Information Geometry of Classical and Quantum States and Applications
A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".
Deadline for manuscript submissions: closed (25 June 2021) | Viewed by 420
Special Issue Editor
2. Departmento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
Interests: information geometry of Hilbert spaces and many-body physics; topological phases of matter and phase transitions; quantum cryptography; quantum mechanics and gravity; entanglement and indistinguishability; classical, quantum and total correlations
Special Issue Information
Dear Colleagues,
Information geometry has a long history of applications in both classical and quantum physics, as well as in statistics, computer science, and other disciplines. Since the pioneering work of Fisher and others from the beginning of the 20th century, distance-like quantities measuring distinguishability between probability distributions, or their information content, have been used to tackle problems in statistics and information science. Various geometric and topological phases (Pancharatnam, Longuet-Higgins, Berry, Aharonov-Bohm, etc.) were in the second half of the last century shown useful in optics, chemistry, and atomic and molecular, as well as in condensed matter physics.
Recently, information geometry of quantum states has drawn considerable attention in various fields. Fidelity susceptibility and the related quantities have shown to be useful figures of merit when probing phase transitions of novel exotic (say, topological) matter, which do not fall within the standard symmetry-breaking paradigm. In high-energy physics, various information metrics were used in AdS/CFT and other holographic approaches, in the “space from Hilbert space” paradigm, as well as in lattice gauge theories. In the context of machine learning, information-based volumes of classical and quantum states were used in estimating the complexity of describing probability distributions and density matrices. At the end of this short, but by no means exhaustive, list of applications, distance measures between the processes were introduced to study channel capacity and communication complexity.
This novel rapid progress shows that in spite of their longevity, information geometry applications are offering research opportunities and open many new questions to be answered. Due to technological advances, the increased computational power of today’s devices allows tackling previously intractable numerical studies and developing new methods. Moreover, novel quantum technologies offer experimental ways of performing quantum state estimation and metrology. Therefore, theoretical, as well as computational and experimental studies are all welcome in this Special Issue.
Dr. Nikola Paunković
Guest Editor
Manuscript Submission Information
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Keywords
- Distinguishability, fidelity, geometric phases, and Fisher information
- Entanglement and correlations
- Equilibrium and dynamical phase transitions
- Topological phases of matter
- Entropy and area laws
- AdS/CFT correspondence
- Tensor networks
- Quantum estimation and metrology
- Machine learning
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