Constant-sized correlations are sufficient to self-test maximally entangled states with unbounded dimension
Let p be an odd prime and let r be the smallest generator of the multiplicative group Z p ∗ . We show that there exists a correlation of size Θ ( r 2 ) that self-tests a maximally entangled state of local dimension p − 1 . The construction of the correlation uses the embedding procedure proposed by...
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| Published in | Quantum (Vienna, Austria) Vol. 6; p. 614 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2022
|
| Online Access | Get full text |
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| Summary: | Let
p
be an odd prime and let
r
be the smallest generator of the multiplicative group
Z
p
∗
. We show that there exists a correlation of size
Θ
(
r
2
)
that self-tests a maximally entangled state of local dimension
p
−
1
. The construction of the correlation uses the embedding procedure proposed by Slofstra (
Forum of Mathematics, Pi.
(
2019
)). Since there are infinitely many prime numbers whose smallest multiplicative generator is in the set
{
2
,
3
,
5
}
(D.R. Heath-Brown
The Quarterly Journal of Mathematics
(
1986
) and M. Murty
The Mathematical Intelligencer
(
1988
)), our result implies that constant-sized correlations are sufficient for self-testing of maximally entangled states with unbounded local dimension. |
|---|---|
| ISSN: | 2521-327X 2521-327X |
| DOI: | 10.22331/q-2022-01-03-614 |