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Sufficient separability criteria via quantum maps

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Màster Oficial de Ciència i Tecnologia Quàntiques / Quantum Science and Technology, Facultat de Física, Universitat de Barcelona. Curs: 2023-2024. Tutors: Anna Sanpera Trigueros, Guillem Müller Rigat

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In this master’s thesis, we consider quantum linear maps as a tool to derive new sufficient conditions for separability in bipartite and multipartite systems.
In specific, we focus on the so-called reduction map to strengthen the existing criteria for absolute separability in bipartite systems, i.e., for states that remain bi-separable under any global unitary transformation. To this aim, using powerful convex geometry techniques, we introduce tighter volumes and characterization of the set of absolutely separable states w.r.t. any bi-partition for arbitrary dimensions. Furthermore, we derive new conditions on the spectrum of bipartite entanglement witnesses. In addition, we address the multipartite
scenario by presenting some non-optimal results. Finally, we provide some insights on the conjecture that having a positive partial transpose from spectrum is equivalent to being separable from spectrum for the symmetric subspace of N−qudits, as well as a new criterion for positive partial transpose from spectrum
for arbitrary system sizes N.

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Màster Oficial - Ciència i Tecnologia Quàntiques / Quantum Science and Technology

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Sufficient separability criteria via quantum maps