Polynomial Separation between One-Way and Two-Way LOCC in Discrimination of Maximally Entangled States

@misc{lim2026polynomial,
  title = {{Polynomial Separation between One-Way and Two-Way LOCC in Discrimination of Maximally Entangled States}},
  author = {Youngrong Lim},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04288},
  eprint = {2610.04288},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04288},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Polynomial Separation between One-Way and Two-Way LOCC in Discrimination of Maximally Entangled States
AU  - Youngrong Lim
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2610.04288
UR  - https://arxiv.org/abs/2610.04288
AB  - One-way local operations and classical communication (LOCC) can fail to distinguish four orthogonal maximally entangled states in every local dimension d≥4. We show that every set of k pairwise orthogonal maximally entangled states in ℂ^d⊗ℂ^d is perfectly distinguishable by an A→ B→ A protocol whenever d≥ Ck^4[log(2k)]^ν, for universal constants C,ν>0. A single feedback message therefore raises the number of candidates that can always be distinguished from a constant to Ω (d^1/4/(log d)^ν/4), establishing a polynomial separation between one-way and two-way LOCC. In our protocol, Alice preserves exact orthogonality while reducing overlaps between Bob's conditional subspaces. Bob reduces the candidates to a singleton or an orthogonal pair and refines his outcome so that Alice can complete the discrimination. As a corollary, nine copies suffice for perfect two-way LOCC discrimination of any orthogonal maximally entangled set in all sufficiently large local dimensions.
ER  -