Qudit lattice states, as the generalization of qubit lattice states, are the maximally entangled states determined by qudit lattice unitaries in a $p^r\otimes p^r$ quantum system with $p$ being a prime and $r$ being an integer. Based on the partitions of qudit lattice unitaries into commuting sets, we present a sufficient condition for local discrimination of qudit lattice states, in which the commutativity plays an efficient role. It turns out that any set of $l$ qudit lattice states with $2\le l\le p^r$, including $k\le l$ mutually commuting qudit lattice unitaries and satisfying $l(l-1)-(k+1)(k-2)\le 2p^r$, can be locally distinguished, not only extending Fan's result [H. Fan, Phys. Rev. Lett. 92, 177905 (2004)] to the prime power quantum system but also involving the local discrimination of a larger number of maximally entangled states.

• Received 30 June 2015

DOI:https://doi.org/10.1103/PhysRevA.92.042320