Parallel Self-Testing of the GHZ State with a Proof by Diagrams

@article{Breiner2019ParallelSO,
  title={Parallel Self-Testing of the GHZ State with a Proof by Diagrams},
  author={Spencer Breiner and Amir Kalev and Carl A. Miller},
  journal={Electronic Proceedings in Theoretical Computer Science},
  year={2019}
}
Quantum self-testing addresses the following question: is it possible to verify the existence of a multipartite state even when one's measurement devices are completely untrusted? This problem has seen abundant activity in the last few years, particularly with the advent of parallel self-testing (i.e., testing several copies of a state at once), which has applications not only to quantum cryptography but also quantum computing. In this work we give the first error-tolerant parallel self-test in… 
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References

SHOWING 1-10 OF 39 REFERENCES

Self-testing multipartite entangled states through projections onto two systems

TLDR
A simple, and potentially unifying, approach is investigated: combining projections onto two-qubit spaces (projecting parties or degrees of freedom) and then using maximal violation of the tilted CHSH inequalities, which allows one to obtain self-testing of Dicke states and partially entangled GHZ states with two measurements per party.

Parallel self-testing of (tilted) EPR pairs via copies of (tilted) CHSH and the magic square game

TLDR
This work shows that EPR pairs can be self-tested in parallel through through copies of the well known CHSH game, and generalises this result further to a parallel self-test of tilted EPR Pair pairs with arbitrary angles.

Robust self-testing of many-qubit states

TLDR
A simple two-player test which certifies that the players apply tensor products of Pauli σX and σZ observables on the tensor product of n EPR pairs is introduced, which is the first robust self-test for n E PR pairs.

All pure bipartite entangled states can be self-tested

TLDR
This work addresses the long-standing open question of whether every pure bipartite entangled state is self-testable and answers it affirmatively by providing explicit self-testing correlations for all such states.

Classical command of quantum systems

TLDR
A scheme is described that can be used to determine the initial state and to classically command the system to evolve according to desired dynamics, and makes it possible to test whether a claimed quantum computer is truly quantum.

Self-testing in parallel

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…

Robust self testing of the 3-qubit W state

Self-testing is a device independent method which can be used to determine the nature of a physical system or device, without knowing any detail of the inner mechanism or the physical dimension of…

Quantum cryptography with imperfect apparatus

  • D. MayersA. Yao
  • Mathematics
    Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
  • 1998
TLDR
This paper proposes and gives a concrete design for a new concept, self-checking source, which requires the manufacturer of the photon source to provide certain tests; these tests are designed such that, if passed, the source is guaranteed to be adequate for the security of the quantum key distribution protocol, even though the testing devices may not be built to the original specification.

Interactive Proofs for BQP via Self-Tested Graph States

  • M. Mckague
  • Computer Science, Mathematics
    Theory Comput.
  • 2016
TLDR
Using the measurement-based quantum computation model, this work constructs interactive proofs with non-communicating quantum provers and a classical verifier and extends the self-testing error bounds on measurements to a very general set which includes the adaptive measurements used for measurement- based quantum computation as a special case.

Optimal Robust Self-Testing by Binary Nonlocal XOR Games

TLDR
A general scheme for proving optimal robust self- testing properties for tests based on nonlocal binary XOR games and some simplified proofs of known results on self-testing are offered, and some new results are proved.