Fidelity of noisy EPR pair

these probam, you will first need to do some research on the definition of "fidelity of quantum states" and "trace distance".

Alice inputs a 00 state into her Bell-state machine to produce an EPR pair 00 Alice's source of input states is unfortunately not 100% reliable: It produces an input state 00 with probability p and an input state 11 with probability 1p.

(a) Determine the density matrix of the resulting noisy output state of the Bell-state machine. (You can express the result in terms of Bell states - they are an orthonormal set of states.)

(b) Compute the fidelity of the noisy output state with respect to the perfect EPR pair 00.

(c) Compute the trace distance of the noisy output state from the perfect EPR pair 00