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Does anyone know anything about quantum information theory?
I am reading a text about transmitting quantum states, represented by density matrices, through channels. Here the depolarising channel is defined as the map:
X: -> (1-p)X + pτ Tr[X]
which with probability (1-p) maps the state onto itself and probability p maps it onto the maximally entangled state τ.
Now my question is: Why did the writers choose to insert Tr[X] = 1 (X is density matrix). Why is that important to have? From what I see, it could just as well be omitted. Come to think of it, I am not sure about the role that the trace of the density matrix plays in the process of transmitting signals and measuring. Could anyone clarify?
I am reading a text about transmitting quantum states, represented by density matrices, through channels. Here the depolarising channel is defined as the map:
X: -> (1-p)X + pτ Tr[X]
which with probability (1-p) maps the state onto itself and probability p maps it onto the maximally entangled state τ.
Now my question is: Why did the writers choose to insert Tr[X] = 1 (X is density matrix). Why is that important to have? From what I see, it could just as well be omitted. Come to think of it, I am not sure about the role that the trace of the density matrix plays in the process of transmitting signals and measuring. Could anyone clarify?