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1) One time pads require a secure channel to transmit the key, which must be the same length of the message. It is not a feasible cryptography scheme, more of a theoretical framework.

2) Integer factorization is trivially in NP (the decision problem "n has a factor < x" has a certificate: the factor)

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A quantum channel provides protection against eavesdropping for random data, but does not provide security for specific data. A shared quantum channel can be used to easily produce a shared one-time key that only the two parties involved know, which can then be used to encrypt specific data over an unsecured channel.

One time pads are not useful in many cases, but they have been used:

http://en.wikipedia.org/wiki/One-time_pad#Historical_uses

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