A new dimension witness, or the Adventures of Alice, an Addicted Traveller

Wojciech Słomczyński, Jagiellonian University, Kraków

Joint work with Anna Szczepanek, based on [1]

Fix a point in a finite-dimensional complex vector space and consider the sequence of iterates of this point under the composition of a unitary map with the orthogonal projection on the hyperplane orthogonal to the starting point. We prove that, generically, the series of the squared norms of these iterates sums to the dimension of the underlying space. This leads us to construct a (device-dependent) dimension witness for quantum systems which involves the probabilities of obtaining certain strings of outcomes in a sequential yes–no measurement.

[1] Orthogonal projections on hyperplanes intertwined with unitaries, J. Phys. A: Math. Theor. 54 (2021) 385303

Recording of the talk