Quantum Complementarity and Operator Structures
arXiv:1811.10425
Abstract
We establish operator structure identities for quantum channels and their error-correcting and private codes, emphasizing the complementarity relationship between the two perspectives. Relevant structures include correctable and private operator algebras, and operator spaces such as multiplicative domains and nullspaces of quantum channels and their complementary maps. For the case of privatizing to quantum states, we also derive related dimension inequalities that may be viewed as operator algebra uncertainty relations.
arXiv commentSome typos are fixed, updated journal reference
References in corpus (18)
- A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
- A Theory of Quantum Error-Correcting Codes
- General Entanglement Breaking Channels
- Optimal Encryption of Quantum Bits
- A Unified and Generalized Approach to Quantum Error Correction
- Entanglement-assisted communication of classical and quantum information
- Generalization of Quantum Error Correction via the Heisenberg Picture
- Quantum Error Correction of Observables
- Decoherence-full subsystems and the cryptographic power of a private shared reference frame
- Quantum Error Correcting Subsystems are Unitarily Recoverable Subsystems
- Classical Enhancement of Quantum Error-Correcting Codes
- Complementarity of Private and Correctable Subsystems in Quantum Cryptography and Error Correction
- The multiplicative domain in quantum error correction
- Random subspaces for encryption based on a private shared Cartesian frame
- Multiplicative Properties of Quantum Channels
- Generalized Multiplicative Domains and Quantum Error Correction
- Private Quantum Subsystems
- Hybrid Codes