Abstract
We study entanglement in a composite system built out of two interacting subsystems. The long-time entanglement is shown to be quantified in terms of the S-matrix of an auxiliary single-particle scattering process. We present exact results for a system consisting of a qubit and an oscillator as well as for the case of a pair of qubits and a single oscillator. We show that entanglement can precisely be controlled by tuning the parameters of the corresponding scattering process. Within tailored parameter regimes, the extremal entanglement is achieved when time of scattering is of order of the oscillator frequency inverse.
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Albeverio S. et al.: Solvable models in quantum mechanics. AMS Chelsea Publishing, Providence (2004)
Alicki R.: Pure decoherence in quantum systems. Open Sys. Inf. Dyn. 11, 53–61 (2004)
Buscemi F., Bordone P., Bertoni A.: Entanglement dynamics of electron–electron scattering in low-dimensional semiconductor systems. Phys. Rev. A 73, 052312–052321 (2006)
Costa A.T., Bose S., Omar Y.: Entanglement of two impurities through electron scattering. Phys. Rev. Lett. 96, 230501 (2006)
Dajka J., Łuczka J.: Origination and survival of qudit–qudit entanglement in open system. Phys. Rev. A 77, 062303–062306 (2008)
Dajka J., Łuczka J.: Bifurcations of the geometric phase of a qubit asymmerically coupled to the environment. J. Phys. A Math. Theor. 41, F442001–F442008 (2008)
Dajka J., Mierzejewski M., Łuczka J.: Entanglement persistence in contact with environment: exact results. J. Phys. A Math. Theor. 40, F879–F886 (2007)
Dajka J., Mierzejewski M., Łuczka J.: Geometric phase of a qubit in dephasing environments. J. Phys. A Math. Theor. 41, F012001–F012007 (2008)
Dajka J., Mierzejwski M., Łuczka J.: Non-Markovian entanglement evolution of two uncoupled qubits. Phys. Rev. A 77, 042316–042318 (2008)
Dajka J., Mierzejewski M., Łuczka J.: Fidelity of asymmetric dephasing channels. Phys. Rev. A 79, 012104–012107 (2009)
Eckart C.: The penetration of a potential barrier by electrons. Phys. Rev. 35, 1303–1309 (1930)
Gardiner S.A., Cirac J.I., Zoller P.: Quantum chaos in an ion trap: the Delta-kicked harmonic oscillator. Phys. Rev. Lett. 79, 4790–4794 (1997)
Habgood M., Jefferson J.H., Briggs G.A.D.: Scattering-induced entanglement between spin qubits at remote two-state structures. J. Phys. Condens. Matter 21, 075503–075511 (2009)
Harshman N.L., Singh P.: Entanglement mechanisms in one-dimensional potential scattering. J. Phys. A Math. Theor. 41, 155304–155316 (2008)
Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement, quant-ph/0703044. Rev. Mod. Phys. 81, 865–943 (2009)
Kiesel N., Schmid C., Weber U., Ursin R., Weinfurter H.: Linear optics controlled-phase gate made simple. Phys. Rev. Lett. 95, 210505–210509 (2005)
Leibfried D., Knill E., Seidelin S., Britton J., Blakestad R.B., Chiaverini J., Hume D.B., Itano W.M., Jost J.D., Langer C., Ozeri R., Reichle R., Wineland D.J.: Creation of a six-atom ‘Schrdinger cat’ state. Nature (London) 438, 639–642 (2005)
Łuczka J.: Spin in contact with thermostat: exact reduced dynamics. Physica A 167, 919–934 (1990)
Mintert F.: Concurrence via entanglement witnesses. Phys. Rev. A 75, 052302–052306 (2007)
Mintert F., Buchleitner A.: Observable entanglement measure for mixed quantum states. Phys. Rev. Lett. 98, 140505–140509 (2007)
Mintert F., Kuś M., Buchleitner A.: Concurrence of mixed multipartite quantum states. Phys. Rev. Lett. 95, 260502–260506 (2005)
Mintert F., Carvalho A.R.R., Kuś M., Buchleitner A.: Mesures and dynamics of entangled states. Phys. Rep. 415, 207–259 (2005)
Mishima K., Hayashi M., Lin S.H.: Entanglement in scattering processes. Phys. Lett. A 333, 371–377 (2004)
Montangero S., Romito A., Benenti G., Fazio R.: Chaotic dynamics in superconducting nanocircuits. Europhys. Lett. 71, 893–899 (2005)
Perelomov A.M., Popov V.S.: Parametric excitation of a quantum oscillator. JETP 56, 1375–1390 (1969)
Peres A.: Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413–1416 (1996)
Pozzo E.N., Dominguez D.: Fidelity and quantum chaos in the mesoscopic device for the Josephson flux qubit. Phys. Rev. Lett. 98, 057006–057010 (2007)
Reed M., Simon B.: Methods of modern mathematical physics. Scattering theory. Academic Press, San Diego (1979)
Roszak K., Machnikowski P.: Complete disentanglement by partial pure dephasing. Phys. Rev. A 73, 022313–022319 (2006)
Schmid C., Kiesel N., Wieczorek W., Weinfurter H., Mintert F., Buchleitner A.: Experimental direct observation of mixed state entanglement. Phys. Rev. Lett. 101, 260505–260509 (2008)
Schwinger J.: The theory of quantized fields. III. Phys. Rev. 91, 728–740 (1953)
Sitenko A.G.: Scattering theory. Spriner, Berlin (1991)
Vidal G., Werner R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314–032325 (2002)
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Dajka, J., Mierzejewski, M. & Łuczka, J. Analytically solvable model for the entanglement via scattering-like mechanisms. Quantum Inf Process 8, 461–475 (2009). https://doi.org/10.1007/s11128-009-0121-1
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DOI: https://doi.org/10.1007/s11128-009-0121-1