# Correcting Quantum Errors with Entanglement

@article{Brun2006CorrectingQE, title={Correcting Quantum Errors with Entanglement}, author={Todd A. Brun and Igor Devetak and Min-Hsiu Hsieh}, journal={Science}, year={2006}, volume={314}, pages={436 - 439} }

We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard quantum error–correcting codes, thus allowing us to “quantize” all of classical linear coding theory. In particular, efficient modern classical codes that attain the Shannon capacity can be made into entanglement-assisted quantum codes attaining the hashing bound…

## 294 Citations

### Two class of entanglement-assisted quantum codes from shortened hamming codes

- Computer Science, Physics2016 IEEE International Conference on Signal and Image Processing (ICSIP)
- 2016

Two class of entanglement-assisted quantum codes are constructed, which require only one copy of maximally entangled state no matter how large the code length is and can achieve the entanglements-assisted hashing bound asymptotically.

### Entanglement-Assisted Quantum Error-Correcting Codes

- Computer Science
- 2009

We develop the theory of entanglement-assisted quantum error correcting codes (EAQECCs), a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to…

### Entanglement-assisted quantum MDS codes from cyclic codes

- Computer ScienceQuantum Inf. Process.
- 2020

This paper constructs seven new families of entanglement-assisted quantum maximum-distance-separable codes from cyclic codes by exploiting less pre-shared entangled states.

### Constructions of good entanglement-assisted quantum error correcting codes

- Computer ScienceDes. Codes Cryptogr.
- 2018

This paper shows that the number of shared pairs required to construct an EAQECC is related to the hull of the classical code, and gives methods to construct EAZECCs requiring desirable amounts of entanglement.

### Some construction of entanglement-assisted quantum MDS codes

- Computer ScienceQuantum Inf. Process.
- 2020

By employing generalized Reed–Solomon codes, several classes of entanglement-assisted quantum maximum distance separable (EAQMDS) codes are constructed, whose required number of maximally entangled states is more flexible.

### Entanglement increases the error-correcting ability of quantum error-correcting codes

- Computer Science, Physics
- 2013

This work shows how to optimize the minimum distance of an entanglement-assisted quantum error-correcting (EAQEC) code, obtained by adding ebits to a regular quantum stabilizer code, over different encoding operators.

### Performance of Entanglement-assisted Quantum LDPC Codes Constructed From Finite Geometries

- Computer Science, Physics
- 2009

This work investigates the performance of entanglement-assisted quantum low-density parity-check codes constructed from finite geometries and provides families of EAQECCs with anEntanglement consumption rate that decreases exponentially.

### How Much Entanglement Does a Quantum Code Need?

- Computer ScienceArXiv
- 2022

This work presents three new propagation rules and discusses how each of them aﬀects the error handling in the setting of entanglement-assisted quantum error-correcting codes (EAQECCs).

### Entanglement-Assisted Quantum Convolutional Coding

- Computer Science, PhysicsArXiv
- 2007

This work shows how to protect a stream of quantum information from decoherence induced by a noisy quantum communication channel and develops a theory of entanglement-assisted quantum convolutional coding.

### New constructions of entanglement-assisted quantum codes

- Computer ScienceCryptogr. Commun.
- 2022

Two new constructions of entanglement-assisted quantum error-correcting codes are presented using some fundamental properties of (classical) linear codes in an effective way to create linear complementary dual codes and related concatenation constructions.

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