Infinite Families of Quantum-Classical Hybrid Codes

@article{Nemec2019InfiniteFO,
  title={Infinite Families of Quantum-Classical Hybrid Codes},
  author={Andrew Nemec and Andreas Klappenecker},
  journal={IEEE Transactions on Information Theory},
  year={2019},
  volume={67},
  pages={2847-2856}
}
Hybrid codes simultaneously encode both quantum and classical information into physical qubits. We give 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. We also introduce the weight enumerators for general hybrid codes, which we then use to derive linear programming bounds. Finally, inspired by the construction of some families of… 

Encoding Classical Information in Gauge Subsystems of Quantum Codes

This paper gives an explicit construction of hybrid codes from two classical linear codes using Bacon–Casaccino subsystem codes, as well as several new examples of good hybrid code.

Nonbinary Error-Detecting Hybrid Codes

This work constructs a family of nonbinary error-detecting hybrid stabilizer codes that can detect one error while also encoding a single classical bit over the residue class rings of $\mathbb{Z}_{q}$ inspired by constructions of non binary non-additive codes.

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

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

References

SHOWING 1-10 OF 40 REFERENCES

Hybrid Codes

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.

Generalized concatenated quantum codes

This work constructs families of single-error-correcting nonadditive quantum codes, in both binary and nonbinary cases, which not only outperform any stabilizer codes for finite block length but also asymptotically meet the quantum Hamming bound for large block length.

Simple family of nonadditive quantum codes.

A family of distance 2 nonadditive quantum codes for all odd block lengths n, that has a particularly simple form that detects single qubit errors while encoding a higher dimensional space than is possible with an additive code or, for n> or =11, any previous codes.

Two Infinite Families of Nonadditive Quantum Error-Correcting Codes

Two infinite families of genuine nonadditive 1-error correcting quantum codes are constructed and it is proved that their coding subspaces are 50% larger than those of the optimal stabilizer codes of the same parameters via the linear programming bound.

Classical Enhancement of Quantum Error-Correcting Codes

A general formalism for quantum error-correcting codes that encode both classical and quantum information (the EACQ formalism) is presented, which unifies the entanglement-assisted formalism and classical error correction.

Remarkable Degenerate Quantum Stabilizer Codes Derived from Duadic Codes

Examples of degenerate quantum codes are constructed that allow some errors of small weight that do not require active error correction, and two new families of degenerates are derived from classical duadic codes.

Non-binary unitary error bases and quantum codes

Error operator bases for systems of any dimension are defined and natural generalizations of the bit-flip/ sign-change error basis for qubits are given. These bases allow generalizing the

Boolean Functions, Projection Operators, and Quantum Error Correcting Codes

A fundamental correspondence between Boolean functions and projection operators in Hilbert space is described, and it is used in this paper to provide a common mathematical framework for the design of both additive and nonadditive quantum error correcting codes.

Theory of quantum error-correcting codes

A general theory of quantum error correction based on encoding states into larger Hilbert spaces subject to known interactions is developed and necessary and sufficient conditions for the perfect recovery of an encoded state after its degradation by an interaction are obtained.