Dr. Carlo Cafaro, SUNY Poly faculty in the Department of Mathematics and Physics, has coordinated a collaborative effort among six scientists: Dr. Paul M. Alsing (Principal Research Physicist at the Air Force Research Laboratory (AFRL) in Rome-NY), Dr. Orlando Luongo (Lecturer in Theoretical Physics at the University of Camerino-Italy and SUNY Poly Visiting Scientist at SUNY Poly’s Utica campus), Dr. Cosmo Lupo (Associate Professor of Theoretical Physics, Politecnico di Bari-Italy), Dr. Stefano Mancini (Professor of Theoretical Physics and Mathematical Methods, University of Camerino-Italy), and Dr. Hernando Quevedo (Professor of Physics, Universidad Nacional Autonoma de Mexico-Mexico) culminating in a work published in Physical Review A. 

Physical Review A (PRA) publishes important developments in the rapidly evolving areas of atomic, molecular, and optical (AMO) physics, quantum information, and related fundamental concepts. Furthermore, PRA is published by the highly regarded American Physical Society (APS).

The research paper, entitled “Comparing metrics for mixed quantum states: Sjoqvist and Bures,” is a relatively simple theoretical piece of work. It combines concepts of quantum physics with elements of differential geometry to clarify the differences between two important metrics for mixed quantum states of great use in quantum information science.

It is known there are infinitely many distinguishability metrics for mixed quantum states. This freedom, in turn, leads to metric-dependent interpretations of physically meaningful geometric quantities such as complexity and volume of quantum states. In this work, Cafaro and collaborators present an explicit and unabridged mathematical discussion on the relation between the Sjoqvist metric and the Bures metric for arbitrary nondegenerate mixed quantum states, using the notion of decompositions of density operators by means of ensembles of pure quantum states. Then, to enhance their comprehension of the difference between these two metrics from a physics standpoint, they compare the formal expressions of these two metrics for arbitrary thermal quantum states specifying quantum systems in equilibrium with a reservoir at non-zero temperature. For illustrative purposes, they show the difference between these two metrics in the case of a simple physical system characterized by a spin-qubit in an arbitrarily oriented uniform and stationary external magnetic field in thermal equilibrium with a finite-temperature bath. Finally, they compare the Bures and Sjoqvist metrics in terms of their monotonicity property.

The team’s published research, featuring Dr. Cafaro as lead author, can be read here:
URL: https://link.aps.org/doi/10.1103/PhysRevA.107.052411
DOI: 10.1103/PhysRevA.107.052411