Affiliation:
1. Department of Physics, University of Latvia, Raina Boulevard 19, LV-1586 Riga, Latvia
Abstract
We extend Bloch sphere formalism to pure two-qubit systems. Combining insights from Geometric Algebra and the analysis of entanglement in different conjugate bases we identify two Bloch sphere geometry that is suitable for representing maximally entangled states. It turns out that the relative direction of the coordinate axes of the two Bloch spheres may be used to describe the states. Moreover, the coordinate axes of one Bloch sphere should be rignt-handed and those of the other one should be left-handed. We describe and depict separable and maximally entangled states as well as entangling and non-entangling rotations. We also offer a graphical representation of the workings of a CNOT gate for different inputs. Finally, we provide a way to also represent partially entangled states and describe entanglement measures related to the surface area of the sphere enclosing the state representation.
Reference41 articles.
1. Nuclear Induction;Bloch;Phys. Rev.,1946
2. Nielsen, M.A., and Chuang, I.L. (2000). Quantum Computation and Quantum Information, Cambridge University Press.
3. Loudon, R. (2000). The Quantum Theory of Light, Oxford University Press.
4. Gerry, C.C., and Knight, P.L. (2023). Introductory Quantum Optics, Cambridge University Press.
5. Abragam, A. (1961). The Principles of Nuclear Magnetism, Oxford University Press.