Random Mixed States

Two subroutines for producing both REAL or CPLX Random Mixed States ρ, distributed according to the so-called “induced” distribution family PN,K(ρ).

As a particular case, the “Hilbert-Schmidt” distribution PHS(ρ) can also be obtained.

The two subroutines here below are designed on the algorithms described in the papers:

H. J. Sommers and K. Zyczkowski
Induced measures in the space of mixed quantum states
J. Phys. A: Math. Gen. 34(35), 7111-7125 (2001)

V. Cappellini, H. J. Sommers and K. Zyczkowski
Distribution of G concurrence of random pure states
Phys. Rev. A 74(6), 062322 (2006)
 
Subroutine ’s Name Precision Version Compatibility
R_mixed_Dmatr.f Single 1.0.0 Fortran 90
Uses:  rgnf_lux.f
Description: 

Generator of a REAL N x N density matrix ρ, representing mixed quantum states, distributed according to the induced measure PN,K(ρ). For this case of REAL density matrix, the Hilbert-Schmidt distribution can be obtained from PHS(ρ) = PN,N+1(ρ).

 
Subroutine ’s Name Precision Version Compatibility
C_mixed_Dmatr.f Complex 1.0.0 Fortran 90
Uses:  rgnf_lux.f
Description: 

Generator of CPLX N x N density matrix ρ, representing mixed quantum states, distributed according to the induced measure PN,K(ρ). For this case of CPLX density matrix, the Hilbert-Schmidt distribution can be obtained from PHS(ρ) = PN,N(ρ).