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… 
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6 Citations
Highly Influential Citations
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Background Citations
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Methods Citations
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6 Citations

Infinite Families of Quantum-Classical Hybrid Codes

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

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…

Quantum complementarity and operator structures

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.

Higher rank matricial ranges and hybrid quantum error correction

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.

Approximate Quasiorthogonality of Operator Algebras and Relative Quantum Privacy

Quantum teleportation in the commuting operator framework

. 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…

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