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

Understand

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.