Complementarity of Private and Correctable Subsystems in Quantum Cryptography and Error Correction

Kretschmann, Dennis; Kribs, David W.; Spekkens, Robert W.

Complementarity of Private and Correctable Subsystems in Quantum Cryptography and Error Correction

Authors

Kretschmann, Dennis

Kribs, David W.

Spekkens, Robert W.

Description

We make an explicit connection between fundamental notions in quantum cryptography and quantum error correction. Error-correcting subsystems (and subspaces) for quantum channels are the key vehicles for contending with noise in physical implementations of quantum information-processing. Private subsystems (and subspaces) for quantum channels play a central role in cryptographic schemes such as quantum secret sharing and private quantum communication. We show that a subsystem is private for a channel precisely when it is correctable for a complementary channel. This result is shown to hold even for approximate notions of private and correctable defined in terms of the diamond norm for superoperators.
5 pages, 2 figures, preprint version