Non-Markovian noise limits for sustaining entanglement in multiparty quantum states

The principal resource in several quantum information-processing tasks is entanglement. Building practically useful versions of such tasks, one often needs to consider multipartite systems. And in such scenarios, it is impossible to eliminate the effects of the environment while distributing the resources. We show how information backflow from the environment due to non-Markovianity in the system dynamics affects the resources in multipartite systems, specifically multiparty entanglement. In particular, we find that the entanglement of multiqubit Greenberger-Horne-Zeilinger cat states saturates with time to a nonzero value for a non-Markovian dephasing noise. The multiqubit <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>W</a:mi> </a:mrow> </a:math> states saturate to a higher value. Such nonzero time-saturated values are washed out if the non-Markovianity in the channel is removed. The multiqubit <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>W</b:mi> </b:mrow> </b:math> states provide a richer set of features, including a nonzero value for an asymptotic number of qubits and an even-odd dichotomy in the entanglement with the number of qubits. Moving to a non-Markovian depolarizing channel, we find that both cat and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>W</c:mi> </c:mrow> </c:math> states exhibit a revival of entanglement after the collapse.