  We prove a version of the quantum de Finetti theorem: permutation-invariant
quantum states are well approximated as a probabilistic mixture of multi-fold
product states. The approximation is measured by distinguishability under fully
one-way LOCC (local operations and classical communication) measurements. Our
result strengthens Brand\~{a}o and Harrow's de Finetti theorem where a kind of
partially one-way LOCC measurements was used for measuring the approximation,
with essentially the same error bound. As main applications, we show (i) a
quasipolynomial-time algorithm which detects multipartite entanglement with
amount larger than an arbitrarily small constant (measured with a variant of
the relative entropy of entanglement), and (ii) a proof that in quantum
Merlin-Arthur proof systems, polynomially many provers are not more powerful
than a single prover when the verifier is restricted to one-way LOCC
operations.
