bibkey: huberlamilancienmullerhermes2018ppt authors: Marcus Huber; Ludovico Lami; Cécilia Lancien; Alexander Müller-Hermes year: 2018 title: “High-Dimensional Entanglement in States with Positive Partial Transposition” doi: 10.1103/PhysRevLett.121.200503 url: https://arxiv.org/abs/1802.04975 claim: “The second Lemma III.1 in arXiv v1, Section III.C, constructs the conjugate-flag state from a state and its partial transpose.” strata_touched:
- D5/S3/Quantum/QuantumChannels/IptPptSquaredEquivalence license: citation-only triage: anchor
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DOI: https://doi.org/10.1103/PhysRevLett.121.200503
Source: https://arxiv.org/abs/1802.04975
Conjugate-flag construction
In arXiv:1802.04975v1, Section III.C, PDF page 8, the second lemma labelled III.1 uses the state $\rho_{AB}\otimes|{+i}\rangle\langle{+i}| + \rho_{AB}^{\Gamma}\otimes|{-i}\rangle\langle{-i}|$. The version also has a different Lemma III.1 on PDF page 4; the page-8 lemma is the conjugate-flag construction used here.
The two-dimensional projectors are
and .
Their transpose exchanges them. The map lift adapts this state
construction, with normalization, a composition law and recovery of a
map’s square as proved in IptPptSquaredEquivalence.