Reduced conditional dynamic of quantum system under indirect quantum measurement
Abstract
In this report, we study the reduced conditional dynamics of a quantum system in the case of indirect quantum measurement. The detector’s microscopic part (pointer) interacts with the measured system (target) and the environment, which results in a nonunitary interaction between target and pointer. The quantum state evolution conditioned by the measurement result is under investigation. Particularly, we are interested in explicit analytical expressions for the conditional evolution superoperators and basic information characteristics of this measurement process, which is applied to the cavity mode photodetection problem.
Keywords
indirect quantum measurements,
conditional evolution,
photodetection problem,
rotating wave approximation,
quantum entropy
Supporting agencies: The work was supported by FTP “Scientific and Educational Human Resources for InnovationDriven Russia” (contract 16.740.11.0030, grant 20121.2.2120001001047), grant 110800267 of RFBR and by FTP “Researches and Development in the Priority Directions Developments of a Scientific and Technological Complex of Russia 20072013” (contract 07.514.11.4146).
About the Authors
A. I. Trifanov
Saint Petersburg National Research University of Information Technologies, Mechanics and Optics
Russian Federation
Russian Federation
197101, 49 Kronverksky, Saint Petersburg
G. P. Miroshnichenko
Saint Petersburg National Research University of Information Technologies, Mechanics and Optics
Russian Federation
Russian Federation
197101, 49 Kronverksky, Saint Petersburg
References
1. M.A. Nielsen, I.L. Chuang. Quantum Computation and Quantum Information, Cmbridge Univrsity Prss, Cambridge, 2001.
2. C.A. PerezDelgado, P. Kok. Quantum computers: Definition and implementations. Phys. Rev. A, 83 (1), P. 012303(15) (2011).
3. V.B. Braginsky, F.Ya. Khalili. Quantum Measurement, Cambridge University Press, Cambridge, 1992.
4. W.H. Zurek. Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys., 75 (3), P. 715(61) (2003).
5. H.P. Breuer, F. Petruccione. The theory of open quantum systems, Oxford University Press Inc., New York, 2002.
6. H. Carmichael. An open system approach to quantum optics, SpringerVerlag Berlin Heidelberg New York, 1991.
7. H. Grabert, P. Schramm, G.L. Ingold. Quantum Brownian motion: The functional integral approach. Phys. Rep., 168, P. 115–207 (1988).
8. T. Mancal, V. May. NonMarkovian relaxation in an open quantum system. EPJ B, 18 (4), P. 633–643 (2000).
9. C.M. Caves. Quantum mechanics of measurements distributed in time. II Connections among formulations. Phys. Rev. D, 35 (6), P. 1815–1830 (1987).
10. C.M. Caves. Quantum mechanics of measurements distributed in time. A pathintegral formulation. Phys. Rev. D, 33 (6), P. 1643–1665 (1986).
11. J. von Neumann. Mathematical foundations of quantum mechanics. Trans. by R.T. Beyer. Princeton: Unive. Press, 1955.
12. K. Kraus. States, Effects and Operations. Fundamental notions of quantum theory, SpringerVerlag Berlin Heldeiberg, 1983.
13. R.P. Feinman. Spacetime approach to nonrelativisticquantum mechanics. Rev. Mod. Phys., 20 (2), P. 367–387 (1948).
14. M.B. Mensky. Continuous quantum measurements and path integrals, IOP Publishing Ltd., London, 1993.
15. JunTao Chang, M. Suhail Zubairy. Threequbit phase gate based on cavity quantum electrodynamics. Phys. Rev. A., 77 (1), P. 012329(8) (2008).
16. G.P. Miroshnichenko, A.I. Trifanov. Conditional phase shift for quantum CCNOT operation. Quantum Inf. Process., 12 (3), P. 1417–1428, 2013.
17. A. Shukla, K.R.K. Rao, T.S. Mahesh. Ancillaassisted quantum state tomography in multiqubit registers. Phys. Rev. A, 87 (6), P. 062317 (8) (2013).
18. A. Bendersky, F. Pastawski, J.P. Paz. Selective and Efficient Estimation of Parameters for Quantum Process Tomography. Phys. Rev. Lett., 100, P. 190403(4) (2008).
19. Seth T. Merkel et al. Selfconsistent quantum process tomography. Phys. Rev. A, 87 (6), P. 062119(9) (2013).
20. M.A. Naimark. About secondkind selfadjoint extensions of symmetrical operator. Izv. Akad. Nauk USSR, Ser. Mat., 4, P. 53–104 (in russian) (1940).
21. C. Sparaciari, M.G.A. Paris. Canonical Naimark extension for generalized measurements involving sets of Pauli quantum observables chosen at random. Phys. Rev. A, 87 (1), P. 012106(7) (2013).
22. Sujit K. Choudhary, T. Konrad, H. Uys. Implementation schemes for unsharp measurements with trapped ions. Phys. Rev. A, 87 (1), P. 012131(8) (2013).
23. A.V. Dodonov, S.S. Mizrahi, V.V. Dodonov. Inclusion of nonidealities in the continuous photodetection model. Phys. Rev. A, 75 (1), P. 013806 (8) (2007).
24. G.P. Miroshnichenko, A.I. Trifanov. The photodetection process under the conditions of an imperfect measurement device. EPJ D, DOI: 10.1140/epjd/e2013307398 (2013).
Review
For citations:
Trifanov A.I., Miroshnichenko G.P. Reduced conditional dynamic of quantum system under indirect quantum measurement. Nanosystems: Physics, Chemistry, Mathematics. 2013;4(5):635–647.
Views:
7
Email this article 