QMA-hardness of Consistency of Local Density Matrices with Applications to Quantum Zero-Knowledge

@article{Broadbent2020QMAhardnessOC,
  title={QMA-hardness of Consistency of Local Density Matrices with Applications to Quantum Zero-Knowledge},
  author={Anne Broadbent and Alex Bredariol Grilo},
  journal={2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)},
  year={2020},
  pages={196-205}
}
  • A. Broadbent, A. B. Grilo
  • Published 2020
  • Computer Science
  • 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
We provide several advances to the understanding of the class of Quantum Merlin-Arthur proof systems (QMA), the quantum analogue of NP. Our central contribution is proving a longstanding conjecture that the Consistency of Local Density Matrices (CLDM) problem is QMA-hard under Karp reductions. The input of CLDM consists of local reduced density matrices on sets of at most $k$ qubits, and the problem asks if there is an n-qubit global quantum state that is locally consistent with all of the k… Expand
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