Permanent conjectures

Permanent and generalized matrix functions conjectures are linked to interesting and practical properties of boson samplers, as emphasized for instance by V. S. Shchesnovich in Universality of Generalized Bunching and Efficient Assessment of Boson Sampling as well as in the author's work Boson bunching is not maximized by indistinguishable particles.

To search for new counter examples of a conjecture, one can implement a user-defined search_function(). For instance, random_search_counter_example_bapat_sunder searches for counter examples of the Bapat-Sunder conjecture (see also violates_bapat_sunder) in a brute-force manner, trying a different random set of matrices at each call. One can then use

search_until_user_stop(search_function)

which will iterate the function until you press Ctrl+C to interrupt the computation.

Another important conjecture is the permaent-on-top conjecture, disproved by V. S. Shchesnovich in The permanent-on-top conjecture is false. Special matrices related to this conjecture are given in this package such as the schur_matrix(H), the general partial distinguishability function J(σ) implemented as J_array. From a matrix J, one can recover the density matrix of the internal states with density_matrix_from_J.