Symmetry reduction for testing k-block-positivity via extendibility

2025/05/28 by Chen, Qian, Collins, Benoît, Fawzi, Omar · 2 citations
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2505.22100

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 (N+1)/(2) \rfloor blocks of size ≈ O( (N-1)^-1 2^N+1 d^N+1 ).

Citations

• Five Open Problems in Quantum Information Theory
• Positive linear maps of operator algebras
• Norms and Cones in the Theory of Quantum Entanglement
• Asymptotics of Young tableaux in the strip, the d-sums
• Complete family of separability criteria
• On the representations of the infinite symmetric group

Cited by

• Partial trace relations beyond normal matrices
• Effective criteria for entanglement witnesses in small dimensions

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