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How to play macroscopic quantum game
| Content Provider | Semantic Scholar |
|---|---|
| Author | Grib, A. A. Parfionov, G. N. |
| Copyright Year | 2008 |
| Abstract | Quantum games are usually considered as games with strategies defined not by the standard Kolmogorovian probabilistic measure but by the probability amplitude used in quantum physics. The reason for the use of the probability amplitude or ”quantum probabilistic measure” is the nondistributive lattice occurring in physical situations with quantum microparticles. In our paper we give examples of getting nondistributive orthomodular lattices in some special macroscopic situations without use of quantum microparticles. Mathematical structure of these examples is the same as that for the spin one half quantum microparticle with two non-commuting observables being measured. So we consider the so called Stern-Gerlach quantum games. In quantum physics it corresponds to the situation when two partners called Alice and Bob do experiments with two beams of particles independently measuring the spin projections of particles on two different directions In case of coincidences defined by the payoff matrix Bob pays Alice some sum of money. Alice and Bob can prepare particles in the beam in certain independent states defined by the probability amplitude so that probabilities of different outcomes are known. Nash equilibrium for such a game can be defined and it is called the quantum Nash equilibrium. The same lattice occurs in the example of the firefly flying in a box observed through two windows one at the bottom another at the right hand side of the box with a line in the middle of each window. This means that two such boxes with fireflies inside them imitate two beams in the SternGerlach quantum game. However there is a difference due to the fact that in microscopic case Alice and Bob freely choose the representation of the lattice in terms of non-commuting projectors in some Hilbert space. In our macroscopic imitation there is a problem of the choice of this representation(of the Department of Theoretical Physics and Astronomy, A.I.Herzen State Pedagogical University, Russia. e-mail: Andrei-grib@mail.ru St.Petersburg State University of Economics and Finances, St. Petersburg, Russia. e-mail: GogaParf@gmail.com |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/0811.3015v1.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/0811.3015v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
