PIRSA:17050071

Video URL

https://pirsa.org/17050071

Estimating entanglement from only a few moments

Carteret, H. (2017). Estimating entanglement from only a few moments. Perimeter Institute for Theoretical Physics. https://pirsa.org/17050071

Carteret, Hilary. Estimating entanglement from only a few moments. Perimeter Institute for Theoretical Physics, May. 09, 2017, https://pirsa.org/17050071 

          @misc{ scivideos_PIRSA:17050071,
            doi = {10.48660/17050071},
            url = {https://pirsa.org/17050071},
            author = {Carteret, Hilary},
            keywords = {Quantum Matter},
            language = {en},
            title = {Estimating entanglement from only a few moments},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2017},
            month = {may},
            note = {PIRSA:17050071 see, \url{https://scivideos.org/pirsa/17050071}}
          }

Hilary Carteret

Talk numberPIRSA:17050071
DOI10.48660/17050071
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

How can we quantify the entanglement between subsystems when we only have access to incomplete information about them and their environment?‎ Existing approaches (such as Rényi entropies) can only detect the short-range entanglement across a boundary between a subsystem and its surroundings, and then only if the whole system is pure. These methods cannot detect the long-range entanglement between two subsystems embedded in a larger system. There is a natural choice of entanglement measure for this situation, called the entanglement negativity, which can do this and cope with mixed states as well. However it is defined in terms of the full density matrix, which we generally won't have access to.

I will begin this talk with a brief overview ‎of some replica trick-based eigenspectrum reconstruction methods, and their various strengths and limitations. Then I will show how to modify these to find the moments of the partially transposed density matrix. Once those numbers have been obtained, it is possible to modify the earlier eigenspectrum reconstruction methods to obtain lower and upper bounds for the entanglement negativity.

Addendum: An audience member pointed out that the adjective "quasi-topological" already has a meaning and it's something different from the subject of this talk. So with hindsight it should have been called `quasi-conformal quantum computing'