Complementarity of Private and Correctable Subsystems in Quantum Cryptography and Error Correction
arXiv:0711.3438 · doi:10.1103/PhysRevA.78.032330
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 (22)
- Mixed State Entanglement and Quantum Error Correction
- Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
- Decoherence Free Subspaces for Quantum Computation
- How to share a quantum secret
- Noiseless Quantum Codes
- A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
- Quantum Computers and Dissipation
- A Theory of Quantum Error-Correcting Codes
- Preserving coherence in quantum computation by pairing quantum bits
- Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
- Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
- Stabilizer Formalism for Operator Quantum Error Correction
- A Unified and Generalized Approach to Quantum Error Correction
- Stabilizing Quantum Information
- A decoupling approach to the quantum capacity
- Theory of Initialization-Free Decoherence-Free Subspaces and Subsystems
- Generalization of Quantum Error Correction via the Heisenberg Picture
- Decoherence-full subsystems and the cryptographic power of a private shared reference frame
- A method to find quantum noiseless subsystems
- On Protected Realizations of Quantum Information
- Quantum Error Correcting Subsystems are Unitarily Recoverable Subsystems
- Random subspaces for encryption based on a private shared Cartesian frame
Cited by in corpus (26)
- Probabilistic theories with purification
- General conditions for approximate quantum error correction and near-optimal recovery channels
- Information theoretic treatment of tripartite systems and quantum channels
- Fundamental energy requirement of reversible quantum operations
- Generalized Semi-Quantum Secret Sharing Schemes
- Quantum error correction with degenerate codes for correlated noise
- Quantum error suppression with commuting Hamiltonians: Two-local is too local
- Approximate reconstructability of quantum states and noisy quantum secret sharing schemes
- Private algebras in quantum information and infinite-dimensional complementarity
- Private Quantum Subsystems
- Computing Stabilized Norms for Quantum Operations via the Theory of Completely Bounded Maps
- The Physics of Quantum Information: Complementarity, Uncertainty, and Entanglement
- Jones index, secret sharing and total quantum dimension
- Quantum Subsystems: Exploring the Complementarity of Quantum Privacy and Error Correction
- Understanding holographic error correction via unique algebras and atomic examples
- Energy requirement for implementing unitary gates on energy-unbounded systems
- Private Quantum Subsystems and Quasiorthogonal Operator Algebras
- An Uncertainty Principle For Completely Positive Maps
- Private quantum codes: introduction and connection with higher rank numerical ranges
- Quantum Complementarity and Operator Structures
- Conditions for the approximate correction of algebras
- Progress on the Kretschmann-Schlingemann-Werner Conjecture
- Structure Theorem for Quantum Replacer Codes
- Zero-error communication under discrete-time Markovian dynamics
- Nullspaces of Entanglement Breaking Channels and Applications
- Quantum Channel Masking