Quantum devices are preparing increasingly more complex entangled quantum
states. How can one effectively study these states in light of their increasing
dimensions? Phase spaces such as Wigner functions provide a suitable framework.
We focus on phase spaces for finite-dimensional quantum states of single qudits
or permutationally symmetric states of multiple qubits. We present methods to
efficiently compute the corresponding phase-space functions which are at least
an order of magnitude faster than traditional methods. Quantum many-body states
in much larger dimensions can now be effectively studied by experimentalists
and theorists using these phase-space techniques.Comment: 12 pages, 3 figure
