Final answer:
The probability of outcome 0 if the first qubit is measured is 2/9.
Step-by-step explanation:
The student's question asks about the probability of measuring an outcome of 0 for the first qubit in a given two-qubit quantum state. The quantum state given is √2/3√3|00> - 1/√6|01> + 2√2i/3√3|10> - 5i/3√6|11>. To find the probability of measuring the first qubit as 0, one must sum the probabilities of the states where the first qubit is 0, which are |00> and |01>. The coefficients of these states represent the amplitude of the state, and the probability of each state is given by the square of the modulus of the amplitude.
To calculate the probability of outcome 0 when measuring the first qubit, we need to find the amplitude of the first qubit in the state |0>.
The given two-qubit state can be expressed as:
√2/3√3|00> - 1/√6|01> + 2√2i/3√3|10> - 5i/3√6|11>
The amplitude of the first qubit in the state |0> is the coefficient in front of the term |00>. In this case, it is √2/3√3.
To find the probability, we square the amplitude:
(√2/3√3)² = 2/9.
Therefore, the probability of outcome 0 if the first qubit is measured is 2/9.