ICTS:31120

Video URL

Detecting PPT entanglement in Symmetric Quantum States

Detecting PPT entanglement in Symmetric Quantum States

(2025). Detecting PPT entanglement in Symmetric Quantum States. SciVideos. https://youtu.be/6LcQkeSikDs

Detecting PPT entanglement in Symmetric Quantum States. SciVideos, Feb. 05, 2025, https://youtu.be/6LcQkeSikDs 

          @misc{ scivideos_ICTS:31120,
            doi = {},
            url = {https://youtu.be/6LcQkeSikDs},
            author = {},
            keywords = {},
            language = {en},
            title = {Detecting PPT entanglement in Symmetric Quantum States},
            publisher = {},
            year = {2025},
            month = {feb},
            note = {ICTS:31120 see, \url{https://scivideos.org/icts-tifr/31120}}
          }
Aabhas Gulati
Talk numberICTS:31120
Source RepositoryICTS-TIFR
Collection

Abstract

We introduce and study bipartite quantum states that are invariant under the local action of the cyclic sign group. Due to symmetry, these states are sparse and can be parameterized by a triple of vectors. Their important semi-definite properties, such as positivity and positivity under partial transpose (PPT), can be simply characterized in terms of these vectors and their discrete Fourier transforms. We study in detail the entanglement properties of this family of symmetric states, showing in particular that it contains PPT entangled states. For states that are diagonal in the Dicke basis, deciding separability is equivalent to a circulant version of the complete positivity problem. We provide some geometric results for the PPT cone, showing in particular that it is polyhedral. In local dimension less than 5, we completely characterize these sets and construct entanglement witnesses; some partial results are also obtained for d = 6, 7. Finally, we present some novel graph-theoretic techniques to detect entanglement in quantum states with symmetry, and construction of various families of PPT entangled states in all dimensions.