# 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.

## References

SHOWING 1-10 OF 10 REFERENCES

### Classical Enhancement of Quantum Error-Correcting Codes

- Computer Science, Physics
- 2008

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.

### Non-binary unitary error bases and quantum codes

- Computer Science
- 1996

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…

### The Capacity of a Quantum Channel for Simultaneous Transmission of Classical and Quantum Information

- Physics
- 2003

An expression is derived characterizing the set of admissible rate pairs for simultaneous transmission of classical and quantum information over a given quantum channel, generalizing both the…

### Entanglement-Assisted Communication of Classical and Quantum Information

- Computer ScienceIEEE Transactions on Information Theory
- 2010

The main result is a capacity theorem that gives a 3-D achievable rate region that justifies the need for simultaneous coding of classical and quantum information over an EAQ channel.

### Capacity theorems for quantum multiple-access channels: classical-quantum and quantum-quantum capacity regions

- Computer ScienceIEEE Transactions on Information Theory
- 2008

This paper gives multiletter characterizations of two different two-dimensional capacity regions for an arbitrary quantum channels with two senders and one receiver, and states that the coherent information over any degradable channel is concave in the input density operator.

### Generalization of quantum error correction via the Heisenberg picture.

- PhysicsPhysical review letters
- 2007

We show that the theory of operator quantum error correction can be naturally generalized by allowing constraints not only on states but also on observables. The resulting theory describes the…

### Codes for simultaneous transmission of quantum and classical information

- Computer Science, Physics2017 IEEE International Symposium on Information Theory (ISIT)
- 2017

This work constructs hybrid codes [n, k:m, d] with length n and distance d, that simultaneously transmit k qudits and m symbols from a classical alphabet of size q.

### Beyond stabilizer codes I: Nice error bases

- Computer ScienceIEEE Trans. Inf. Theory
- 2002

Nice error bases have been introduced by Knill (1996) as a generalization of the Pauli basis. These bases are shown to be projective representations of finite groups. We classify all nice error bases…

### Nice error bases: Constructions, equivalence, and applicatio ns

- Applied Algebra, Algebraic Algorithms, and Error Correcting Co des – 15th International Symposium,
- 2003