Private Quantum Subsystems
arXiv:1208.2246 · doi:10.1103/PhysRevLett.111.030502
Abstract
We investigate the most general notion of a private quantum code, which involves the encoding of qubits into quantum subsystems and subspaces. We contribute to the structure theory for private quantum codes by deriving testable conditions for private quantum subsystems in terms of Kraus operators for channels; establishing an analogue of the Knill-Laflamme conditions in this setting. For a large class of naturally arising quantum channels, we show that private subsystems can exist even in the absence of private subspaces. In doing so, we also discover the first examples of private subsystems that are not complemented by operator quantum error correcting codes; implying that the complementarity of private codes and quantum error correcting codes fails for the general notion of private quantum subsystem.
5 pages, 1 figure
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Cited by in corpus (9)
- Private algebras in quantum information and infinite-dimensional complementarity
- Quantum Privacy and Schur Product Channels
- Quantum Subsystems: Exploring the Complementarity of Quantum Privacy and Error Correction
- Private Quantum Subsystems and Quasiorthogonal Operator Algebras
- Quantum teleportation in the commuting operator framework
- An Uncertainty Principle For Completely Positive Maps
- Quantum Complementarity and Operator Structures
- Structure Theorem for Quantum Replacer Codes
- Nullspaces of Entanglement Breaking Channels and Applications