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

Abstract

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

References in corpus (3)

• Theory of Initialization-Free Decoherence-Free Subspaces and Subsystems
• Decoherence-full subsystems and the cryptographic power of a private shared reference frame
• Random subspaces for encryption based on a private shared Cartesian frame

Cited by in corpus (1)

• Computing Stabilized Norms for Quantum Operations via the Theory of Completely Bounded Maps