  Self-testing protocols are methods to determine the presence of shared
entangled states in a device independent scenario, where no assumptions on the
measurements involved in the protocol are made. A particular type of
self-testing protocol, called parallel self-testing, can certify the presence
of copies of a state, however such protocols typically suffer from the problem
of requiring a number of measurements that increases with respect to the number
of copies one aims to certify. Here we propose a procedure to transform
single-copy self-testing protocols into a procedure that certifies the tensor
product of an arbitrary number of (not necessarily equal) quantum states,
without increasing the number of parties or measurement choices. Moreover, we
prove that self-testing protocols that certify a state and rank-one
measurements can always be parallelized to certify many copies of the state.
Our results suggest a method to achieve device-independent unbounded randomness
expansion with high-dimensional quantum states.
