Abstract
Self-testing allows us to determine, through classical interaction only, whether some players in a non-local game share particular quantum states. Most work on self-testing has concentrated on developing tests for small states like one pair of maximally entangled qubits, or on tests where there is a separate player for each qubit, as in a graph state. Here we consider the case of testing many maximally entangled pairs of qubits shared between two players. Previously such a test was shown where testing is sequential, i.e., one pair is tested at a time. Here we consider the parallel case where all pairs are tested simultaneously, giving considerably more power to dishonest players. We derive sufficient conditions for a self-test for many maximally entangled pairs of qubits shared between two players and also two constructions for self-tests where all pairs are tested simultaneously.
Highlights
A non-local game is a scenario where two or more non-communicating players receive challenges or questions from a referee
We have introduced techniques for performing many self-tests in parallel in the case where we do not have no-signalling restrictions between tests
We gave two constructions which allow for testing many e-bits which are shared between two parties, and we have no other restrictions on the structure of the state or measurements
Summary
A non-local game is a scenario where two or more non-communicating players receive challenges or questions from a referee. In the language of non-local games, self-testing means that for some non-local games there essentially exists only one strategy that obtains the maximal probability of winning. These results are robust, allowing us to put error bounds on the state in the case of small amounts of noise in the devices. A natural and desirable extension to any self-test would be the ability to repeat it, allowing us to self-test many copies of the same state This can be done quite naturally if the many copies are held in separate non-communicating devices. Instead we have the considerably weaker division into only two subsystems
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