Quantum entanglement involved in Grover's and Shor's algorithms: the four-qubit case

H Jaffali, F Holweck - Quantum Information Processing, 2019 - Springer
In this paper, we study the nature of entanglement in quantum Grover's and Shor's
algorithms. So far, the authors who have been interested in this problem have approached …

Fine-structure classification of multiqubit entanglement by algebraic geometry

M Gharahi, S Mancini, G Ottaviani - Physical Review Research, 2020 - APS
We present a fine-structure entanglement classification under stochastic local operation and
classical communication (SLOCC) for multiqubit pure states. To this end, we employ specific …

Algebraic-geometric characterization of tripartite entanglement

M Gharahi, S Mancini - Physical Review A, 2021 - APS
To characterize entanglement of tripartite C d⊗ C d⊗ C d systems, we employ algebraic-
geometric tools that are invariants under stochastic local operation and classical …

Grover's algorithm and the secant varieties

F Holweck, H Jaffali, I Nounouh - Quantum Information Processing, 2016 - Springer
In this paper we investigate the entanglement nature of quantum states generated by
Grover's search algorithm by means of algebraic geometry. More precisely we establish a …

Entanglement of four qubit systems: A geometric atlas with polynomial compass I (the finite world)

F Holweck, JG Luque, JY Thibon - Journal of Mathematical Physics, 2014 - pubs.aip.org
We investigate the geometry of the four qubit systems by means of algebraic geometry and
invariant theory, which allows us to interpret certain entangled states as algebraic varieties …

Asymptotic properties of entanglement polytopes for large number of qubits

T Maciążek, A Sawicki - Journal of Physics A: Mathematical and …, 2018 - iopscience.iop.org
Entanglement polytopes have been recently proposed as a way of witnessing the stochastic
local operations and classical communication (SLOCC) multipartite entanglement classes …

Role of the pair potential for the saturation of generalized Pauli constraints

Ö Legeza, C Schilling - Physical Review A, 2018 - APS
The dependence of the (quasi-) saturation of the generalized Pauli constraints on the pair
potential is studied for ground states of few-fermion systems. For this, we consider spinless …

Multipartite quantum correlations: symplectic and algebraic geometry approach

A Sawicki, T Maciażek, K Karnas… - … on Mathematical Physics, 2018 - Elsevier
We review a geometric approach to classification and examination of quantum correlations
in composite systems. Since quantum information tasks are usually achieved by …

Geometric Constructions over and for Quantum Information

F Holweck - Quantum Physics and Geometry, 2019 - Springer
In this review paper I present two geometric constructions of distinguished nature, one is
over the field of complex numbers ℂ C and the other one is over the two elements field 𝔽 2 F …

[PDF][PDF] Masoud Gharahi

S Mancini - arxiv preprint arxiv:2408.12265, 2024 - researchgate.net
Quantum Entanglement is one of the key manifestations of quantum mechanics that
separate the quantum realm from the classical one. Characterization of entanglement as a …