Środowiskowe Seminarium z Informacji i Technologii Kwantowych

To what extent does the spectrum of a quantum state constrain its entanglement properties? Since global unitary transformations preserve the spectrum while generally changing the entanglement structure that underlies in the basis, this question naturally leads to the notion of absolute separability: states that remain separable under arbitrary global unitaries. In this talk, I aim to present my PhD work so far, exploring the role of spectral constraints in quantum entanglement. First, I will discuss new analytical sufficient conditions for absolute separability in arbitrary dimensions. I will then extend this framework beyond separability, showing how spectral information can (upper) bound the entanglement attainable under global unitary transformations, focusing on the entanglement measures of negativity and Schmidt number. Finally, I will address the multipartite setting, where absolute separability can be seen as a quantum marginal constraint. In particular, I will introduce Threshold Entanglement Sharing states: globally entangled pure states whose reduced states, up to a certain subsystem size, are absolutely separable. They conform a relaxation of Absolutely Maximally Entangled states.