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Quantum Reports
Special Issues
Relevance of Information Geometry in Quantum Information Science
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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 10663

Special Issue Editor

Dr. Carlo Cafaro

E-Mail Website
Guest Editor
Department of Nanoscale Science and Engineering, University at Albany-SUNY, Albany, NY 12222, USA
Interests: classical and quantum information physics; complexity; entropy; inference; information geometry
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

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
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Quantum Reports is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • complexity
  • differential geometry
  • entanglement
  • entropy
  • phase transitions
  • probability theory
  • quantum computing
  • quantum information
  • quantum mechanics
  • thermodynamics

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Published Papers (3 papers)

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Research

20 pages, 4464 KiB  
Article
From Geometry to Coherent Dissipative Dynamics in Quantum Mechanics
by Hans Cruz-Prado, Alessandro Bravetti and Angel Garcia-Chung
Quantum Rep. 2021, 3(4), 664-683; https://doi.org/10.3390/quantum3040042 - 12 Oct 2021
Cited by 1 | Viewed by 3376
Abstract
Starting from the geometric description of quantum systems, we propose a novel approach to time-independent dissipative quantum processes according to which energy is dissipated but the coherence of the states is preserved. Our proposal consists of extending the standard symplectic picture of quantum [...] Read more.
Starting from the geometric description of quantum systems, we propose a novel approach to time-independent dissipative quantum processes according to which energy is dissipated but the coherence of the states is preserved. Our proposal consists of extending the standard symplectic picture of quantum mechanics to a contact manifold and then obtaining dissipation by using appropriate contact Hamiltonian dynamics. We work out the case of finite-level systems for which it is shown, by means of the corresponding contact master equation, that the resulting dynamics constitute a viable alternative candidate for the description of this subclass of dissipative quantum systems. As a concrete application, motivated by recent experimental observations, we describe quantum decays in a 2-level system as coherent and continuous processes. Full article
(This article belongs to the Special Issue Relevance of Information Geometry in Quantum Information Science)
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32 pages, 451 KiB  
Article
How Does the Planck Scale Affect Qubits?
by Matthew J. Lake
Quantum Rep. 2021, 3(1), 196-227; https://doi.org/10.3390/quantum3010012 - 1 Mar 2021
Cited by 11 | Viewed by 3046
Abstract
Gedanken experiments in quantum gravity motivate generalised uncertainty relations (GURs) implying deviations from the standard quantum statistics close to the Planck scale. These deviations have been extensively investigated for the non-spin part of the wave function, but existing models tacitly assume that spin [...] Read more.
Gedanken experiments in quantum gravity motivate generalised uncertainty relations (GURs) implying deviations from the standard quantum statistics close to the Planck scale. These deviations have been extensively investigated for the non-spin part of the wave function, but existing models tacitly assume that spin states remain unaffected by the quantisation of the background in which the quantum matter propagates. Here, we explore a new model of nonlocal geometry in which the Planck-scale smearing of classical points generates GURs for angular momentum. These, in turn, imply an analogous generalisation of the spin uncertainty relations. The new relations correspond to a novel representation of SU(2) that acts nontrivially on both subspaces of the composite state describing matter-geometry interactions. For single particles, each spin matrix has four independent eigenvectors, corresponding to two 2-fold degenerate eigenvalues ħ±(ħ+β)/2, where β is a small correction to the effective Planck’s constant. These represent the spin states of a quantum particle immersed in a quantum background geometry and the correction by β emerges as a direct result of the interaction terms. In addition to the canonical qubits states, |0⟩=|↑⟩ and |1⟩=|↓⟩, there exist two new eigenstates in which the spin of the particle becomes entangled with the spin sector of the fluctuating spacetime. We explore ways to empirically distinguish the resulting "geometric" qubits, |0′⟩ and |1′⟩, from their canonical counterparts. Full article
(This article belongs to the Special Issue Relevance of Information Geometry in Quantum Information Science)
23 pages, 7118 KiB  
Article
Information Geometric Perspective on Off-Resonance Effects in Driven Two-Level Quantum Systems
by Carlo Cafaro, Steven Gassner and Paul M. Alsing
Quantum Rep. 2020, 2(1), 166-188; https://doi.org/10.3390/quantum2010011 - 5 Feb 2020
Cited by 8 | Viewed by 2968
Abstract
We present an information geometric analysis of off-resonance effects on classes of exactly solvable generalized semi-classical Rabi systems. Specifically, we consider population transfer performed by four distinct off-resonant driving schemes specified by su 2 ; ℂ time-dependent Hamiltonian models. For each scheme, we [...] Read more.
We present an information geometric analysis of off-resonance effects on classes of exactly solvable generalized semi-classical Rabi systems. Specifically, we consider population transfer performed by four distinct off-resonant driving schemes specified by su 2 ; ℂ time-dependent Hamiltonian models. For each scheme, we study the consequences of a departure from the on-resonance condition in terms of both geodesic paths and geodesic speeds on the corresponding manifold of transition probability vectors. In particular, we analyze the robustness of each driving scheme against off-resonance effects. Moreover, we report on a possible tradeoff between speed and robustness in the driving schemes being investigated. Finally, we discuss the emergence of a different relative ranking in terms of performance among the various driving schemes when transitioning from on-resonant to off-resonant scenarios. Full article
(This article belongs to the Special Issue Relevance of Information Geometry in Quantum Information Science)
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