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Relating Local Time Evolutions with Bipartite States: An Exact Map Manifested by Weak Measurements

  • S. Marcovitch
  • B. ReznikEmail author
Conference paper

Abstract

We suggest a natural mapping between bipartite states and quantum evolutions of local states, which is a Jamiolkowski map. It is shown that spatial correlations of weak measurements in bi-partite systems precisely coincide with temporal correlations of local systems. This mapping has several practical and conceptual implications on the correspondence between Bell and Leggett-Garg inequalities, the statistical properties of evolutions in large systems, temporal decoherence and computational gain, in evaluation of spatial correlations of large systems. [Editor’s note: for a video of the talk given by Prof. Reznik at the Aharonov-80 conference in 2012 at Chapman University, see quantum.chapman.edu/talk-23.]

Notes

Acknowledgements

We are deeply grateful to Y. Aharonov whose insights initiated this work. We also thank A. Botero and P. Skrzypczyk. This work has been supported by the Israel Science Foundation grant number 920/09, the German-Israeli foundation, and the European Commission (PICC).

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Copyright information

© Springer-Verlag Italia 2014

Authors and Affiliations

  1. 1.School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact SciencesTel-Aviv UniversityTel-AvivIsrael

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