Geometric properties of qudit systems

López-Saldívar, J.A.; Castaños, O.; Cordero, S.; Nahmad-Achar, E.; López-Peña, R.

doi:10.1088/1402-4896/adbec6

Geometric properties of qudit systems

May 2, 2024

32 pages

Published in:

Phys.Scripta 100 (2025) 4, 045112

Published: Mar 24, 2025

e-Print:

2405.01759 [quant-ph]

DOI:

10.1088/1402-4896/adbec6

View in:

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Abstract: (IOP)

We discuss in general the geometric properties of qudit systems, with a particular interest in thermal states. The principle of maximum entropy is used to study the geometric properties of an ensemble of finite dimensional Hamiltonian systems with known average energy. These geometric characterizations are given in terms of the generalized diagonal Bloch vectors and the invariants of the special unitary group in n dimensions. As examples, Hamiltonians written in terms of linear and quadratic generators of the angular momentum algebra are considered and explicitly visualized with J = 1 and J = 3/2. For these cases, paths as functions of the temperature are established in the corresponding simplex representations, which show first- and second-order quantum phase transitions, as well as the adiabatic evolution of the interaction strengths (control parameters) of the Hamiltonian models. For the Lipkin-Meshkov-Glick Hamiltonian the quantum phase diagram is explicitly shown for different temperature values in parameter space.

Note:

32 pages, 12 figures

thermal qudit states
geometric properties
maximum entropy
invariant spaces
LMG model

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