  This paper presents a prepare-and-measure scheme using $N$-dimensional
quantum particles as information carriers where $N$ is a prime power. One of
the key ingredients used to resist eavesdropping in this scheme is to
depolarize all Pauli errors introduced to the quantum information carriers.
Using the Shor-Preskill-type argument, we prove that this scheme is
unconditionally secure against all attacks allowed by the laws of quantum
physics. For $N = 2^n > 2$, each information carrier can be replaced by $n$
entangled qubits. In this case, there is a family of eavesdropping attacks on
which no unentangled-qubit-based prepare-and-measure quantum key distribution
scheme known to date can generate a provably secure key. In contrast, under the
same family of attacks, our entangled-qubit-based scheme remains secure
whenever $2^n \geq 4$. This demonstrates the advantage of using entangled
particles as information carriers and of using depolarization of Pauli errors
to combat eavesdropping attacks more drastic than those that can be handled by
unentangled-qubit-based prepare-and-measure schemes.
