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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.
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Tighter Einstein-Podolsky-Rosen steering inequality based on the sum uncertainty relation
Ananda G. Maity, Shounak Datta, A. S. Majumdar
- Year
- 2017
- Journal
- arXiv preprint
- DOI
- arXiv:1711.01401
- arXiv
- 1711.01401
We consider the uncertainty bound on the sum of variances of two incompatible observables in order to derive a corresponding steering inequality. Our steering criterion when applied to discrete variables yields the optimum steering range for two qubit Werner states in the two measurement and two outcome scenario. We further employ the derived steering relation for several classes of continuous variable systems. We show that non-Gaussian entangled states such as the photon subtracted squeezed vacuum state and the two-dimensional harmonic oscillator state furnish greater violation of the sum steering relation compared to the Reid criterion as well as the entropic steering criterion. The sum steering inequality provides a tighter steering condition to reveal the steerability of continuous variable states.
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