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If |X|=|Y|=1 then xy-xy′=xy(1±xy′)-xy′(1±x′y). So |xy-xy′|≤|xy(1±x′y′)|+|xy′ (1±x′y)|≤(1±x′y′) +(1±x′y)=2±(x′y′+x′y). Thus -(2+(x′y′+x′y))≤xy -xy′≤2-(x′y′+x′y); the last inequality is Eq. (3).
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33646616177
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note
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This condition excludes processes where, e.g., an electron quasiparticle in lead 1 is not absorbed by the terminals 3,5, but is reflected back to the superconductor and finally transformed into a hole propagating through lead 2.
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46
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33646615425
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note
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Spin-orbit interactions and spin-flip processes (e.g., due to paramagnetic impurities) in the leads are neglected and we assume that rotation of the magnetizations a,b does not change the conductances of the contacts between the lead 1 and the terminals 3,5 (lead 2 and terminals 4,6).
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