Pure state entanglement in terms of nilpotent variables: η-toolbox

Frydryszak, Andrzej

doi:10.1142/9789814317443_0005

Cited by 1 publication

(6 citation statements)

References 21 publications

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“…At the same time quantum information theory is basically done in n-qubit space. It is well know that qubit is neither boson nor fermion (Frydryszak, 2011). In some sense it combines both fermionic and bosonic features.…”

Section: Cision Makingmentioning

confidence: 99%

“…The number operator can be represented in the standard way N = a a and the free Hamiltonian as H 0 = ωa a. We remark that in quantum information theory (Frydryszak, 2011) these anti-commutation relations are written in the following form [? ]:…”

Section: Cision Makingmentioning

confidence: 99%

“…However, up to my knowledge, this formalism is not so widely explored, see, however, again (Frydryszak, 2011).…”

Section: Cision Makingmentioning

confidence: 99%

“…I would like to thank A. Khrennikov for discussions and consultations on the mathematical formalism of quantum theory, in particular, for kindly pointing out that the mixed fermionic-bosonic algebra of creation and annihilation operators is known in quantum information theory as the qubit algebra of creation and annihilation operators and suggesting the relevant references to this field (Frydryszak, 2011). I also would like to thank the anonymous reviewers for their kind remarks on the usage of fermionic-bosonic algebra of creation and annihilation operators, as well as their remarks on the generalizability of the proposed model to broader contexts of decision making.…”

Section: Acknowledgementsmentioning

confidence: 99%

“…On the other hand, the qubit formalism of creation-annihilation operators is not so widely applied. 3 We can only mention a detailed presentation of this formalism by Frydryszak (2011). One of the primary aims of this paper is to present essentials of this quantization formalism to readers interested in applications of the quantum methods to cognitive psychology and decision theory in sociology, economics and finance.…”

Section: Introductionmentioning

confidence: 99%

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Modeling behavior of decision makers with the aid of algebra of qubit creation–annihilation operators

Khrennikova

2017

Journal of Mathematical Psychology

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We present a general model of the process of decision making based on the representation of the basic behavioral variables with the aid of an algebra of qubit creation-annihilation operators, adopted from the quantum information theory. In contrast to the genuine quantum physical systems, which are divided into either bosons or fermions and modeled with the aid of operators, satisfying canonical commutation or anti-commutation relations, decision makers preferences for possible actions are constructed with the aid of operators satisfying the socalled qubit commutation relations. Systems described by operators, satisfying such commutation relations, combine the features of bosons and fermions. Thus, one of the basic consequences of the presented model is that decision makers mimic the combined bosonic-fermionic behavior. By using the algebra of qubit creation-annihilation operators, we proceed with the construction of the concrete operators, describing the process of decision making. In particular, the generators of the quantum Markov dynamics, which is used for modeling human decision making process, are expressed as polynomials of the qubit creation-annihilation operators. The devised coefficients have a natural cognitive and social meaning.

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Section: Cision Makingmentioning

confidence: 99%

Section: Cision Makingmentioning

confidence: 99%

“…However, up to my knowledge, this formalism is not so widely explored, see, however, again (Frydryszak, 2011).…”

Section: Cision Makingmentioning

confidence: 99%

Section: Acknowledgementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%