Quantum Superpositions of Life. Or not.


For everyone familiar with the quantum superposition principal (or have heard the folklore of a cat owned by a certain Schrodinger), the state of a quantum system is determined by the superposition of square-rooted probabilities of all possible states that the system can take. Practically speaking your future is

\sqrt{\alpha}*\left|bright\right\rangle + \sqrt{1-\alpha}*\left|bleak\right\rangle

where 0 < \alpha < 1 andĀ \left|bright\right\rangle \:\:and\:\: \left|bleak\right\rangle are orthonormal states.

While there is no inherent ‘quantumness’ to this scenario, it still obeys a superposition principal, except that \alpha is undetermined. It however, is not impossible to fit a probabilistic model into this framework, based on past experiences.

The brightness or bleakness of the future gets determined, when one gets to the future (or in other words, performs a direct measurement of the system). It’s the same with a quantum system. The superposition collapses once a measurement is performed.

What I’m trying to say is that, the superposition principle isn’t unique to the quantum world. However, what physicists take advantage of, in quantum systems, is retainingĀ the super-imposibility of the system. The idea is to perform a series of operations on a superimposed system, that does not at any point destroy the superposition, and to take advantage of the fact that the value of \alpha is known.

For instance, one may seek to turn tables. In which case, one applies a NOT gate, which happens to be a Pauli X matrix.

X*(\sqrt{\alpha}*\left|bright\right\rangle + \sqrt{1-\alpha}*\left|bleak\right\rangle ) = \sqrt{\alpha}*\left|bleak\right\rangle + \sqrt{1-\alpha}*\left|bright\right\rangle .

The idea of teleportation has forever fascinated mankind, and somehow people believe that if quantum teleportation is possible, an equivalent human form will exist some day. However, the idea behind teleportation, even in the quantum world, pertains to teleportation of information, not the particle itself. So while it might entail faster that light communication, it does not validate the simultaneous disappearance and reappearance of the qubit. This is where the ‘quantumness’ comes to play, due to a concept called quantum ‘entanglement’, that I shall discuss in the next post. Probably.