Relating local time evolutions with bipartite states: An exact map manifested by weak measurements

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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.]

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Marcovitch, S., & Reznik, B. (2014). Relating local time evolutions with bipartite states: An exact map manifested by weak measurements. In Quantum Theory: A Two-Time Success Story: Yakir Aharonov Festschrift the Global Financial Crisis and the Indian Economy (pp. 337–354). Springer-Verlag Milan. https://doi.org/10.1007/978-88-470-5217-8_24

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