Entropy, purity, and fidelity in Majorana phase space

摘要: Majorana phase-space representations for fermions map fermionic many-body physics into a distribution over one of the Cartan symmetric spaces Lie group theory. The representation is in terms $2M\ifmmode\times\else\texttimes\fi{}2M$ complex antisymmetric matrices, which generate Gaussian operators. Here we show how this expansion can be utilized to calculate quantities arising quantum thermodynamics and information. Purity linear entropy are calculated, as well fidelity between two general states, with numerical examples pure states. We describe geometrical properties phase space, that overlap states depends on product their matrices. Fermionic space divided up orthogonal subspaces different number parity, whose matrix differ by an reflection space.