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Title: Measurement-driven quantum evolution

Abstract

We study the problem of mapping an unknown mixed quantum state onto a known pure state without the use of unitary transformations. This is achieved with the help of sequential measurements of two noncommuting observables only. We show that the overall success probability is maximized in the case of measuring two observables whose eigenstates define mutually unbiased bases. We find that for this optimal case the success probability quickly converges to unity as the number of measurement processes increases and that it is almost independent of the initial state. In particular, we show that to guarantee a success probability close to one the number of consecutive measurements must be larger than the dimension of the Hilbert space. We connect these results to quantum copying, quantum deleting, and entanglement generation.

Authors:
; ; ;  [1];  [2];  [3]
  1. Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile)
  2. (Chile)
  3. (Mexico)
Publication Date:
OSTI Identifier:
20786667
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.73.012322; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; EIGENSTATES; ENERGY LEVELS; EVOLUTION; HILBERT SPACE; MAPPING; PROBABILITY; QUANTUM ENTANGLEMENT; TRANSFORMATIONS; UNITARITY

Citation Formats

Roa, L., Delgado, A., Ladron de Guevara, M. L., Klimov, A. B., Departamento de Fisica, Universidad Catolica del Norte, Casilla 1280, Antofagasta, Chile and Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion, and Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco. Measurement-driven quantum evolution. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.73.0.
Roa, L., Delgado, A., Ladron de Guevara, M. L., Klimov, A. B., Departamento de Fisica, Universidad Catolica del Norte, Casilla 1280, Antofagasta, Chile and Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion, & Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco. Measurement-driven quantum evolution. United States. doi:10.1103/PHYSREVA.73.0.
Roa, L., Delgado, A., Ladron de Guevara, M. L., Klimov, A. B., Departamento de Fisica, Universidad Catolica del Norte, Casilla 1280, Antofagasta, Chile and Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion, and Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco. Sun . "Measurement-driven quantum evolution". United States. doi:10.1103/PHYSREVA.73.0.
@article{osti_20786667,
title = {Measurement-driven quantum evolution},
author = {Roa, L. and Delgado, A. and Ladron de Guevara, M. L. and Klimov, A. B. and Departamento de Fisica, Universidad Catolica del Norte, Casilla 1280, Antofagasta, Chile and Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion and Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco},
abstractNote = {We study the problem of mapping an unknown mixed quantum state onto a known pure state without the use of unitary transformations. This is achieved with the help of sequential measurements of two noncommuting observables only. We show that the overall success probability is maximized in the case of measuring two observables whose eigenstates define mutually unbiased bases. We find that for this optimal case the success probability quickly converges to unity as the number of measurement processes increases and that it is almost independent of the initial state. In particular, we show that to guarantee a success probability close to one the number of consecutive measurements must be larger than the dimension of the Hilbert space. We connect these results to quantum copying, quantum deleting, and entanglement generation.},
doi = {10.1103/PHYSREVA.73.0},
journal = {Physical Review. A},
number = 1,
volume = 73,
place = {United States},
year = {Sun Jan 15 00:00:00 EST 2006},
month = {Sun Jan 15 00:00:00 EST 2006}
}
  • We study the problem of driving an unknown initial mixed quantum state onto a known pure state without using unitary transformations. This can be achieved, in an efficient manner, with the help of sequential measurements on at least two unbiased bases. However here we found that, when the system is affected by a decoherence mechanism, only one observable is required in order to achieve the same goal. In this way the decoherence can assist the process. We show that, depending on the sort of decoherence, the process can converge faster or slower than the method implemented by means of twomore » complementary observables.« less
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  • A methodology to calculate generalized coherent states for a periodically driven system is presented. We study wave packets constructed as a linear combination of suitable Floquet states of the three-dimensional Rydberg atom in a microwave field. The driven coherent states show classical space localization, spreading, and revivals and remain localized along the classical trajectory. The microwave strength and frequency have a great effect in the localization of Floquet states, since quasienergy avoided crossings produce delocalization of the Floquet states, showing that tuning of the parameters is very important. Using wavelet-based time-frequency analysis, the classical phase-space structure is determined, which allowsmore » us to show that the driven coherent state is located in a large regular region in which the z coordinate is in resonance with the external field. The expectation values of the wave packet show that the driven coherent state evolves along the classical trajectory.« less