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… 

Figures from this paper

Computational self-testing of multi-qubit states and measurements
TLDR
A simplified version of this protocol is the first that can efficiently certify an arbitrary number of qubits of a cloud quantum computer, on which the authors cannot enforce spatial separation, using only classical communication.
Device-independent certification of tensor products of quantum states using single-copy self-testing protocols
TLDR
It is proved that self-testing protocols that certify a state and rank-one measurements can always be parallelized to certify many copies of the state, suggesting a method to achieve device-independent unbounded randomness expansion with high-dimensional quantum states.
Self-testing of quantum systems: a review
TLDR
This work gives a thorough and self-contained introduction and review of self-testing and its application to other areas of quantum information.
Certified Quantum Measurement of Majorana Fermions.
TLDR
It is shown that observing a set of ideal measurement statistics implies anti-commutativity of the implemented Majorana fermion parity operators, a necessary prerequisite for Majorana detection.
Categorical composable cryptography
TLDR
It is shown that protocols secure against abstract attacks form a symmetric monoidal category, thus giving an abstract model of composable security definitions in cryptography, able to incorporate computational security, set-up assumptions and various attack models in a modular, flexible fashion.
Mathematical methods for resource-based type theories.
TLDR
A logical framework that captures two mathematical approaches to resource theory based on monoids (algebraic) and monoidal categories (categorical) is presented, and it is proved soundness and completeness of an algebraic and categorical semantics that recover these approaches.
Constant-sized correlations are sufficient to self-test maximally entangled states with unbounded dimension
<jats:p>Let <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math> be an odd prime and let <mml:math
Robust semi-device-independent certification of all pure bipartite maximally entangled states via quantum steering
TLDR
The notion of Assemblage based robust state certification is used to provide robustness bounds for the certification result in the case of pure maximally entangled states of any local dimension.

References

SHOWING 1-10 OF 46 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.
Self-testing in parallel with CHSH
TLDR
The parallel self-testing framework is extended to build parallel CHSH self-tests for any number of pairs of maximally entangled qubits, and achieves an error bound which is polynomial in the number of tested qubit 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.
A quantum linearity test for robustly verifying entanglement
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.
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. Mayers, A. 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.
...
...