https://doi.org/10.1140/epjp/s13360-023-04267-9
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Bures and Sjöqvist metrics over thermal state manifolds for spin qubits and superconducting flux qubits
1
SUNY Polytechnic Institute, 12203, Albany, NY, USA
2
Air Force Research Laboratory, Information Directorate, 13441, Rome, NY, USA
Received:
7
March
2023
Accepted:
6
July
2023
Published online:
27
July
2023
The interplay among differential geometry, statistical physics, and quantum information science has been increasingly gaining theoretical interest in recent years. In this paper, we present an explicit analysis of the Bures and Sjöqvist metrics over the manifolds of thermal states for specific spin qubit and the superconducting flux qubit Hamiltonian models. While the two metrics equally reduce to the Fubini-Study metric in the asymptotic limiting case of the inverse temperature approaching infinity for both Hamiltonian models, we observe that the two metrics are generally different when departing from the zero-temperature limit. In particular, we discuss this discrepancy in the case of the superconducting flux Hamiltonian model. We conclude the two metrics differ in the presence of a nonclassical behavior specified by the noncommutativity of neighboring mixed quantum states. Such a noncommutativity, in turn, is quantified by the two metrics in different manners. Finally, we briefly discuss possible observable consequences of this discrepancy between the two metrics when using them to predict critical and/or complex behavior of physical systems of interest in quantum information science.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
