A stochastic treatment of the dynamics of an integer spin

Wigner functions on a lattice

“…(55) and its inverse transformation naturally lead to the anti-periodic boundary conditions for a half-integer spin: ψ(α + 2s + 1) = −ψ(α) andψ(β + 2s + 1) = −ψ(β). This reminds us of some flavor of the spin statistics theorem as mentioned in [7]. Discussions on this issue, in conjunction with the reduction method introduced in Sec.…”

“…al. [7] studied Wigner functions for a finite discrete space like a spin space. For an integer spin s in a pure state, they found a possible …”

“…Their results, however, can not be applied to halfinteger spin systems. The total number of sites is N ≡ 2s + 1 and the Wigner function given in [6] and [7] is only for the lattice with odd number sites. Leonhardt proposed the Wigner function for an even number of sites N and discussed applications to the quantum tomography in a finite discrete space [8].…”

Discrete phase-space structure of n-qubit mutually unbiased bases

“…Now we have det W α = 1 and det W β = 0, which leads to the following explicit form of the α-curve 15) whose coefficients satisfy again the condition (4.3). The corresponding W φ matrix is degenerate in this case.…”

“…This line was started by Buot [12], who introduced a discrete Weyl transform that generates a Wigner function on the toroidal lattice Z d (with d odd). More recently, these ideas have been developed further by other authors [13][14][15][16][17][18][19][20][21][22][23][24]. In particular, when the dimension is a power of a prime, one can label the points in the d × d grid with elements of the finite Galois field GF(d).…”