Comparing metrics for mixed quantum states: Sjöqvist and Bures
Alsing P.M. Cafaro C. Luongo O. Lupo C. Mancini S. Quevedo H.
May 2023American Physical Society
Physical Review A
2023#107Issue 5
It is known that 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 paper, we first present an explicit and unabridged mathematical discussion on the relation between the Sjöqvist 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 our comprehension of the difference between these two metrics from a physics standpoint, we compare the formal expressions of these two metrics for arbitrary thermal quantum states specifying quantum systems in equilibrium with a reservoir at nonzero temperature. For illustrative purposes, we 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, we compare the Bures and Sjöqvist metrics in terms of their monotonicity property.
Text of the article Перейти на текст статьи
Air Force Research Laboratory, Information Directorate, Rome, 13441, NY, United States
Suny Polytechnic Institute, Albany, 12203, NY, United States
Università di Camerino, Camerino, 62032, Italy
Suny Polytechnic Institute, Utica, 13502, NY, United States
Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Politecnico di Bari, Bari, 70126, Italy
INFN, Sezione di Perugia, Perugia, 06123, Italy
Universidad Nacional Autonoma de Mexico, D.F., Mexico, 04510, Mexico
Università di Roma la Sapienza, Roma, 00185, Italy
Air Force Research Laboratory
Suny Polytechnic Institute
Università di Camerino
Suny Polytechnic Institute
Al-Farabi Kazakh National University
Politecnico di Bari
INFN
Universidad Nacional Autonoma de Mexico
Università di Roma la Sapienza
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026