The Postulates of Quantum Mechanics
Let’s begin by summarizing what we know about quantum states so far. In previous lessons, we’ve seen that quantum states are vectors in 2-D complex vector space. These bras (row vectors) and kets (column vectors) depict the possible locations that we might find a qubit in. We form a multi-qubit system by taking the tensor product of the state vectors of single qubits. To know which state a qubit is in, we must measure it. We measure it using complex hardware in the computational basis and transfer the state information into classical bits that we can read. Which state we end up getting is entirely probabilistic until the first measurement. The complex amplitudes dictate this probability associated with the state vectors. And lastly, no measurement on the system is gentle enough to leave the qubit in an unperturbed state.
All these ideas take root from the postulates at the heart of quantum mechanics. We’ve already discussed a bunch of them, as you’ll notice. But going through them in a sequence revises the concepts we have learned so far and makes it easier for us to understand the ones we haven’t discussed.