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Paper 1

Stabilizer Formalism for EAQECCs with Noise ebits

Ruihu Li, Guanmin Guo, Yang Liu, Hao Song

Year

2026

Journal

arXiv preprint

DOI

arXiv:2603.19597

arXiv

2603.19597

We introduce a stabilizer formalism for EAQECCs with noise ebits, using special subgroups of product groups of two Pauli groups. This formalism includes the two coding schemes,given by Lai and Brun (C.Y. Lai and T. A. Brun, PHYSICAL REVIEW A 86, 032319 (2012)), for EAQECCs with imperfect ebits as special cases. Then two equivalent formalisms of the formalism are derived in nomenclature of sympletic geometry and additive codes. We apply this theory to construct some EAQECCs with noise ebits, and analyze their performance.

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Paper 2

Geometry and Entanglement of Super-Qubit Quantum States

Oktay K. Pashaev, Aygul Kocak

Year

2024

Journal

arXiv preprint

DOI

arXiv:2410.04361

arXiv

2410.04361

We introduce the super-qubit quantum state, determined by superposition of the zero and the one super-particle states, which can be represented by points on the super-Bloch sphere. In contrast to the one qubit case, the one super-particle state is characterized by points in extended complex plain, equivalent to another super-Bloch sphere. Then, geometrically, the super-qubit quantum state is represented by two unit spheres, or the direct product of two Bloch spheres. By using the displacement operator, acting on the super-qubit state as the reference state, we construct the super-coherent states, becoming eigenstates of the super-annihilation operator, and characterized by three complex numbers, the displacement parameter and stereographic projections of two super-Bloch spheres. The states are fermion-boson entangled, and the concurrence of states is the product of two concurrences, corresponding to two Bloch spheres. We show geometrical meaning of concurrence as distance from point-state on the sphere to vertical axes - the radius of circle at horizontal plane through the point-state. Then, probabilities of collapse to the north pole state and to the south pole state are equal to half-distances from vertical coordinate of the state to corresponding points at the poles. For complimentary fermion number operator, we get the flipped super-qubit state and corresponding super-coherent state, as eigenstate of transposed super-annihilation operator. The infinite set of Fibonacci oscillating circles in complex plain, and corresponding set of quantum states with uncertainty relations as the ratio of two Fibonacci numbers, and in the limit at infinity becoming the Golden Ratio uncertainty, is derived.

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