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Quantum J-channels on Krein spaces

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Abstract

In this paper, we consider Krein spaces and completely J-positive maps between the algebras of bounded linear operators. We first give a Stinespring type representation for a completely J-positive map. We introduce the Choi J-matrix of a linear map and also establish the equivalence of Kraus J-decompositions and Choi J-matrices. We give the J-PPT criterion for separability of J-states and discuss the entanglement breaking condition of quantum J-channels and suggest to prove the J-PPT squared conjecture to solve the PPT squared conjecture. Finally, we gave a concrete example of a completely J-positive map and some examples of \(3 \otimes 3\) quantum J-states which are J-entangled and J-separable.

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Acknowledgements

J. Heo was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science and ICT (NRF-2020R1A4A3079066).

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  1. Department of Mathematics Research Institute for Natural Sciences, Hanyang University, Seoul, 04763, Korea

    Jaeseong Heo

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Heo, J. Quantum J-channels on Krein spaces. Quantum Inf Process 22, 16 (2023). https://doi.org/10.1007/s11128-022-03771-8

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