  Quantum speed limits (QSLs) provide an upper bound for the speed of evolution
of quantum states in any physical process. Based on the Stratonovich-Weyl
correspondence, we derive a universal QSL bound in arbitrary phase spaces that
is applicable for both continuous variable systems and finite-dimensional
discrete quantum systems. This QSL bound allows the determination of speed
limit bounds in specific phase spaces that are tighter than those in Wigner
phase space or Hilbert space under the same metric, as illustrated by several
typical examples, e.g., a single-mode free field and $N$-level quantum systems
in phase spaces. This QSL bound also provides an experimentally realizable way
to examine the speed limit in phase spaces relevant to applications in quantum
information and quantum optics.
