  In this paper, we introduce a general framework to study the concept of
robust self testing which can be used to self test EPR pairs and local
measurement operators. The result is based only on probabilities obtained from
experiment, with tolerance to experimental errors. In particular, we show that
if results of experiment come approach the Cirel'son bound, or approximates the
Mayers-Yao type correlation, then the experiment must contain an approximate
EPR pair. More specifically, there exist local bases in which the physical
state is close to an EPR pair, possibly all encoded in a larger environment or
ancilla. Moreover, in theses bases the measurements are close to the qubit
operators used to achieve the Cirel'son bound or the Mayers-Yao results.
