Quantum Mysteries

Most recent answer: 10/22/2007

Q:
I have read about quantum information and is confused. 1) In quantum information, it mentions about splitting of wave function in a unitary evolution. What is a unitary evolution, does it means reversible? Can a wave function really split into 2 separate wave functions? If yes, how? Under what situation would this happens. 2) in Einstein’s EPR paradox, one state can instantly effect another entangled state. How does it happens? Is there any information transferred? Is it the same as the information we transfer in a message? 3)In 1 qubit there is two possible states, 0 and 1. Can I store a string of numbers e.g. 1001101 and convert it into the angle 10.01101 degrees? Please help, Thanks!
- Eve
California
A:
Eve-
These are about the toughest questions we’ve ever gotten. I’ll work backwards, from the easiest.

3) Actually a qubit doesn’t have to be in either 0 or 1. It can be in combinations of part 0 and part 1. So can various classical systems, although digital computers are built around bits which are designed to be in only one of two states. A classical part (say the charge on a capacitor) which can take on a continuum of values can be used in an analog, as opposed to digital, computer. One example would be a pointer which could point at different angles. You could use a pointer like that to encode 1001101 by pointing at the angle 10.01101 degrees. Of course, a little jiggle would make errors in the reading. That’s why analog computers are used only for special purposes, not to substitute for digital computers.

But now I have to tell you the strange part. If you have two separate classical parts, whether analog or digital, each one can be in any of its states. For two qubits, the states they are in can be entangled. The first one can be in both 0 and 1 and so can the second one, yet due to entanglement you can have only the states (0,0) and (1,1) possible, not the combinations ((0,1) and (1,0). Or you can have the opposite entanglement. That’s what makes these qubits and not just classical analog parts.

2) The EPR effect, now repeatedly confirmed by experiments, says that the crazy entanglement we just described is real. If you ’measure’ the first qubit, you might find either a 0 or 1. It’s completely unpredictable. The same is true for the second qubit. And yet, the possible pairs of results are completely determined by the entanglement. Nature doesn’t know either of the results ahead of time, yet it knows the connection between the results.

We absolutely do not understand how this happens. It may be the deepest mystery in the universe.

At any rate, no information is transmitted from one place to another when these measurements are made. That’s because the results at both ends are purely random.

1) The quantum states are represented as something called vectors, sort of like arrows in 3-dimensions. Unitary operations are like rotations, preserving the length of the arrows. They are indeed reversible, at least in principle.
If you try to describe the quantum state of some system that’s interacting with other things, different parts of the system’s state get entangled with different versions of the other stuff. Then the quantum description of the system breaks up into the equivalent of different pieces of quantum state, which are no longer connected to each other. However, if you write a quantum description of ALL the interacting stuff, the quantum state does not break up, at least according to the unitary time development.

Trying to make sense of what becomes of a quantum state, e.g. whether the overall development is truly unitary or not, is known as the measurement problem. There are a variety of ideas about it, ranging from crazy to crazier. There are many books on the topic, but for a non-specialist I recommend E. Squires’ book "The Mystery of the Quantum World".

mike w

(published on 10/22/2007)