Thermal quantum Fisher information in quantum dot system

S. Abdel‐Khalek, K. Berrada, A.‐S. F. Obada

Fernando Iniguez, Mark Srednicki

The quantum Fisher information (QFI) associated with a particular process applied to a many-body quantum system has been suggested as a diagnostic for the nature of the system's quantum state, e.g., a thermal density matrix vs. a pure state in a system that obeys the eigenstate thermalization hypothesis (ETH). We compute the QFI for both an energy eigenstate and a thermal density matrix for a variety of processes in a system obeying ETH, including a change in the hamiltonian that is either sudden (a quench), slow (adiabatic), or followed by contact with a heat bath. We compare our results with earlier results for a local unitary transformation.

Marlon Brenes, Silvia Pappalardi, John Goold +1 more

We study the quantum Fisher information (QFI) and, thus, the multipartite entanglement structure of thermal pure states in the context of the eigenstate thermalization hypothesis (ETH). In both the canonical ensemble and the ETH, the quantum Fisher information may be explicitly calculated from the response functions. In the case of the ETH, we find that the expression of the QFI bounds the corresponding canonical expression from above. This implies that although average values and fluctuations of local observables are indistinguishable from their canonical counterpart, the entanglement structure of the state is starkly different; with the difference amplified, e.g., in the proximity of a thermal phase transition. We also provide a state-of-the-art numerical example of a situation where the quantum Fisher information in a quantum many-body system is extensive while the corresponding quantity in the canonical ensemble vanishes. Our findings have direct relevance for the entanglement structure in the asymptotic states of quenched many-body dynamics.

pJ Berakdarp

Angelo Plastino

PHILIP CHRISTOPHER CRUZ

In a recent study concerning the multipartite entanglement structure in states satisfying the eigenstate thermalization hypothesis (ETH), a measure known as the quantum Fisher information (QFI) was observed to detect differences in the entanglement content between thermal states of the same temperature; thus establishing a new, distinct way to distinguish between thermal states of different types (pure or mixed). In this work, we try to extend the previous analysis to the class of integrable models–i.e., systems which do not thermalize in the conventional way. We start this investigation with the simplest case, that of noninteracting systems. We derive exact analytic expressions of the QFI for a state described by the generalized Gibbs ensemble (GGE) and for a quenched pure state. We then show through various examples that this hierarchy of entanglement content persists