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Initial Correlations and Complete Positivity of Dynamical Maps

Vinayak Jagadish

Instytut Fizyki Teoretycznej, Uniwersytet Jagielloński, Łojasiewicza 11, 30-348 Kraków, Poland

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R. Srikanth

Poornaprajna Institute of Scientific Research, Bangalore, 560 080, India

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Francesco Petruccione

School for Data Science and Computational Thinking, Stellenbosch University, Stellenbosch 7600, South Africa

National Institute for Theoretical and Computational Sciences (NITheCS), Stellenbosch 7600, South Africa

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https://doi.org/10.1142/S1230161223500117Cited by:1 (Source: Crossref)

Abstract

It is now increasingly realized in the study of open system dynamics that initial correlations do not pose a conceptual difficulty as traditionally believed. A similar methodology as used to describe initial product states can be adopted, with the only difference being that the reduced dynamics is possibly not completely positive, entailing that only a restricted set of initial reduced states lead to a physically valid dynamics. Here we study the interplay between the initial correlations, especially in the form of highly entangled states, and the system–environment unitary. In particular, for almost any initial entangled state, one can furnish infinitely many joint unitaries that generate CP dynamics on the system. Restricting to the case of initial, pure entangled states, we obtain the scaling of the dimension of the set of these unitaries and show that it is of zero measure in the set of all possible interaction unitaries.

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