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Abstract
We show that the amount of coherent quantum information that can be reliably transmitted down a dephasing channel with memory is maximized by separable input states. In particular, we model the channel as a Markov chain or a multimode environment of oscillators. While in the first model, the maximization is achieved for the maximally mixed input state, in the latter it is convenient to exploit the presence of a decoherence-protected subspace generated by memory effects. We explicitly compute the quantum channel capacity for the first model while numerical simulations suggest a lower bound for the latter. In both cases memory effects enhance the coherent information. We present results valid for arbitrary input size.
Highlights
PII: S1367-2630(07)50691-9 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft represented starting from an enlarged vector space including a suitably chosen environment E, initially in a pure state: w0 ≡ |0 E 0|
We show that the amount of coherent quantum information that can be reliably transmitted down a dephasing channel with memory is maximized by separable input states
The quantum capacity Q refers to the coherent transmission of quantum information, and it is related to the dimension of the largest subspace of HN reliably transmitted down the channel, in the limit of large N
Summary
Where |φ j are environment states, in general nonmutually orthogonal, describing the conditional evolution. Since w only depends on the populations ρ j j which are conserved, we can write as well. We show that for a generalized dephasing channel, the coherent information Ic(EN , ρ) is maximized by input states diagonal in the reference basis. This latter relation, together with the concavity of the coherent information for degradable channels (a direct consequence of the concavity of the conditional von Neumann entropy) implies that. Diagonal input states maximize the coherent information. These states are separable, since they can be written in the form ρN =.
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