Research areas

The Q-TheorySI Group focuses on developing theoretical tools based on geometric and topological methods for characterizing entanglement and quantum correlation properties in multipartite quantum states.

Quantum Science Theory

Entanglement has an important role in quantum science theory and the development of quantum technologies. It is a valuable resource in quantum cryptography, in quantum computation, in teleportation and in quantum metrology. Nevertheless, entanglement measure and characterisation remain elusive and the problem of its quantification in the case of a general system, is still open. In the last decades, several approaches have been developed to quantify the entanglement in the variety of quantum states. Rigorous achievements in the explicit quantification of entanglement, are limited to bipartite systems case. The entropy of entanglement is uniquely accepted as a measure of entanglement for pure states of bipartite systems. Entanglement of formation, entanglement distillation and relative entropy of entanglement are largely acknowledged as faithful measures for bipartite mixed systems. An extensive literature is devoted to the study of entanglement in multipartite systems. Up to now, different approaches have been proposed including, e.g. in the case of pure states, the study of the equivalence classes in the set of multipartite entangled states, whereas, the study of entanglement in mixed multipartite states has been addressed, e.g., with a Schmidt measure or with a generalisation of concurrence. In the last years, have been proposed entanglement estimation-oriented approaches and derived from a statistical distance concept, such as, for instance, the quantum Fisher information. In [1] we have put forward a new entanglement measure able to quantify by a direct calculation, the degree of entanglement of a general multi-qudit hybrid pure state. Such entanglement measure, named entanglement distance (ED), derives from a minimum distance principle.

A pure state is entangled if manifests any quantum correlation between its components and vice versa. In fact, entanglement and correlation are rather equivalent in the case of pure states. On the contrary, in the case of mixed states, one can observe states that manifest correlations detached from entanglement. In the [2] we have proposed a new measure of quantum correlation, and a related entanglement measure for mixed states, derived from the first through a regularisation process. Such entanglement measure derives from a minimum distance principle and, for this reason, we name it entanglement distance.

Related papers:

[1] D. Cocchiarella, S. Scali, S. Ribisi, B. Nardi, G. Bel-Hadj-Aissa, and R. Franzosi, “Entanglement distance for arbitrary M-qudit hybrid systems”, Phys. Rev. A 101, 042129 (2020).

[2] A. Vesperini, G. Bel-Hadj-Aissa, and R. Franzosi, Entanglement and quantum correlation measures for quantum multipartite mixed states, Scientific Reports 13 2852 (2023).

[3] A. Nourmandipour, A. Vafafard, A. Mortezapour and R. Franzosi, “Entanglement protection of classically driven qubits in a lossy cavity”, Scientific Reports (2021) 11:16259.

[4] A. Vafafard, A. Nourmandipour, and R. Franzosi, Multipartite stationary entanglement generation in the presence of dipole-dipole interaction in an optical cavity, Phys Rev A 105, 052439 (2022).

[5] S. Scali and R. Franzosi, “Entanglement estimation in non-optimal qubit states”, Annal of Physics 411 (2019) 167995.