Complexity and efficiency of minimum entropy production probability paths from quantum dynamical evolutions

Abstract

We present an information geometric characterization of quantum driving schemes specified by su(2;C) time-dependent Hamiltonians in terms of both complexity and efficiency concepts. By employing a minimum action principle, the optimum path connecting initial and final states on the manifold in finite-time is the geodesic path between the two states. In particular, the total entropy production that occurs during the transfer is minimized along these optimum paths. For each optimum path that emerges from the given quantum driving scheme, we evaluate the so-called information geometric complexity (IGC) and our newly proposed measure of entropic efficiency constructed in terms of the constant entropy production rates that specify the entropy minimizing paths being compared. From our analytical estimates of complexity and efficiency, we provide a relative ranking among the driving schemes being investigated. Finally, we conclude by commenting on the fact that an higher entropic speed in quantum transfer processes seems to necessarily go along with a lower entropic efficiency together with a higher information geometric complexity.

arXiv comment21 pages, 2 figures, 1 table

References in corpus (25)

• Quantum algorithms: an overview
• Generalized uncertainty relations: Theory, examples, and Lorentz invariance
• Measuring thermodynamic length
• Thermodynamic Geometry of Microscopic Heat Engines
• Geometrical Bounds of the Irreversibility in Markovian Systems
• Elementary Derivation for Passage Times
• A geometric approach to optimal nonequilibrium control: Minimizing dissipation in nanomagnetic spin systems
• Action quantum speed limits
• Thermodynamic Length, Time, Speed and Optimum Path to Minimize Entropy Production
• Jacobi Fields on Statistical Manifolds of Negative Curvature
• Information geometric methods for complexity
• Geometry of work fluctuations versus efficiency in microscopic thermal machines
• Nonequilibrium uncertainty principle from information geometry
• Initial-State Dependence of Thermodynamic Dissipation for any Quantum Process
• Classes of Exactly Solvable Generalized Semi-Classical Rabi Systems
• Evolution speed of open quantum dynamics
• The Effect Of Microscopic Correlations On The Information Geometric Complexity Of Gaussian Statistical Models
• Unified framework for the entropy production and the stochastic interaction based on information geometry
• A Geometric Algebra Perspective On Quantum Computational Gates And Universality In Quantum Computing
• Information Geometry Aspects of Minimum Entropy Production Paths from Quantum Mechanical Evolutions
• Decrease of Fisher information and the information geometry of evolution equations for quantum mechanical probability amplitudes
• Geometric aspects of analog quantum search evolutions
• Theoretical investigations of an information geometric approach to complexity
• Theoretical analysis of a nearly optimal analog quantum search
• Information Geometric Aspects of Probability Paths with Minimum Entropy Production for Quantum State Evolution

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