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Quantum depolarizing channel
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Quantum depolarizing channel : ウィキペディア英語版
Quantum depolarizing channel
A quantum depolarizing channel is a model for noise in quantum systems. The d-dimensional depolarizing channel can be viewed as a completely positive trace-preserving map \Delta_\lambda, depending on one parameter \lambda, which maps a state \rho onto a linear combination of itself and the maximally mixed state:
:\Delta_\lambda(\rho)=\lambda\rho+\fracI
The condition of complete positivity requires \lambda to satisfy the bounds:
:-\frac\le\lambda\le 1
== Classical capacity ==

The HSW theorem states that the classical capacity of a quantum channel \Psi can be characterized as its regularized Holevo information:
:\lim_\frac\chi\left(\Psi^\right)
This quantity is difficult to compute and this reflects our ignorance on quantum channels. However, if the Holevo information is additive for a channel \Psi, i.e.,
:\chi\left(\Psi\otimes\Psi\right)=\chi\left(\Psi\right)+\chi\left(\Psi\right)
Then we can get its classical capacity by computing the Holevo information of the channel.
The additivity of Holevo information for all channels was a famous open conjecture in quantum information theory, but it is now known that this conjecture doesn't hold in general. This was proved by showing that the additivity of minimum output entropy for all channels doesn't hold, which is an equivalent conjecture.
Nonetheless, the additivity of the Holevo information is shown to hold for the quantum depolarizing channel, and an outline of the proof is given below. As a consequence, entanglement across multiple uses of the channel cannot increase the classical capacity. In this sense, the channel behaves like a classical channel. To achieve the optimal rate of communication, it suffices to choose an orthonormal basis to encode the message, and perform measurements that project onto to the same basis at the receiving end.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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