Quantum information with conserved quantities

TL;DR

This paper explores a general framework for Hamiltonians with conserved quantities, providing analytical tools like the characteristic operator and quantum Fisher information, and applies it to su(2) and canonical systems.

Contribution

It introduces a unified scenario for Hamiltonians with conserved quantities, deriving analytical expressions for the characteristic operator and quantum Fisher information.

Findings

Analytical form of the characteristic operator for the scenario

Explicit quantum Fisher information calculations for specific systems

Application to su(2) and canonical Hamiltonian classes

Abstract

Conserved quantities are crucial in quantum physics. Here we discuss a general scenario of Hamiltonians. All the Hamiltonians within this scenario share a common conserved quantity form. For unitary parametrization processes, the characteristic operator of this scenario is analytically provided, as well as the corresponding quantum Fisher information (QFI). As the application of this scenario, we focus on two classes of Hamiltonians: su(2) category and canonical category. Several specific physical systems in these two categories are discussed in detail. Besides, we also calculate an alternative form of QFI in this scenario.