- #1
vj3336
- 15
- 0
Homework Statement
Given a matrix
M(a) = (a -(1/4)i ; (1/4)i a)
(semicolon separates rows)
a) Determine a so that M(a) is a density matrix.
b) Show that the system is in a mixed state.
c) Purify M(a)
The Attempt at a Solution
a) from conditions for a density matrices
1) M(a)=M(a)*
2) tr(M(a))=1
3) M(a)>=0
form 1) a must be real
from 2) a=1/2
I'm not sure what 3) means, but if it means trace and determinant
must be non-negative, than this is also fulfilled if a=1/2.
b) I think that condition for system to be in mixed state is:
M(a)^2 /= M(a)
since this is true for M(a), system is in mixed state.
c) Don't know how to solve this part, Maybe it has to do something with decomposing a matrix ?