Hybrid Codes
@article{Nemec2018HybridC, title={Hybrid Codes}, author={Andrew Nemec and Andreas Klappenecker}, journal={2018 IEEE International Symposium on Information Theory (ISIT)}, year={2018}, pages={796-800} }
A hybrid code can simultaneously encode classical and quantum information into quantum digits such that the information is protected against errors when transmitted through a quantum channel. It is shown that a hybrid code has the remarkable feature that it can detect more errors than a comparable quantum code that is able to encode the classical and quantum information. Weight enumerators are introduced for hybrid codes that allow to characterize the minimum distance of hybrid codes…
6 Citations
Infinite Families of Quantum-Classical Hybrid Codes
- Computer ScienceIEEE Transactions on Information Theory
- 2021
This work gives several general results about hybrid codes, most notably that the quantum codes comprising a genuine hybrid code must be impure and that hybrid codes can always detect more errors than comparable quantum codes.
Singleton bounds for entanglement-assisted classical and quantum error correcting codes
- Computer Science2022 IEEE International Symposium on Information Theory (ISIT)
- 2022
We show that entirely information theoretic methods, based on von Neumann entropies and their properties, can be used to derive Singleton bounds on the performance of entanglement-assisted hybrid…
Higher rank matricial ranges and hybrid quantum error correction
- Computer ScienceLinear and Multilinear Algebra
- 2020
Borders on Hilbert space dimension are established in terms of properties of a tuple of operators that guarantee a matricial range is non-empty and hence additionally guarantee the existence of hybrid codes for a given quantum channel.
Quantum Teleportation in the Commuting Operator Framework
- MathematicsAnnales Henri Poincaré
- 2022
. We introduce a notion of teleportation scheme between subalgebras of semi-finite von Neumann algebras in the commuting operator model of locality. Using techniques from subfactor theory, we present…
Quantum complementarity and operator structures
- MathematicsQuantum Inf. Comput.
- 2018
It is established that operator structure identities for quantum channels and their error-correcting and private codes are established, emphasizing the complementarity relationship between the two perspectives.
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