Measurementdriven 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:
 Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160C, Concepcion (Chile)
 (Chile)
 (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 160C, Concepcion, and Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco. Measurementdriven 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 160C, Concepcion, & Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco. Measurementdriven 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 160C, Concepcion, and Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco. Sun .
"Measurementdriven quantum evolution". United States.
doi:10.1103/PHYSREVA.73.0.
@article{osti_20786667,
title = {Measurementdriven 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 160C, 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 »

Evolution of a quantum system subject to continuous measurement
The path integration method is used to describe the evolution of a quantum system subject to continuous (in time) measurement. It is shown that nonselective continuous measurement leads to a continuous increase in the degree of mixing of states. A scheme is developed for calculating a family of partial evolution operators that describe the dynamics of the system with allowance for the back reaction of the instrument, and a generalized unitarity condition for them is formulated. The general results are then applied to the case of spectral measurements of a harmonic oscillator. The nature of the mixing which arises asmore » 
Comment on 'Connection between entanglement and the speed of quantum evolution' and on 'Entanglement and the lower bounds on the speed of quantum evolution'
Batle et al.[Phys. Rev. A 72, 032337 (2005)] and Borras et al.[Phys. Rev. A 74, 022326 (2006)] studied the connection between entanglement and speed of quantum evolution for certain lowdimensional bipartite quantum states. However, their studies did not cover all possible cases. And the relation between entanglement and the maximum possible quantum evolution speed for these uncovered cases can be very different from the ones that they have studied. 
Reply to 'Comment on 'Connection between entanglement and the speed of quantum evolution' and on 'Entanglement and the lower bounds on the speed of quantum evolution''
Chau's Comment deals with the properties exhibited by a particular set of twoqubit states in connection with entanglement and the quantum evolution of some lowdimensional composite systems. However, there is an important aspect of the previously mentioned twoqubit states and of the role they play in relation with the ''speed'' of quantum evolution that was not mentioned by Chau and deserves to be pointed out: for the twoqubit system under consideration, these states require the longest possible absolute time to evolve to an orthogonal state. 
Coherent states of the driven Rydberg atom: Quantumclassical correspondence of periodically driven systems
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 threedimensional 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 waveletbased timefrequency analysis, the classical phasespace structure is determined, which allowsmore »