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Perfect discrimination of an orthogonal 2⊗2 basis may require collective separable measurements on two copies
Abstract
We consider an orthogonal basis of ℂ2⊗ℂ2 with three entangled states and one product state. This basis is not perfectly distinguishable by LOCC or even by separable measurements when a single copy of the unknown state is available. We show that with two copies no adaptive separable protocol, which measures the copies one at a time, distinguishes the basis perfectly. We then show that a collective separable measurement on the two copies does. Whether two copies suffice for LOCC remains open.
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BibTeX
@misc{bandyopadhyay2026perfect,
title = {{Perfect discrimination of an orthogonal $2\otimes2$ basis may require collective separable measurements on two copies}},
author = {Somshubhro Bandyopadhyay},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16138},
eprint = {2610.16138},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16138},
}
RIS
TY - UNPB
TI - Perfect discrimination of an orthogonal 2⊗2 basis may require collective separable measurements on two copies
AU - Somshubhro Bandyopadhyay
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16138
UR - https://arxiv.org/abs/2610.16138
AB - We consider an orthogonal basis of ℂ^2⊗ℂ^2 with three entangled states and one product state. This basis is not perfectly distinguishable by LOCC or even by separable measurements when a single copy of the unknown state is available. We show that with two copies no adaptive separable protocol, which measures the copies one at a time, distinguishes the basis perfectly. We then show that a collective separable measurement on the two copies does. Whether two copies suffice for LOCC remains open.
ER -