# Rigidity of the magic pentagram game

@article{Kalev2018RigidityOT, title={Rigidity of the magic pentagram game}, author={Amir Kalev and Carl A. Miller}, journal={Quantum Science and Technology}, year={2018}, volume={3} }

A game is rigid if a near-optimal score guarantees, under the sole assumption of the validity of quantum mechanics, that the players are using an approximately unique quantum strategy. Rigidity has a vital role in quantum cryptography as it permits a strictly classical user to trust behavior in the quantum realm. This property can be traced back as far as 1998 (Mayers and Yao) and has been proved for multiple classes of games. In this paper we prove ridigity for the magic pentagram game, a…

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## References

SHOWING 1-10 OF 35 REFERENCES

### Characterization of Binary Constraint System Games

- Computer ScienceICALP
- 2014

This work investigates a simple class of multi-prover interactive proof systems, called binary constraint system (BCS) games, and characterize those that admit a perfect entangled strategy (i.e., a strategy with value 1 when the provers can use shared entanglement) in terms of a system of matrix equations.

### Maximally Entangled State in Pseudo-Telepathy Games

- MathematicsComputing with New Resources
- 2014

It is shown that maximally entangled states suffice for weak projection games which the paper introduces as a relaxation of projection games and implies that any pseudo-telepathy weak projection game yields a device-independent certification of a maximally entangling state.

### Maximally entangled states in pseudo-telepathy games

- Computer Science
- 2015

It is shown that maximally entangled states suffice for weak projection games which the author introduces as a relaxation of projection games and implies that any pseudo-telepathy weak projection game yields a device-independent certification of a maximally entangling state.

### A quantum linearity test for robustly verifying entanglement

- Mathematics, Computer ScienceSTOC
- 2017

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.

### Device-Independent bounds for Hardy's experiment.

- Computer SciencePhysical review letters
- 2012

An analogue of Tsirelson's bound for Hardy's test of nonlocality is computed, that is, the maximum violation of locality constraints allowed by the quantum formalism, irrespective of the dimension of the system.

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

- Computer ScienceQuantum Inf. Comput.
- 2017

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.

### Classical command of quantum systems

- Physics, Computer ScienceNature
- 2013

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

- Mathematics
- 2016

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…

### Quantum cryptography with imperfect apparatus

- MathematicsProceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
- 1998

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.

### Device-independent parallel self-testing of two singlets

- Computer Science
- 2016

It is demonstrated that the magic square game can only be perfectly won by measuring a two-singlet state and the tolerance to noise is well within reach of state-of-the-art experiments.