Entanglement assisted binary quantum tensor product codes

Nadkarni, Priya J.; Garani, Shayan Srinivasa

doi:10.1109/itw.2017.8277961

Cited by 9 publications

(10 citation statements)

References 6 publications

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“…In [17], Galindo et al have provided the code parameters of the EA CSS code. In [18], we have provided the code parameters of the EA CSS code, along with an explicit form of the matrix H (q) R as provided in (5).…”

Section: Transactions On Ieeementioning

confidence: 99%

“…In this section, we provide a procedure to extend the operators corresponding to H (q) R based on the idea used in [5]. The procedure involves the following two steps.…”

Section: Construction Of Ea Css Codes Over Quditsmentioning

confidence: 99%

“…We note that the idea of the proposed construction procedure for the EA CSS codes is similar to that of the construction procedure for the EA TPC obtained from two binary classical codes in [5]. However, the extension procedure and the mathematical transformations used in the Euclidean Gram-Schmidt orthogonalization algorithm described in this article differ from those in [5].…”

Section: Introductionmentioning

confidence: 97%

“…Classical TPCs are obtained from two classical codes, called its component codes, and the parity check matrix is the tensor product of the parity check matrices of the component codes. Classical TPCs can also correct burst errors with the aid of an interleaver proposed in [5].…”

Section: Introductionmentioning

confidence: 99%

“…Also, we have shown in [7] that there exist dual-containing TPCs beyond those that satisfy the conditions specified in [6]. In [5], we proposed a construction of the EA quantum TPCs from classical TPCs whose component codes are both binary codes. In this article, we generalize it further by providing a previously unreported procedure to construct quantum codes from all classical TPCs over any field F q , without any dual-containing constraint and without any constraint on the field over which the component codes are defined.…”

Section: Introductionmentioning

confidence: 99%

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Coding Analog of Superadditivity Using Entanglement-Assisted Quantum Tensor Product Codes Over $\mathbb {F}_{p^k}$

Nadkarni

Garani

2020

IEEE Trans. Quantum Eng.

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We provide a procedure to construct entanglement-assisted Calderbank-Shor-Steane (CSS) codes over qudits from the parity check matrices of two classical codes over F q , where q = p k , p is prime, and k is a positive integer. The construction procedure involves the proposed Euclidean Gram-Schmidt orthogonalization algorithm, followed by a procedure to extend the quantum operators to obtain stabilizers of the code. Using this construction, we provide a construction of entanglement-assisted tensor product codes from classical tensor product codes over F q . We further show that a nonzero rate entanglement-assisted tensor product code can be obtained from a classical tensor product code whose component codes yield zero rate entanglement-assisted CSS codes. We view this result as the coding analog of superadditivity.INDEX TERMS Entanglement-assisted (EA) codes, entanglement-assisted Calderbank-Shor-Steane (CSS) code, extension procedure, quantum error correction, tensor product codes (TPCs). Engineering uantum Transactions on IEEENadkarni and Garani: Coding Analog of Superadditivity Using Entanglement-Assisted Quantum Tensor Product Codes

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Section: Transactions On Ieeementioning

confidence: 99%

“…In this section, we provide a procedure to extend the operators corresponding to H (q) R based on the idea used in [5]. The procedure involves the following two steps.…”

Section: Construction Of Ea Css Codes Over Quditsmentioning

confidence: 99%