There are some keywords at TFA that give a hint. The computer is "measurement based", what I'll understand as "the computer only does measurements", also, "without knowing the original states, nobody can decode the output".
Turns out that are infinite ways (normaly over a finite continuum space) to encode your original bits, and if your computer only does measurements, the answer will be encoded the same way you encoded the data. If the computer operators don't know your encoding, they won't be able to read your data.
The hard thing is getting those phothons already encoded through the world into the computer, and getting the results back. Also, the above assumes that you can't discover the encoding, but it doesn't survive known plaintext attacks.
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