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The counterexample for rank-3 case is the quantum state |Ψ□ A1 A1′ A2 A3 = (2 | 0010 □ +2 | 0101 □ + | 1000 □ + | 1011 □) /6, for which the strong monogamy relation in Eq.m 4/3<8/9+8/9. The counterexample for rank-4 case is the tensor product of two Bell states |Φ□ A1 A1′ A2 A2′ = | ψ+ □ A1 A2 □ | ψ+ □ A1′ A2′, for which neither the strong nor the weak monogamy relation is satisfied.
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The counterexample for rank-3 case is the quantum state |Ψ□ A1 A1′ A2 A3 = (2 | 0010 □ +2 | 0101 □ + | 1000 □ + | 1011 □) /6, for which the strong monogamy relation in Eq. does not hold and has the form 4/3<8/9+8/9. The counterexample for rank-4 case is the tensor product of two Bell states |Φ□ A1 A1′ A2 A2′ = | ψ+ □ A1 A2 □ | ψ+ □ A1′ A2′, for which neither the strong nor the weak monogamy relation is satisfied.
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