  Quantum Process Tomography (QPT) methods aim at identifying, i.e. estimating,
a given quantum process. QPT is a major quantum information processing tool,
since it especially allows one to characterize the actual behavior of quantum
gates, which are the building blocks of quantum computers. However, usual QPT
procedures are complicated, since they set several constraints on the quantum
states used as inputs of the process to be characterized. In this paper, we
extend QPT so as to avoid two such constraints. On the one hand, usual QPT
methods requires one to know, hence to precisely control (i.e. prepare), the
specific quantum states used as inputs of the considered quantum process, which
is cumbersome. We therefore propose a Blind, or unsupervised, extension of QPT
(i.e. BQPT), which means that this approach uses input quantum states whose
values are unknown and arbitrary, except that they are requested to meet some
general known properties (and this approach exploits the output states of the
considered quantum process). On the other hand, usual QPT methods require one
to be able to prepare many copies of the same (known) input state, which is
constraining. On the contrary, we propose "single-preparation methods", i.e.
methods which can operate with only one instance of each considered input
state. These two new concepts are here illustrated with practical BQPT methods
which are numerically validated, in the case when: i) random pure states are
used as inputs and their required properties are especially related to the
statistical independence of the random variables that define them, ii) the
considered quantum process is based on cylindrical-symmetry Heisenberg spin
coupling. These concepts may be extended to a much wider class of processes and
to BQPT methods based on other input quantum state properties.
