Zeno effect in degree of polarization of a single photon or quantum-state purity of a spin-1/2 system

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We describe a version of the Zeno effect where the monitored physical property cannot be represented by a standard operator in the system space and the evolution to be prevented by observation is not unitary. This is the case of quantum-state purity of a spin-1/2 system, which is equivalent to the degree of polarization of a single photon. By a suitable embedding of the system (say, a single photon) in an enlarged space of a pair of photons, pure and fully mixed components lead to orthogonal subspaces, with lack of purity becoming equivalent to entanglement. By imposing desirable properties the representation of the system in the enlarged space is unique. We show that the Zeno effect is possible, and experimentally feasible, in the enlarged space. The peculiarity that photons in identical polarization states are involved in pairs to observe the dynamics of each photon allows us to refer it as the self-Zeno effect or Narcissus effect.
©2013 American Physical Society. A. L. acknowledges support from Projects No. FIS2012-35583 of the Spanish Direccion General de Investigacion del Ministerio de Economia y Competitividad and QUITEMAD No. S2009-ESP-1594 of the Consejeria de Educacion de la Comunidad de Madrid. I. G. and M. A. P. acknowledge support from Project No. FIS2010-22082 of the Spanish Ministerio de Economia y Competitividad. M. A. P. acknowledges support from Project No. MTM2012-39101-C02-01 of the Spanish Ministerio de Economia y Competitividad.
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