Practical parallel self-testing of Bell states via magic rectangles
- URL: http://arxiv.org/abs/2105.04044v4
- Date: Thu, 31 Mar 2022 17:14:18 GMT
- Title: Practical parallel self-testing of Bell states via magic rectangles
- Authors: Sean A. Adamson, Petros Wallden
- Abstract summary: Self-testing is a method to verify that one has a particular quantum state from purely classical statistics.
We use the $3 times n$ magic rectangle games to obtain a self-test for $n$ Bell states where the one side needs only to measure single-qubit Pauli observables.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Self-testing is a method to verify that one has a particular quantum state
from purely classical statistics. For practical applications, such as
device-independent delegated verifiable quantum computation, it is crucial that
one self-tests multiple Bell states in parallel while keeping the quantum
capabilities required of one side to a minimum. In this work, we use the $3
\times n$ magic rectangle games (generalizations of the magic square game) to
obtain a self-test for $n$ Bell states where the one side needs only to measure
single-qubit Pauli observables. The protocol requires small input sizes
[constant for Alice and $O(\log n)$ bits for Bob] and is robust with robustness
$O(n^{5/2} \sqrt{\varepsilon})$, where $\varepsilon$ is the closeness of the
ideal (perfect) correlations to those observed. To achieve the desired
self-test, we introduce a one-side-local quantum strategy for the magic square
game that wins with certainty, we generalize this strategy to the family of $3
\times n$ magic rectangle games, and we supplement these nonlocal games with
extra check rounds (of single and pairs of observables).
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