A qubit can be in two states (0) and (1) and its Hamiltonian Ê is described in that basis, by the following matrix: A =

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A Qubit Can Be In Two States 0 And 1 And Its Hamiltonian E Is Described In That Basis By The Following Matrix A 1 (46.54 KiB) Viewed 44 times

A qubit can be in two states (0) and (1) and its Hamiltonian Ê is described in that basis, by the following matrix: A = () 1 3 4 4 -3 where I is a known, positive constant with dimensions of energy. (a) Obtain formulae giving the two allowed values of the energy, E, and Eu, ex- pressed as functions of 12 (assume Eo < Ei). Display your reasoning. (b) The corresponding state vector corresponding to the the ground state takes the form А -B Find the two constants A and B, showing how you arrive at your result. You can assume both constants to be real and positive. (c) Suppose now that the qubit is in the basis state 1). What is the probability that an energy measurement would yield the ground state energy, Ey? Justify your answer. |E.) = ( 6 )