Open access
Autor(in)
Datum
2023Typ
- Student Paper
ETH Bibliographie
yes
Altmetrics
Abstract
In 1935 Einstein first stated that quantum theory, as we know it, is an in-
complete theory. In fact, quantum theory, as given by the Born rule, has an
inherently random component, restricting it to providing probabilities for a cer-
tain measurement outcome rather than specific predictions of outcomes.
We explore a new approach that aims to lift this restriction with the help of
game theory. It has been shown that Nashian game theory is incompatible with
quantum theory. Hence, a new non-Nashian equilibrium has been introduced.
This equilibrium is attained by relaxing the free choice assumption commonly
found in quantum theory in favour of Einstein’s localism. The use of such a
method is thought to enable making deterministic predictions over the out-
comes of quantum experiments.
There already exists a method for solving games with non-Nashian theory. It
does, however, require as input a game in extensive form with imperfect infor-
mation and therefore still misses the link to quantum experiments.
We present a practical framework for representing quantum experiments
mathematically based on the process matrix framework. This transition, from
a physical experiment to the mathematical representation, makes use of the
Choi-Jamiolkowski representation of quantum channels and states, as well as
the process matrix representation of quantum processes.
The implementation detailed in this report includes both a JSON storage for-
mat and a Python library. This library comprises an algorithm for mapping a
quantum experiment to a game in extensive form with imperfect information,
as well as other (visualisation) utility functions.
This report lays the way for future work to advance our understanding of
non-Nashian game theory and to prove its consistency with quantum theory. Mehr anzeigen
Persistenter Link
https://doi.org/10.3929/ethz-b-000665746Publikationsstatus
publishedVerlag
ETH ZurichOrganisationseinheit
03506 - Alonso, Gustavo / Alonso, Gustavo
Zugehörige Publikationen und Daten
ETH Bibliographie
yes
Altmetrics