The equivalence between correctability of deletions and insertions of separable states in quantum codes

AbstractWe propose an architecture of quantum-error-correction-based quantum repeaters that combines techniques used in discrete- and continuous-variable quantum information. Specifically, we propose to encode the transmitted qubits in a concatenated code consisting of two levels. On the first level we use a continuous-variable GKP code encoding the qubit in a single bosonic mode. On the second level we use a small discrete-variable code. Such an architecture has two important features. Firstly, errors on each of the two levels are corrected in repeaters of two different types. This enables for achieving performance needed in practical scenarios with a reduced cost with respect to an architecture for which all repeaters are the same. Secondly, the use of continuous-variable GKP code on the lower level generates additional analog information which enhances the error-correcting capabilities of the second-level code such that long-distance communication becomes possible with encodings consisting of only four or seven optical modes.

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Quantum Codes Derived from One-Generator Quasi-Cyclic Codes with Hermitian Inner Product

International Journal of Theoretical Physics ◽

10.1007/s10773-019-04324-z ◽

2019 ◽

Vol 59 (1) ◽

pp. 300-312 ◽

Cited By ~ 1

Author(s):

Jingjie Lv ◽

Ruihu Li ◽

Junli Wang

Keyword(s):

Cyclic Codes ◽

Inner Product ◽

Quantum Codes ◽

Hermitian Inner Product ◽

Quasi Cyclic Codes

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ON TWO PROBLEMS OF ASYMMETRIC QUANTUM CODES

International Journal of Modern Physics B ◽

10.1142/s0217979214500179 ◽

2014 ◽

Vol 28 (06) ◽

pp. 1450017 ◽

Cited By ~ 6

Author(s):

RUIHU LI ◽

GEN XU ◽

LUOBIN GUO

Keyword(s):

Cyclic Codes ◽

Error Correcting Codes ◽

Bch Code ◽

Quantum Codes ◽

Quantum Code ◽

Asymmetric Quantum ◽

Asymmetric Quantum Codes ◽

Special Cases ◽

Quantum Error ◽

Better Than

In this paper, we discuss two problems on asymmetric quantum error-correcting codes (AQECCs). The first one is on the construction of a [[12, 1, 5/3]]2 asymmetric quantum code, we show an impure [[12, 1, 5/3 ]]2 exists. The second one is on the construction of AQECCs from binary cyclic codes, we construct many families of new asymmetric quantum codes with dz> δ max +1 from binary primitive cyclic codes of length n = 2m-1, where δ max = 2⌈m/2⌉-1 is the maximal designed distance of dual containing narrow sense BCH code of length n = 2m-1. A number of known codes are special cases of the codes given here. Some of these AQECCs have parameters better than the ones available in the literature.

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