# Constant-sized correlations are sufficient to self-test maximally entangled states with unbounded dimension

@article{Fu2022ConstantsizedCA, title={Constant-sized correlations are sufficient to self-test maximally entangled states with unbounded dimension}, author={Honghao Fu}, journal={Quantum}, year={2022}, volume={6}, pages={614} }

<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 xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>r</mml:mi></mml:math> be the smallest generator of the multiplicative group <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi mathvariant="double-struck">Z</mml:mi></mml:mrow><mml:mi>p</mml:mi><mml:mo>∗</mml:mo></mml:msubsup></mml:math>. We show…

## 7 Citations

### The membership problem for constant-sized quantum correlations is undecidable

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There is a family of constant-sized correlations such that solving the quantum membership problem for this family is computationally impossible, and the undecidability that arises in understanding Bell experiments is not dependent on varying the number of measurements in the experiment.

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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.

### Practical Parallel Self-testing of Bell States via Magic Rectangles

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This work uses the 3 × n magic rectangle games to obtain a self-test for n Bell states where the one side needs only to measure single-qubit Pauli observables, and introduces a one-side-local quantum strategy for the magic square game that wins with certainty.

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The study of quantum correlation sets initiated by Tsirelson in the 1980s and originally motivated by questions in the foundations of quantum mechanics has more recently been tied to questions in…

### Constant-sized robust self-tests for states and measurements of unbounded dimension

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We consider correlations, ?=,G , arising from measuring a maximally entangled state using = measurements with two outcomes each, constructed from = projections that add up to G . We show that the…

### Robust semi-device-independent certification of all pure bipartite maximally entangled states via quantum steering

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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.

### A three-player coherent state embezzlement game

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We introduce a three-player nonlocal game, with a finite number of classical questions and answers, such that the optimal success probability of $1$ in the game can only be achieved in the limit of…

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