Quantum and Classical Bayesian Agents

John B. DeBrota; Peter J. Love

doi:10.22331/q-2022-05-16-713

Quantum and Classical Bayesian Agents

John B. DeBrota¹ and Peter J. Love

¹Department of Physics and Astronomy, Tufts University, Medford, MA 02155, USA

Published:	2022-05-16, volume 6, page 713
Eprint:	arXiv:2106.09057v2
Doi:	https://doi.org/10.22331/q-2022-05-16-713
Citation:	Quantum 6, 713 (2022).

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Abstract

We describe a general approach to modeling rational decision-making agents who adopt either quantum or classical mechanics based on the Quantum Bayesian (QBist) approach to quantum theory. With the additional ingredient of a scheme by which the properties of one agent may influence another, we arrive at a flexible framework for treating multiple interacting quantum and classical Bayesian agents. We present simulations in several settings to illustrate our construction: quantum and classical agents receiving signals from an exogenous source, two interacting classical agents, two interacting quantum agents, and interactions between classical and quantum agents. A consistent treatment of multiple interacting users of quantum theory may allow us to properly interpret existing multi-agent protocols and could suggest new approaches in other areas such as quantum algorithm design.

Featured image: Bloch ball plots of the final posterior densities within the standard deviation ellipsoids for two simulations, (a) and (b), of 100 interactions by expectation sampling between two N = 4, i.e. qubit, quantum agents who, for each interaction, take one of the three Pauli measurements on the system received from the other. Both agents have uniform utility functions across all six outcomes of these three actions; hence, at each interaction, both choose a Pauli measurement randomly with equal probability. Each agents’ initial prior is uniform over the Bloch ball. In each plot, the blue and red dots are the means of the final posteriors and the blue and red lines are the paths of the previous posterior means. By the end of each simulation, the final means and standard deviations are similar, that is, it seems the agents are coming to agreement. Where their final posteriors end up depends on their choices and their outcomes.

► BibTeX data

@article{DeBrota2022quantumclassical,
  doi = {10.22331/q-2022-05-16-713},
  url = {https://doi.org/10.22331/q-2022-05-16-713},
  title = {Quantum and {C}lassical {B}ayesian {A}gents},
  author = {DeBrota, John B. and Love, Peter J.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {713},
  month = may,
  year = {2022}
}

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[1] Alireza Tavanfar, Aliasghar Parvizi, and Marco Pezzutto, "Unitary Evolutions Sourced By Interacting Quantum Memories: Closed Quantum Systems Directing Themselves Using Their State Histories", Quantum 7, 1007 (2023).

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