Simple questions

I couldn't understand the relationships between the qubits and their bloch sphere representation. I do not understand the very equation itself. If someone can help me uderstand the equation and how the rotations and reflections are equivalent to gates, it would be a great help.

Thanking you
Vivek Kumar

I feel really stupid asking this question, but I just can't figure out why I am wrong. Here goes:

I am giving a lecture about Quantum Cryptography, and as I am studying it again, I don't see why the following attack doesn't work (I am thinking about BB84):

finaly i've found something interesting for me ,but i don't know what books to search.could somebody tell me the best books about quantum.thanks

I ve read about the power of quantum computing and its prospects. I have a good knowledge of binary arithmetic and classical computing. But at the very basics i dont understand how quantum computers carry out operations on simple arithmetic like addition, subtraction, multiplication and division and how logical operations are done.

I understand how keys are sent via quantum entanglement. So that Alice and Bob each receive one of the entangled bits, and upon measuring it, assuming they used the same basis will be certain of the others result. Then using this they can detect the presence of an eavesdropper.

My question is can this be used to distribute the same key to more than two people?

Where can I get a sequence of random qubits (without investing in a laboratory!)? It is critical that these be random bits sampled from an unbiased quantum phenomenon, not simply random numbers.

I had been using http://www.randomnumbers.info/content/Download.htm but they appear to no longer be functioning.

what are fluctuations in nanoparticles?
how are they produced?
what is the state of particles on the surface of nanomaterials, i mean vibration of particles?

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?

i have a quantum circuit which is

it is combination of two hadamarded gates and one CNOT gate and my input state is (1/sqrt(2))*(|00>+|11>)
what is the basis unitary matrix for these combination gates and what is the out put state

-------(H)---------|-----------
|
|
------- (H)-------(+)-----------

what are quantum dots?
what is the physics behind their existance ?
what theory explains all the properties of quantum dots?
finally i would like to ask what are the funamentals of quantum dots?