Direct experimental reconstruction of the Bloch sphere

          @misc{ pirsa_16090052,
            doi = {10.48660/16090052},
            url = {https://pirsa.org/16090052},
            author = {Mazurek, Michael and Pusey, Matthew},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Direct experimental reconstruction of the Bloch sphere},
            publisher = {Perimeter Institute},
            year = {2016},
            month = {sep},
            note = {PIRSA:16090052 see, \url{https://pirsa.org}}
          }
          

Abstract

The scientific journey from the first hints of quantum behaviour to the Bloch sphere in your textbook was a long and tortuous one. But using some of the technological and conceptual fruits of that journey, we show that an experiment can manifest the Bloch sphere via an analysis that doesn't require any quantum theory at all. Our technique is to fit experimental data to a generalised probabilistic theory, which allows us to infer both the dimension and shape of the state and measurement spaces of the system under study. We test our technique on an experiment measuring a variety of single-photon polarization states. As expected, the reconstructed state space closely resembles the Bloch sphere, and we are able to place small upper bounds on how much the true theory describing our experiment could possibly deviate from quantum mechanics.