Phase retrieval and norm retrieval sequences for Hilbert spaces were introduced by Balan et al. in 2006 and by Bahmanpour et al. in 2015, respectively. In signal processing, phase retrieval plays a crucial role in reconstructing a signal from its intensity measurements. Similarly, norm retrieval restores the norm of a signal from its intensity measurements. Bemrose et al., in 2016, instigated weaving frames for Hilbert spaces. Weaving phase and norm retrieval sequences for a Hilbert space were recently studied by Dowerah et al.

In this paper, we study weaving phase and weaving norm retrieval sequences in the tensor product of Hilbert spaces defined by Folland, in the year 1995, as a space of bounded antilinear maps between Hilbert spaces. We investigate the preservation and transfer of the weaving property of spanning sequences, the complement property, phase retrieval, and norm retrieval when passing from Hilbert spaces to their tensor product spaces. Several characterizations and methods of construction of weaving phase and norm retrieval sequences in tensor product spaces are discussed.

Authors acknowledge DST, FIST (SR/FST/MSI/ 2019/53) for providing infrastructural support. We also sincerely thank the reviewers for their valuable comments and constructive suggestions, which have helped us improve the quality and presentation of the manuscript.