consider a 2 qubit entangled state ($\sqrt 3/2)\left|00\right> + (1/2)\left|11\right>$
Q1) Is the above entangled state a valid one? q2) If valid then What is the probability of measuring the second qubit as $\left|0\right>$?
consider a 2 qubit entangled state ($\sqrt 3/2)\left|00\right> + (1/2)\left|11\right>$
Q1) Is the above entangled state a valid one? q2) If valid then What is the probability of measuring the second qubit as $\left|0\right>$?
It is valid, as $|00\rangle$ and $|11\rangle$ are the two computational basis states and the amplitudes are normalized $(\frac{\sqrt{3}}{2})^2+(\frac{1}{2})^2=1$.
The probability of measuring the second qubit as $|0\rangle$ is $\frac{3}{4}$. BTW, as the result of the measurement, the first qubit will be also in $|0\rangle$ due to the entanglement.
Regarding Q2, lets take the case of making a measurement on first qubit, then the probability of finding first qubit is 0.75 in |0> and 0.25 in |1> (explanation given in answer @czwang). Now say, the first qubit is found to be in |0> post measurement then the probability of second qubit to be in |0> is ONE and if the first qubit is found in |1> post measurement, then the probability of the second qubit to be in |0> is ZERO.
However, if you first perform the measurement on second qubit then the probability of second qubit to be in |0> is 0.75.