I thought of an application on the way back. Communication. Assuming you have some sort of time synchronisation, there are four sorts of photon you might send: photon, no photon, R-photon, and S-photon. These fulfil both possible axes of "visible directly" and "visible in a mirror".

Thus you can use the standard quantum polarisation cryptography technique of sending bits according to a randomly chosen axis, the other chosen randomly, and the receiver determining the value on a random axis, and then later collaborating, publicly to work out which half of the bits were sent and measured on the same axis, which are known to sender and recipient, and then comparing a small proportion of them to determine none have changed. (As any eavesdropper will lose information, due to eg. looking directly, and then not knowing if the photon would have been visible reflected off a mirror or not.)

I couldn't work out why this was better than the quantum angle, but gerald_duck helpfully provided that :)

But does the No-Cloning Theorem pertain? I think not: you can simultaneously detect all four possible states by using a mirror-vampire. That would give you a reflected R-photon iff an R-photon or photon was incident and a passed-through S-photon iff an S-photon or photon was incident.

Oh, bugger. You're right.

Ah! How about you also transmit information in the polarisation of the light? Either as well as the vampireness of the photon, or just use polarised S (or R) photons. Then you can't use a vampire to split the light and get the polarity, because R and S photons don't split.

(Unless there are nestedly RRRSR-photons, but I think we thought Rness and Sness are idempotent...)