Geometric Quantum Mechanics ‒ A exploratory seminar series

            Complexity Sciences Center

Co-Organizers: Fabio Anza (UC Davis) and Sebastian Deffner (UMBC)

Background & Goals

Differential geometric foundations bring quantum mechanics much closer to classical dynamics. We seek a new dynamical systems framing for (and hope to import its tools to) quantum physics. One hope is that this will lead to a more structural and information-theoretic view—a basis for quantum computational mechanics that identifies the loci of information storage and processing in quantum dynamics.

Topical Areas

This seminar aims to address the following:

1. •Quantum computational mechanics
   

2. •Prediction, inference, and tomography in GQM
   

3. •Nonequilibrium quantum thermodynamics
   

4. •Quantum Darwinism
   

5. •Information measures and processing for quantum stochastic processes
   

Presentations:

1. 1.1 February 2021: Kickoff Meeting
   

    Introductions all around, discussion of our common starting point, and the need for a common setting.

   Meeting recording

2. 15 February 2021: Fabio Anza on Geometric Quantum Mechanics

   Paper: Beyond Density Matrices: Geometric Quantum States.

   Meeting recording

3. 3.1 March 2021: Akira Sone on The Geometric Approach to Quantum Thermodynamics
   

    In this talk, I will outline our most recent manuscript on the geometric approach to quantum thermodynamics. In this work, we show that geometric quantum mechanics is a consistent manner of bridging quantum and classical formulations of the second law of thermodynamics. To this end, we take into account the informational contributions derived from concept of coherence, both classically as well as quantumly. Particularly, by formulating the relative entropy in the geometric approach, we can explicitly demonstrate its relation to quantum ergotropy, which also leads us to introduce the classical correspondence to the quantum ergotropy. These analyses further elucidate the relation between the maximum work extraction from geometric canonical ensembles and their coherence.

    Talk slides

    Quantum and Classical Ergotropy from relative entropies, https://arxiv.org/abs/2103.10850

4. 12 April 2021: Akram Touil on Watching the watcher---quantum Darwinism and the inevitable classicality of open systems

Understanding everyday observations of our classical world from seemingly peculiar quantum principles is a fundamental problem. We address it by relying on the insights of quantum Darwinism: We study the emergence of objective classical reality in the example of a central spin undergoing decoherence in a many-spin environment. The system-environment interactions are modeled by imperfect c-not (or "c-maybe") operations, which enables us to tune and quantify the reliability with which the environment monitors the central spin. We derive analytic expressions for the quantum mutual information, Holevo bound, as well as quantum discord between the central spin and an arbitrary fragment of the environment. We consider information extracted by measurements of either the system or collection of  environment spins -- environment fragments.  We show that agents will inevitably reach the classical plateau (that assures emergence of the consensus about classical reality of the inferred states) by intercepting sufficiently large fragments of the environment, also in the realistic case of non-ideal measurements. We also compute mutual information between two fragments of the environment. This corresponds to the situation responsible for emergence of the objective classical reality from within our quantum Universe where observers find out about the systems of interest by eavesdropping on independent environment fragments.

Upcoming:

1. •Sebastian Deffner: Information Scrambling
   

2. •Alec Boyd: Information Engines and their Thermodynamic Computing Principles
   

3. •David Gier: Information in Quantum Processes
   

4. •Ariadna Venegas-Li: Measurement-Induced Randomness and Complexity
   

5. •And others