Fidelity of noisy EPR pair For this problem, you first need to do some research on the definition of "fidelity of quantum states" and "trace distance". (Think of it as a warm-up exercise for your own project.) Alice inputs a |00 state into her Bell-state machine to produce an EPR pair |00 (see slide 5 of Quantum Communication 1 for Bell states and the Bell-state machine). 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 1 p. (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.