#1
Wed, 30/04/2008 - 15:11
entanglement
what is entanglement?
how can a single particle exist in different states at same time?
and how can we control the state of one particle by controlling the state of other?
how is parallel processing possible in quantum computers?
why dont anyone answer my
why dont anyone answer my question on fluctuations in cnt's and entanglement
Answers
1) Single particle CAN exist at different states at the same time, we don't know how. We only know, that it can. This effect is called "superposition", not entanglement. I.e. one can say, that particle IS in superpostion of states A, B, C, with some weights.
2) Entanglement is the effect, when TWO (or more) particles (or systems) exist in several states each, and each single state of one particle correlates somehow with anothes single state of second particle. This is not influence, this is just correlation. Entagled particles are not independent.
3) We cannot control the state of a distant entangled particle. We can just observe correlation. Particles ignore us and our influations, they just correlates with each other. I.e. they depends on each other, but independent of us.
4) The superpusition is the key. If we encode many input parameters in superposition of many states of one particle, we can parform operations against the full collection of states simultaneously.
What is a state?
1) Maybe more appropiate: One particle is in one state at a time! The superposition principle tells you that the superposition of twp states again is a state. If A is a state and B is a state then (A+B) is a state, too. Of course one particle can be in the single state (A+B). The superposition principle is not an effect but rather and by definition a property of the vector space where the states live in.
As an experimentalist you are easily tricked into thinking that a particle exits in different states at a time: Identical measurements on a bunch of particles ( all prepared to be in one and the same single state ) in general produce different measurement results. This is not because the (single) particles were in different states, but rather because the state of the particles is in general not an eigenstate of the measurement apparatus. A measurement changes the state of the particle to one of the eigenstates of the measurement apparatus. The probability for which eigenstate is taken depends on the 'similarity' of the initial state and the detector eigenstates.
2) Same point. Two particles can be in one entangled state. Certain Measurements on these particles are correlated in a way, which is classically not imaginable. A measurement on one particle destroys the entanglement (in general).
Doubt: Classical versus Quantum Correlations
The correlations of two spin measurements at two different locations is given by:
C(i,j) = trace(rho * A(i)xB(j))
With rho a density operator and A(i)xB(j) stand for tensor product of two measurements.
For the singlet state the correlations fulfil the well known curve C(i,j) = -cos(theta), where theta is the angle between different measurements.
Can anybody tell me why, for the classically correlated state:
rho = (1/2)*|1><1|x|0><0| + (1/2)*|0><0|x|1><1|
the correlations still fulfil this cosine law??? Being a classical state, the correlations should be just a line, if I got it right.
Thanks
1) Maybe more appropiate:
1) Maybe more appropiate: One particle is in one state at a time. The superposition principle tells you that the superposition of two state again is a state! -> (A+B+C) is a state if A and B and C each are states. And one particle can either be in the state A or in the state B ... or in the state (A+B+C). This state is not necessarily an eigenstate of the measurement device you have in mind. After the mesurement the particle is in general in a different state than before. Not all measurable quantities of the particle exist at the same time.
2) The two particles are entangled if they are in one entangled state! Some of measurement results of measurements on these particles are correlated. A measurement on one particle in general destroys the entanglement.