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Paper 1

Entanglement-assisted Quantum Codes from Cyclic Codes

Francisco Revson F. Pereira

Year

2019

Journal

arXiv preprint

DOI

arXiv:1911.06384

arXiv

1911.06384

Entanglement-assisted quantum (QUENTA) codes are a subclass of quantum error-correcting codes which use entanglement as a resource. These codes can provide error correction capability higher than the codes derived from the traditional stabilizer formalism. In this paper, it is shown a general method to construct QUENTA codes from cyclic codes. Afterwards, the method is applied to Reed-Solomon codes, BCH codes, and general cyclic codes. We use the Euclidean and Hermitian construction of QUENTA codes. Two families of QUENTA codes are maximal distance separable (MDS), and one is almost MDS or almost near MDS. The comparison of the codes in this paper is mostly based on the quantum Singleton bound.

Open paper

Paper 2

Necessary and sufficient state condition for two-qubit steering using two measurement settings per party and monogamy of steering

Shiladitya Mal, Debarshi Das, Souradeep Sasmal, A. S. Majumdar

Year

2017

Journal

arXiv preprint

DOI

arXiv:1711.00872

arXiv

1711.00872

We consider the Cavalcanti-Foster-Fuwa-Wiseman inequality~\cite{achsh} which is a necessary and sufficient steerability condition for two-qubit states with two measurement settings on each side. We derive the criterion which an arbitrary two-qubit state must satisfy in order to violate this inequality, and obtain its maximum attainable violation in quantum mechanics. The derived condition on the state parameters enables us to establish a tight monogamy relation for two-qubit steering.

Open paper