#%autosave 0
%matplotlib inline
import sglib
reload(sglib)
from sglib import *
from sympy import Symbol
alpha = Symbol('alpha'); beta = Symbol('beta')

col(1,0)

ket('+z')

col(1,0,0,0)

ket('-y')

ket('0'), ket('1')

psi = 1/sqrt(2)*ket('+z') + 1/sqrt(2)*ket('-z')
fm = latex
fm = sg_latex
fm = sg_format_state(['+z','-z'], ',').format
Print(r'$\psi = %s$' % fm(psi))


string_tensor(2, ['0','1'], separator=',', D=False)

fs1 = sg_format_state(basis=['0', '1'], separator='').format
fs2 = sg_format_state(basis=['+z', '-z'], separator='').format
fs3 = sg_format_state(
    basis=[r'\mathrm{Heads}', '\mathrm{Tails}'], separator='').format
Print('-----------------------------------------------------------')
psi = 1/sqrt(2)*col(1,0)+1/sqrt(2)*col(0,1)
Print('$\psi=%s$'%fs1(psi))
Print('$\psi=%s$'%fs2(psi))
Print('$\psi=%s$'%fs3(psi))
Print('-----------------------------------------------------------')
psi = 1/sqrt(2)*col(1,0)-1/sqrt(2)*col(0,1)
Print('$\psi=%s$'%fs1(psi))
Print('$\psi=%s$'%fs2(psi))
Print('$\psi=%s$'%fs3(psi))
Print('-----------------------------------------------------------')
psi = -1/sqrt(2)*col(1,0)+1/sqrt(2)*col(0,1)
Print('$\psi=%s$'%fs1(psi))
Print('$\psi=%s$'%fs2(psi))
Print('$\psi=%s$'%fs3(psi))
Print('-----------------------------------------------------------')
psi = -1/sqrt(2)*col(1,0)-1/sqrt(2)*col(0,1)
Print('$\psi=%s$'%fs1(psi))
Print('$\psi=%s$'%fs2(psi))
Print('$\psi=%s$'%fs3(psi))
Print('-----------------------------------------------------------')
psi = alpha*col(1,0) + beta*col(0,1)
Print('$\psi=%s$'%fs1(psi))
psi = alpha*col(1,0) - beta*col(0,1)
Print('$\psi=%s$'%fs1(psi))
psi = -alpha*col(1,0) + beta*col(0,1)
Print('$\psi=%s$'%fs1(psi))
psi = -alpha*col(1,0) - beta*col(0,1)
Print('$\psi=%s$'%fs1(psi))

#
# The Bell States
#
bell_1 = 1/sqrt(2)*TP(pZ,pZ) + 1/sqrt(2)*TP(mZ,mZ) # phi+
bell_2 = 1/sqrt(2)*TP(pZ,pZ) - 1/sqrt(2)*TP(mZ,mZ) # phi-
bell_3 = 1/sqrt(2)*TP(pZ,mZ) + 1/sqrt(2)*TP(mZ,pZ) # psi+ (Triplet)
bell_4 = 1/sqrt(2)*TP(pZ,mZ) - 1/sqrt(2)*TP(mZ,pZ) # psi- (Singlet)
#
# pick a format
#
fs = sg_format_state(basis=['+z', '-z'], separator=',').format
fs = sg_format_state(basis=['0', '1'], separator='').format
Print('Bell$_1 = %s$' %(fs(bell_1)))
Print('Bell$_2 = %s$' %(fs(bell_2)))
Print('Bell$_3 = %s$' %(fs(bell_3)))
Print('Bell$_4 = %s$' %(fs(bell_4)))

foo = 1/sqrt(2)
Print(r'$%s \rightarrow %s$' %(latex(foo), myltx(foo)))
foo = 1/sqrt(2)*col(1,1)
Print(r'$%s \rightarrow %s$' %(latex(foo), myltx(foo)))
foo = 1/sqrt(2)*mat(1,1,1,-1)
Print(r'$%s \rightarrow %s$' %(latex(foo), myltx(foo)))

foo = 1/sqrt(2)*col(alpha, beta)
Print(r'$%s \rightarrow %s$' %(latex(foo), myltx(foo)))
foo = 1/sqrt(2)*mat(1,1,1,-1)
Print(r'$%s \rightarrow %s$' %(latex(foo), myltx(foo)))
foo = 1/sqrt(2)*col(alpha, beta)


state = oo = 1/sqrt(2)*col(1,1)
M = OP(state,state)
Print(r'$%s \rightarrow %s$' %(latex(M), myltx(M)))
state = oo = 1/sqrt(2)*col(alpha, beta)
M = OP(state,state)
Print(r'$%s \rightarrow %s$' %(latex(M), myltx(M)))

foo = 2/sqrt(3)*mat(1,0,0,1)
Print(r'$%s \rightarrow %s$' %(latex(foo), myltx(foo)))

foo = sqrt(3)*mat(1,0,0,1)
Print(r'$%s \rightarrow %s$' %(latex(foo), myltx(foo)))

foo = 5/sqrt(2)
Print(r'$%s \rightarrow %s$' %(latex(foo), myltx(foo)))
foo = alpha/sqrt(2)
Print(r'$%s \rightarrow %s$' %(latex(foo), myltx(foo)))