Properties of complex chaos in conditional qubit dynamics

T. Kiss, I. Jex, G. Alber, E. Kollár

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Complex chaos is specified by an iterated mapping on complex numbers. It has recently been found in the dynamics of qubits where each time step is conditioned on a measurement result on part of the system. We analyse the simplest case of one qubit dynamics with one complex parameter in some detail. We point out that two attractive cycles can exist and provide examples how the fractal like Julia set divides the areas of corresponding initial states. We show how to determine the set of parameters for which one, two or no stable fixed cycles exists and provide the numerically calculated images of the sets. The results can be relevant for the quantum state purification protocol based on the similar dynamics of two or more qubits and in general for any protocol based on conditioned nonlinear dynamics where truly chaotic behavior may occur.

Original languageEnglish
Pages (from-to)695-700
Number of pages6
JournalInternational Journal of Quantum Information
Volume6
Issue numberSUPL.
DOIs
Publication statusPublished - 2008

Fingerprint

chaos
complex numbers
cycles
purification
fractals

Keywords

  • Complex chaos
  • Purification
  • Quantum chaos

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

Properties of complex chaos in conditional qubit dynamics. / Kiss, T.; Jex, I.; Alber, G.; Kollár, E.

In: International Journal of Quantum Information, Vol. 6, No. SUPL., 2008, p. 695-700.

Research output: Contribution to journalArticle

Kiss, T. ; Jex, I. ; Alber, G. ; Kollár, E. / Properties of complex chaos in conditional qubit dynamics. In: International Journal of Quantum Information. 2008 ; Vol. 6, No. SUPL. pp. 695-700.
@article{669ba101f4f6467e9520ee61b0221fbc,
title = "Properties of complex chaos in conditional qubit dynamics",
abstract = "Complex chaos is specified by an iterated mapping on complex numbers. It has recently been found in the dynamics of qubits where each time step is conditioned on a measurement result on part of the system. We analyse the simplest case of one qubit dynamics with one complex parameter in some detail. We point out that two attractive cycles can exist and provide examples how the fractal like Julia set divides the areas of corresponding initial states. We show how to determine the set of parameters for which one, two or no stable fixed cycles exists and provide the numerically calculated images of the sets. The results can be relevant for the quantum state purification protocol based on the similar dynamics of two or more qubits and in general for any protocol based on conditioned nonlinear dynamics where truly chaotic behavior may occur.",
keywords = "Complex chaos, Purification, Quantum chaos",
author = "T. Kiss and I. Jex and G. Alber and E. Koll{\'a}r",
year = "2008",
doi = "10.1142/S0219749908003979",
language = "English",
volume = "6",
pages = "695--700",
journal = "International Journal of Quantum Information",
issn = "0219-7499",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "SUPL.",

}

TY - JOUR

T1 - Properties of complex chaos in conditional qubit dynamics

AU - Kiss, T.

AU - Jex, I.

AU - Alber, G.

AU - Kollár, E.

PY - 2008

Y1 - 2008

N2 - Complex chaos is specified by an iterated mapping on complex numbers. It has recently been found in the dynamics of qubits where each time step is conditioned on a measurement result on part of the system. We analyse the simplest case of one qubit dynamics with one complex parameter in some detail. We point out that two attractive cycles can exist and provide examples how the fractal like Julia set divides the areas of corresponding initial states. We show how to determine the set of parameters for which one, two or no stable fixed cycles exists and provide the numerically calculated images of the sets. The results can be relevant for the quantum state purification protocol based on the similar dynamics of two or more qubits and in general for any protocol based on conditioned nonlinear dynamics where truly chaotic behavior may occur.

AB - Complex chaos is specified by an iterated mapping on complex numbers. It has recently been found in the dynamics of qubits where each time step is conditioned on a measurement result on part of the system. We analyse the simplest case of one qubit dynamics with one complex parameter in some detail. We point out that two attractive cycles can exist and provide examples how the fractal like Julia set divides the areas of corresponding initial states. We show how to determine the set of parameters for which one, two or no stable fixed cycles exists and provide the numerically calculated images of the sets. The results can be relevant for the quantum state purification protocol based on the similar dynamics of two or more qubits and in general for any protocol based on conditioned nonlinear dynamics where truly chaotic behavior may occur.

KW - Complex chaos

KW - Purification

KW - Quantum chaos

UR - http://www.scopus.com/inward/record.url?scp=49349095294&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49349095294&partnerID=8YFLogxK

U2 - 10.1142/S0219749908003979

DO - 10.1142/S0219749908003979

M3 - Article

VL - 6

SP - 695

EP - 700

JO - International Journal of Quantum Information

JF - International Journal of Quantum Information

SN - 0219-7499

IS - SUPL.

ER -