Localizable measurements are joint quantum measurements that can be implemented using only nonadaptive local operations and shared entanglement. We provide a protocol-independent characterization of localizable projection-valued measures (PVMs) by exploiting algebraic structures that any such measurement must satisfy. We first show that a rank-1 PVM on ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ containing an element with the maximal Schmidt rank can be localized using entanglement of a Schmidt number of, at most, $d$ if and only if it forms a maximally entangled basis corresponding to a nice unitary error basis. This reveals strong limitations imposed by nonadaptive local operations, in contrast to the adaptive setting where any joint measurement is implementable. We then completely characterize two-qubit rank-1 PVMs that can be localized with two-qubit entanglement, resolving a conjecture of Gisin and Del Santo, and, finally, extend our characterization to ideal two-qudit measurements, strengthening earlier results.

Close

PrevNext

View figure in article

• Quantum entanglement
• Quantum foundations
• Quantum measurements