On monogamy of four-qubit entanglement

  • S. Shelly Sharma
  • N. K. Sharma


Our main result is a monogamy inequality satisfied by the entanglement of a focus qubit (one-tangle) in a four-qubit pure state and entanglement of subsystems. Analytical relations between three-tangles of three-qubit marginal states, two-tangles of two-qubit marginal states and unitary invariants of four-qubit pure state are used to obtain the inequality. The contribution of three-tangle to one-tangle is found to be half of that suggested by a simple extension of entanglement monogamy relation for three qubits. On the other hand, an additional contribution due to a two-qubit invariant which is a function of three-way correlations is found. We also show that four-qubit monogamy inequality conjecture of Regula et al. (Phys Rev Lett 113:110501, 2014), in which three-tangles are raised to the power \(\frac{3}{2}\), does not estimate the residual correlations, correctly, for certain subsets of four-qubit states. A lower bound on residual four-qubit correlations is obtained.


Monogamy inequality Quantum entanglement Determinants of negativity fonts Unitary invariants Four-qubit correlations 



Financial support from Universidade Estadual de Londrina PR, Brazil, is acknowledged.


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Authors and Affiliations

  1. 1.Departamento de FísicaUniversidade Estadual de LondrinaLondrinaBrazil
  2. 2.Departamento de MatematicaUniversidade Estadual de LondrinaLondrinaBrazil

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