Separability and Entanglement in the Hilbert Space Reference Frames Related Through the Generic Unitary Transform for Four Level System

• Published in: International journal of theoretical physics Vol. 57; no. 5; pp. 1285 - 1303
• Main Authors: Man’ko, V. I., Markovich, L. A.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-05-2018; Springer Nature B.V
• Subjects: Elementary Particles; Hilbert space; Mathematical and Computational Physics; Physics; Physics and Astronomy; Quantum entanglement; Quantum Field Theory; Quantum Physics; Quantum theory; Theoretical; Qudit state; Unitary transform; Entanglement; Peres-Horodecki criterion
• ISSN: 0020-7748; 1572-9575
• DOI: 10.1007/s10773-017-3658-2

Quantum correlations in the state of four-level atom are investigated by using generic unitary transforms of the classical (diagonal) density matrix. Partial cases of pure state,
X
-state, Werner state are studied in details. The geometrical meaning of unitary Hilbert reference-frame rotations generating entanglement in the initially separable state is discussed. Characteristics of the entanglement in terms of concurrence, entropy and negativity are obtained as functions of the unitary matrix rotating the reference frame.