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arXiv · 2505.22100

Symmetry reduction for testing $k$-block-positivity via extendibility

Qian Chen·Benoît Collins·Omar Fawzi
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Abstract

We study the problem of testing $k$-block-positivity via symmetric $N$-extendibility by taking the tensor product with a $k$-dimensional maximally entangled state. We exploit the unitary symmetry of the maximally entangled state to reduce the size of the corresponding semidefinite programs (SDP). For example, for $k=2$, the SDP is reduced from one block of size $2^{N+1} d^{N+1}$ to $\lfloor \frac{N+1}{2} \rfloor$ blocks of size $\approx O( (N-1)^{-1} 2^{N+1} d^{N+1} )$.

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Qian Chen, Benoît Collins, Omar Fawzi. 2025-05-28. Symmetry reduction for testing $k$-block-positivity via extendibility. https://doi.org/10.1088/1751-8121%2Fae2076

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