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Semidefinite programming relaxations for quantum correlations

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arxiv 2307.02551 v4 pith:ATWIPG4N submitted 2023-07-05 quant-ph

classification quant-ph
keywords quantumsemidefinitecorrelationsproblemsrelaxationsadaptedappliedapproached
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Semidefinite programs are convex optimisation problems involving a linear objective function and a domain of positive semidefinite matrices. Over the last two decades, they have become an indispensable tool in quantum information science. Many otherwise intractable fundamental and applied problems can be successfully approached by means of relaxation to a semidefinite program. Here, we review such methodology in the context of quantum correlations. We discuss how the core idea of semidefinite relaxations can be adapted for a variety of research topics in quantum correlations, including nonlocality, quantum communication, quantum networks, entanglement, and quantum cryptography.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Semi-Device-Independent Quantum Key Distribution from Operational Assumptions

    quant-ph 2026-07 accept novelty 7.5 of 10

    Operational bounds on state exclusion (not only identification) plus a three-setting retained-key protocol certify positive SDI-QKD rates down to nearly vanishing preparation visibility.

  2. Detecting high-dimensional entanglement with simple measurements

    quant-ph 2026-08 conditional novelty 7.0 of 10

    A witness method detects high-dimensional Schmidt numbers using only strings of single-qubit Pauli measurements, demonstrated up to 16-dimensional photonic entanglement.

  3. Sequential quantum processes with group symmetries

    quant-ph 2025-10 conditional novelty 7.0 of 10

    A canonical streaming circuit decomposition for (G×H)-invariant quantum combs is derived, and numerical optimization suggests a deterministic 7-query transposition protocol for qutrits that is reported as exact.

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