Self-testing of universal and fault-tolerant sets of quantum gates
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
On the Power of Quantum Encryption Keys
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
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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 [1, Section 3]. 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.