Rank-1 PVMs on two qudits with a maximal-Schmidt-rank element are localizable with Schmidt number at most d exactly when they correspond to nice unitary error bases; the two-qubit case is fully classified, resolving a prior conjecture.
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Generalizing the Elegant Joint Measurement, the authors construct symmetric, locally encodable entangled measurement bases as Pauli-group orbits and classify their entanglement-assisted local implementability by Clifford-hierarchy level.
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Localization of joint quantum measurements on $\mathbb{C}^d \otimes \mathbb{C}^d$ by entangled resources with Schmidt number at most $d$
Rank-1 PVMs on two qudits with a maximal-Schmidt-rank element are localizable with Schmidt number at most d exactly when they correspond to nice unitary error bases; the two-qubit case is fully classified, resolving a prior conjecture.
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Symmetric Localizable Multipartite Quantum Measurements from Pauli Orbits
Generalizing the Elegant Joint Measurement, the authors construct symmetric, locally encodable entangled measurement bases as Pauli-group orbits and classify their entanglement-assisted local implementability by Clifford-hierarchy level.