Positive Partial Transpose Matrix Inequalities

Mohammad Bagher Ghaemi (), Nahid Gharakhanlu, Themistocles M. Rassias and Reza Saadati
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Mohammad Bagher Ghaemi: Iran University of Science and Technology
Nahid Gharakhanlu: Iran University of Science and Technology
Themistocles M. Rassias: National Technical University of Athens
Reza Saadati: Iran University of Science and Technology

Chapter Chapter 6 in Advances in Matrix Inequalities, 2021, pp 221-266 from Springer

Abstract: Abstract In this chapter, we present some inequalities related to $$2\times 2$$ 2 × 2 block PPT matrices and positive matrices partitioned in blocks. When these positive block matrices are PPT, some nice results have been obtained, motivated by the Quantum Information Science. Our study follows a natural thought that conclusions drawn under the PPT assumption should be stronger than those drawn under only the usual positivity assumption. Moreover, we believe the new result presented in this work is of interest in its own right and may serve to understand better the intrinsic properties of PPT matrices in quantum sciences and information theory. Note that multipartite quantum states that have a positive partial transpose concerning all bipartitions of the particles can outperform the separable state in linear interferometers.

Date: 2021
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DOI: 10.1007/978-3-030-76047-2_6

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