The Wikipedia entry to get you started:
http://en.wikipedia.org/wiki/Quantum_entanglement
Quoting from the above:
"Broadly speaking, quantum mechanics incorporates four classes of phenomena that classical physics cannot account for: (i) the quantization (discretization - note, this is NOT quantification - the root word is quantum, not quantity) of certain physical quantities, (ii) wave-particle duality, (iii) the uncertainty principle, and (iv) quantum entanglement."
The long and the short of it is that elementary particles, of which light is the most famous example, possess the properties of both particles (like solid matter) AND waves. This discovery was the genesis for quantum physics. Understanding this concept (below) is VITAL to the remainder of my example.
The basic experiment was:

1) shoot a bunch of particles, lets say BBs, through a barrier with one slit in the center. The "pattern" of particles on the wall behind the slit were, as you would presume, within the same general shape as the slit.
With two slits, you get two "slit patterns", next to each other, of particles striking the wall, like you would expect.

2) produce a wave, such as a normal roundish ripple in water, that moves toward the single slit barrier. On the wall behind the barrier, the wave will have a much different and more broad appearance - nothing at all like the slit pattern, which means the wave hits the slit and is changed slightly but more or less retains its normal wave shape, though reduced because some of the wave was unable to penetrate the barrier - it produces a "wave pattern" on the wall, very different than the slit pattern of the particle.
When the barrier has two slits, the single wave hits both slits and breaks apart and creates TWO smaller waves on the other side of the barrier - where the two waves overlap, a new, strong wave is created - the new wave and the two existing and weaker waves ALL travel from the barrier and strike the wall, leaving what is called an "interference pattern" because the waves interfere with each other. The most intense result is where the "new" wave, which is reinforced when the other two waves overlap, strikes the wall, with the original two barrier waves having less but still noticeable effect on the wall - no real "slit" pattern can be seen, as the waves themselves affected each other's trajectories, basically "knocking each other off course" and exaggerating the scattered "wave pattern".

3) shoot a beam of photons (light) through the single-slit barrier. On the wall you see the standard slit pattern just like the particle. The photons behave as particles when shot through a single slit.
Now shoot a beam of photons at a barrier with two slits - instead of two slit patterns like you would expect (since it behaved as a particle when shot through a single slit), the photon beam breaks apart and creates two smaller waves, with the overlap in between creating the third central wave, which all strike the wall and produce an interference pattern like wave, instead of a dual slit pattern like a particle!
4) Confused by this, scientists decided to measure the beam of photons, so they placed a measuring device next to the two-slit barrier, but when they shot the beam of light through the barrier, it created two slit patterns, as if it were a PARTICLE - Even though they had just SEEN the wave interference pattern on the wall from this SAME experiment!
PERCEPTION AND REALITY
The act of OBSERVING the photons themselves, rather than their resulting patterns on the wall behind the barrier, caused the NATURE of the beam of photons to CHANGE. Merely by LOOKING at the beam of photons, reality itself was changed and the beam of photons behaved differently, almost as though "it knew it was being watched".
Years later, scientists next shot two identical photons in opposite directions and attempted to measure the location and momentum of each. Even more baffling than the wave-particle duality, scientists found that observing and measuring one photon, its location for example, affected the other, and vice-versa.
This leads to the idea of "quantum entanglement", which basically indicates that any two particles or photons or what-have-you, are inter-related and communicating with each other in a way that we are as-yet unable to detect or understand but which Einstein's Special Theory of Relativity states can NOT exceed the speed of light, even though the observation and of particle 1 and a change in particle 2 seems to be simultaneous.
GHOSTS?
So what does any of this have to do with ghosts, you ask me? To be perfectly honest, I can't quite explain it. Some people see ghosts all the time, some never do - sometimes in the very same place. "Haunted" locations get tourists from all over - some tourists excitedly report their own sighting or experience, while others shrug and shake their heads, saying "maybe next time". "Psychics" can walk through a house, "see" and "hear" all sorts of things (and people), detect "cold spots", get "bad feelings", while a non-psychic may follow them immediately and even stand in the same spot and shrug, saying "Mmm. This step's loose?" but otherwise perceive nothing close to what the psychic did.
Do "ghosts" work on a quantum level? The light needed for us to see an object - does it behave as a wave or a particle when someone perceives a "ghost"? Since everything is made of particles or photons, when someone "observes" a ghost, what mechanical effect does this have on reality? Does it change the ghost itself? Does it change the person, if the ghost is OBSERVING THEM?
Do some people NOT see ghosts because their vision gives them only "slit pattern" results, while someone else's vision may be only "interference pattern"? And what if you're LOOKING for a ghost, but you're skeptical you'll find one? You are observing the surroundings, but in so doing, you are altering the basic environment, changing photonic manifestations from wave back to particle.
I am not a scientist, nor a mathematician, nor a scholar, so I cannot possibly put forth a THEORY on what, if anything, any of this means, but I feel these vital concepts of quantum reality and its malleability due to the effect of conscious observation most likely hold THE "key" to a more profound understanding not just of ghosts and the paranormal, but the ultimate reality of the universe and existance itself.
Thank you for your time.
New Scientist magazine is a good starting place to read about Quantum Mechanics.