Monogamy constraints on entanglement of four-qubit pure states · arXivDesk
2002.00701Feb 3, 202020 pages, Three figures, An expanded new version with additional sections on classification of four-qubit states and entanglement transfer. This version is an application to four-qubits of the general formalism reported in a recently uploaded letter "Beyond the entanglement of qubit pair in a mixed state"
Monogamy constraints on entanglement of four-qubit pure states
We report a set of monogamy constraints on one-tangle, two-tangles, three-tangles and four-way correlations of a general four-qubit pure state. It is found that given a two-qubit marginal state ρ of a four qubit pure state ∣Ψ4⟩, the non-Hermitian matrix ρρ
Nearby in the stack
where
ρ
=(σy⊗σy)ρ∗(σy⊗σy)
, contains information not only about the entanglement properties of the two-qubits in state
ρ
but also about three tangles involving the selected pair as well as four-way correlations of the pair of qubits in
∣Ψ4⟩
. To extract information about tangles of a four-qubit state
∣Ψ4⟩
, the coefficients in the characteristic polynomial of matrix
ρρ
are analytically expressed in terms of
2×2
matrices of state coefficients. Four-tangles distinguish between different types of entangled four-qubit pure states.