Invertible quantum operations and perfect encryption of quantum states (pp103-110)
           Ashwin Nayak and Pranab Sen 
          doi: https://doi.org/10.26421/QIC7.1-2-6
Abstracts: In this note, we characterize the form of an invertible quantum operation, i.e., a completely positive trace preserving linear transformation (a CPTP map) whose inverse is also a CPTP map. The precise form of such maps becomes important in contexts such as self-testing and encryption. We show that these maps correspond to applying a unitary transformation to the state along with an ancilla initialized to a fixed state, which may be mixed. The characterization of invertible quantum operations implies that one-way schemes for encrypting quantum states using a classical key may be slightly more general than the "private quantum channels'' studied by Ambainis, Mosca, Tapp and de Wolf {AmbainisMTW00}. Nonetheless, we show that their results, most notably a lower bound of 2n bits of key to encrypt n quantum bits, extend in a straightforward manner to the general case.
Key words: quantum operation, linear transformation, completely positive trace preserving map, invertible map, superoperator, encryption of quantum states, lower bounds, private key encryption, key length