- #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 ?