Special Issue "Relevance of Information Geometry in Quantum Information Science"
A special issue of Quantum Reports (ISSN 2624-960X).
Deadline for manuscript submissions: closed (31 July 2021) | Viewed by 7956
Interests: classical and quantum information physics; complexity; entropy; inference; information geometry
Special Issues, Collections and Topics in MDPI journals
Special Issue in Entropy: Entropic Aspects Arising from Geometric Descriptions of Physical Phenomena
Special Issue in Entropy: Information Geometric Characterization of Classical and Quantum Complex Systems
Special Issue in Entropy: On the Role of Geometric and Entropic Arguments in Physics: From Classical Thermodynamics to Quantum Mechanics
Information geometry is the application of differential geometric techniques to the investigation of families of probabilities, either parametric or nonparametric, both classical and quantum. In its quantum version, much of the work has been focused on manifolds of density operators for both finite and infinite dimensional quantum systems and their associated monotone metrics, alpha connections, and quantum entropies. In particular, Riemannian geometric techniques combined with methods of probability calculus find several applications in the quantum world. The relevance of these methods appears in both foundational and computational aspects of quantum information science. Within the framework of foundations of physics, information geometric techniques combined with methods of probable inference are currently being employed by researchers to find a path towards the unification of quantum theory with gravity. In quantum computing, methods of information geometry linked to aspects of thermodynamics are currently being used to suggest the design of quantum search algorithms that are both fast and thermodynamically efficient. The Fisher information, a pivotal quantity in information geometry, plays a fundamental role in the geometric characterization of complexity of motion, quantum entanglement, quantum coherence, phase transitions and, in particular, the quantification of the maximum speed achievable by a quantum state undergoing a given quantum mechanical evolution. More boldly, Riemannian geometric techniques applied to the special unitary modular group in 2n dimensions are being exploited to suggest new quantum algorithms yielding efficient quantum circuits capable of solving relevant quantum computational problems. Within this latter Riemannian geometric framework, determining the quantum circuit complexity of a unitary operation is closely related to the problem of finding minimal length paths in a particular curved geometry.
The aim of this Special Issue is to collect the works that are being performed in the application of information geometry to describe and, to a certain extent, understand all aspects of quantum behavior in nature in terms of information geometrical reasoning.
Dr. Carlo Cafaro
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- differential geometry
- phase transitions
- probability theory
- quantum computing
- quantum information
- quantum mechanics