  Quantum teleportation (QT) is a fundamentally remarkable communication
protocol that also finds many important applications for quantum informatics.
Given a quantum entangled resource, it is crucial to know to what extent one
can accomplish the QT. This is usually assessed in terms of output fidelity,
which can also be regarded as an operational measure of entanglement. In the
case of multipartite communication when each communicator possesses a part of
$N$-partite entangled state, not all pairs of communicators can achieve a high
fidelity due to monogamy property of quantum entanglement. We here investigate
how such a monogamy relation arises in multipartite continuous-variable (CV)
teleportation particularly using a Gaussian entangled state. We show a strict
monogamy relation, i.e. a sender cannot achieve a fidelity higher than optimal
cloning limit with more than one receiver. While this seems rather natural
owing to the no-cloning theorem, a strict monogamy relation still holds even if
the sender is allowed to individually manipulate the reduced state in
collaboration with each receiver to improve fidelity. The local operations are
further extended to non-Gaussian operations such as photon subtraction and
addition, and we demonstrate that the Gaussian cloning bound cannot be beaten
by more than one pair of communicators. Furthermore we investigate a
quantitative form of monogamy relation in terms of teleportation capability,
for which we show that a faithful monogamy inequality does not exist.
