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- Physics
- 2005

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- Physics, Mathematics
- 2000

The capacity of quantum channel with product input states was formulated by the quantum coding theorem. However, whether entangled input states can enhance the quantum channel is still open. It turns…

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- Mathematics, Physics
- 2008

A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of…

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- Mathematics, Physics
- 2005

We consider generalizations of depolarizing channels to maps of the form with Vk being unitary and ∑kak = a < 1. We show that one can construct unital channels of this type for which the input which…

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- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2017

An upper bound for the minimum output entropy of a unital quantum channel is found, and an exact formula for general qubit channels is obtained that gives the precise quantity of classical capacity of the Werner–Holevo channel.

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