Jarosław Pykacz | University of Gdansk (original) (raw)
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Papers by Jarosław Pykacz
International Journal of Theoretical Physics
It is shown that any quantum logic in the Birkhoff-von Neumann sense that possesses an ordering s... more It is shown that any quantum logic in the Birkhoff-von Neumann sense that possesses an ordering set of probability measures can be isomorphically represented as a particular kind of infinite-valued Łukasiewicz logic with partially defined conjunction and disjunction. It is argued that such non-classical features of BvN quantum logic as lack of distributivity or validity of the orthomodular law follow from properties of Łukasiewicz conjunction and disjunction.
International Journal of Theoretical Physics
It is shown that any quantum logic in the Birkhoff-von Neumann sense that possesses an ordering s... more It is shown that any quantum logic in the Birkhoff-von Neumann sense that possesses an ordering set of probability measures can be isomorphically represented as a particular kind of infinite-valued Łukasiewicz logic with partially defined conjunction and disjunction. It is argued that such non-classical features of BvN quantum logic as lack of distributivity or validity of the orthomodular law follow from properties of Łukasiewicz conjunction and disjunction.
International Journal of Theoretical Physics
The aim of the paper is to draw attention to a special class of two parameter unitary strategies ... more The aim of the paper is to draw attention to a special class of two parameter unitary strategies in the Eisert-Wilkens-Lewenstein scheme for quantum games. We identify the players' strategies with basis change matrices. Then we prove that the resulting quantum game is invariant with respect to isomorphic transformations of the input game. Moreover, it is shown that the game so obtained may not be trivial with respect to pure Nash equilibria, compared with the model with strategies being the special unitary group SU(2).
International Journal of Theoretical Physics
The aim of the paper is to draw attention to a special class of two parameter unitary strategies ... more The aim of the paper is to draw attention to a special class of two parameter unitary strategies in the Eisert-Wilkens-Lewenstein scheme for quantum games. We identify the players' strategies with basis change matrices. Then we prove that the resulting quantum game is invariant with respect to isomorphic transformations of the input game. Moreover, it is shown that the game so obtained may not be trivial with respect to pure Nash equilibria, compared with the model with strategies being the special unitary group SU(2).
International Journal of Theoretical Physics
The long-lasting problem of proper mathematical representation of conjunctions and disjunctions i... more The long-lasting problem of proper mathematical representation of conjunctions and disjunctions in quantum logics is reviewed and three recent proposals of solutions are described.
Journal of Electrical Engineering, 2016
The paper gives an overview and compares various bi-varilable maps from orthomodular lattices int... more The paper gives an overview and compares various bi-varilable maps from orthomodular lattices into unit interval. It focuses mainly on such bi-variable maps that may be used for constructing joint probability distributions for random variables which are not defined on the same Boolean algebra.
SpringerBriefs in Physics, 2015
Waves and Particles in Light and Matter, 1994
![Research paper thumbnail of Publisher's Note: Quantum morphogenesis: A variation on Thom's catastrophe theory [Phys. Rev. E 67, 051926 (2003)]](https://attachments.academia-assets.com/66730712/thumbnails/1.jpg)
](Physical Review E, 2004
Non-commutative propositions are characteristic of both quantum and non-quantum (sociological, bi... more Non-commutative propositions are characteristic of both quantum and non-quantum (sociological, biological, psychological) situations. In a Hilbert space model states, understood as correlations between all the possible propositions, are represented by density matrices. If systems in question interact via feedback with environment their dynamics is nonlinear. Nonlinear evolutions of density matrices lead to phenomena of morphogenesis which may occur in non-commutative systems. Several explicit exactly solvable models are presented, including 'birth and death of an organism' and 'development of complementary properties'.
Quantum Structures and the Nature of Reality, 1999
Language, Quantum, Music, 1999
The Concept of Probability, 1989
Fundamental Problems in Quantum Physics, 1995
Studies in Fuzziness and Soft Computing, 2013
New Developments on Fundamental Problems in Quantum Physics, 1997
SpringerBriefs in Physics, 2015
SpringerBriefs in Physics, 2015
SpringerBriefs in Physics, 2015
SpringerBriefs in Physics, 2015
International Journal of Theoretical Physics
It is shown that any quantum logic in the Birkhoff-von Neumann sense that possesses an ordering s... more It is shown that any quantum logic in the Birkhoff-von Neumann sense that possesses an ordering set of probability measures can be isomorphically represented as a particular kind of infinite-valued Łukasiewicz logic with partially defined conjunction and disjunction. It is argued that such non-classical features of BvN quantum logic as lack of distributivity or validity of the orthomodular law follow from properties of Łukasiewicz conjunction and disjunction.
International Journal of Theoretical Physics
It is shown that any quantum logic in the Birkhoff-von Neumann sense that possesses an ordering s... more It is shown that any quantum logic in the Birkhoff-von Neumann sense that possesses an ordering set of probability measures can be isomorphically represented as a particular kind of infinite-valued Łukasiewicz logic with partially defined conjunction and disjunction. It is argued that such non-classical features of BvN quantum logic as lack of distributivity or validity of the orthomodular law follow from properties of Łukasiewicz conjunction and disjunction.
International Journal of Theoretical Physics
The aim of the paper is to draw attention to a special class of two parameter unitary strategies ... more The aim of the paper is to draw attention to a special class of two parameter unitary strategies in the Eisert-Wilkens-Lewenstein scheme for quantum games. We identify the players' strategies with basis change matrices. Then we prove that the resulting quantum game is invariant with respect to isomorphic transformations of the input game. Moreover, it is shown that the game so obtained may not be trivial with respect to pure Nash equilibria, compared with the model with strategies being the special unitary group SU(2).
International Journal of Theoretical Physics
The aim of the paper is to draw attention to a special class of two parameter unitary strategies ... more The aim of the paper is to draw attention to a special class of two parameter unitary strategies in the Eisert-Wilkens-Lewenstein scheme for quantum games. We identify the players' strategies with basis change matrices. Then we prove that the resulting quantum game is invariant with respect to isomorphic transformations of the input game. Moreover, it is shown that the game so obtained may not be trivial with respect to pure Nash equilibria, compared with the model with strategies being the special unitary group SU(2).
International Journal of Theoretical Physics
The long-lasting problem of proper mathematical representation of conjunctions and disjunctions i... more The long-lasting problem of proper mathematical representation of conjunctions and disjunctions in quantum logics is reviewed and three recent proposals of solutions are described.
Journal of Electrical Engineering, 2016
The paper gives an overview and compares various bi-varilable maps from orthomodular lattices int... more The paper gives an overview and compares various bi-varilable maps from orthomodular lattices into unit interval. It focuses mainly on such bi-variable maps that may be used for constructing joint probability distributions for random variables which are not defined on the same Boolean algebra.
SpringerBriefs in Physics, 2015
Waves and Particles in Light and Matter, 1994
Physical Review E, 2004
Non-commutative propositions are characteristic of both quantum and non-quantum (sociological, bi... more Non-commutative propositions are characteristic of both quantum and non-quantum (sociological, biological, psychological) situations. In a Hilbert space model states, understood as correlations between all the possible propositions, are represented by density matrices. If systems in question interact via feedback with environment their dynamics is nonlinear. Nonlinear evolutions of density matrices lead to phenomena of morphogenesis which may occur in non-commutative systems. Several explicit exactly solvable models are presented, including 'birth and death of an organism' and 'development of complementary properties'.
Quantum Structures and the Nature of Reality, 1999
Language, Quantum, Music, 1999
The Concept of Probability, 1989
Fundamental Problems in Quantum Physics, 1995
Studies in Fuzziness and Soft Computing, 2013
New Developments on Fundamental Problems in Quantum Physics, 1997
SpringerBriefs in Physics, 2015
SpringerBriefs in Physics, 2015
SpringerBriefs in Physics, 2015
SpringerBriefs in Physics, 2015