SAMOP 2023 – scientific programme

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QI: Fachverband Quanteninformation

QI 20: Concepts and Methods II

QI 20.3: Talk

Wednesday, March 8, 2023, 15:00–15:15, B302

Resource Theory of Fermionic Correlation — •Kaustav Chatterjee, Damiano Aliverti Piuri, Lexin Ding, and Christian Schilling — Faculty of Physics, Arnold Sommerfeld Centre for Theoretical Physics, Ludwig-Maximilian-University of Munich, Germany

Resource theories are a generic approach used to manage any valuable resource, such as entanglement, purity and asymmetry. Such settings provide a novel framework to discuss information theoretic tasks like quantum state transformations and characterizing the utility of quantum states with respect to some resource measure. Analogous to resource theories of correlations and entanglement for distinguishable parties, we establish a hierarchy of resource theories for indistinguishable fermionic systems where each theory corresponds to a specific resource involving fermionic total correlation, fermionic quantum correlation or fermionic entanglement. In our theory, easily implementable operations (the free operations) are related to the set of fermionic linear optics (FLO) operations and their extensions, which naturally selects out the subset of Gaussian states as a candidate for free states in particular case where the resource is fermionic total correlations. We also introduce monotones (based on quantum relative entropy) to quantify the hierarchy of resources and explore quantum state transformation properties under such theories. We further comment on efficient classical simulation of our free operations and reveal how non-free resource states can be connected to the idea of complexity of fermionic sampling