Correcting Quantum Errors with Entanglement

  title={Correcting Quantum Errors with Entanglement},
  author={Todd A. Brun and Igor Devetak and Min-Hsiu Hsieh},
  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… 

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

  • Jianfa QianLina Zhang
  • Computer Science, Physics
    2016 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

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

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

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

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

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

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?

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

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

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.



Quantum error correction via codes over GF(4)

In the present paper the problem of finding quantum-error-correcting codes is transformed into one of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product.

Entanglement required in achieving entanglement-assisted channel capacities

Bounds are derived on the minimum amount of entanglement required per use of a channel, in order to asymptotically achieve the capacity, by introducing a class ofEntanglement-assisted quantum 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.

Stabilizer Codes and Quantum Error Correction

An overview of the field of quantum error correction and the formalism of stabilizer codes is given and a number of known codes are discussed, the capacity of a quantum channel, bounds on quantum codes, and fault-tolerant quantum computation are discussed.

Sparse-graph codes for quantum error correction

Sparse-graph codes appropriate for use in quantum error-correction are presented and some of the codes are believed to be unsurpassed by previously publishedquantum error-correcting codes.

Error Correcting Codes in Quantum Theory.

  • Steane
  • Physics
    Physical review letters
  • 1996
It is shown that a pair of states which are, in a certain sense, “macroscopically different,” can form a superposition in which the interference phase between the two parts is measurable, providing a highly stabilized “Schrodinger cat” state.

Mixed-state entanglement and quantum error correction.

It is proved that an EPP involving one-way classical communication and acting on mixed state M (obtained by sharing halves of Einstein-Podolsky-Rosen pairs through a channel) yields a QECC on \ensuremath{\chi} with rate Q=D, and vice versa, and it is proved Q is not increased by adding one- way classical communication.

On the role of entanglement in quantum-computational speed-up

  • R. JozsaN. Linden
  • Physics, Computer Science
    Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 2003
It is argued that it is nevertheless misleading to view entanglement as a key resource for quantum‐computational power, as it is necessary for any quantum algorithm to offer an exponential speed‐up over classical computation.

A family of quantum protocols

This paper describes the family of quantum protocols, aNoiseless qubit channel, noiseless classical bit channel and pure ebit (EPR pair) that reflect their classical-quantum and dynamic-static nature.

Theory of fault-tolerant quantum computation

It is demonstrated that fault-tolerant universal computation is possible for any stabilizer code, including the five-quantum-bit code.