Density matrix Definition and 111 Threads

Hi, I am trying to calculate the time evolution of a density matrix. Like if there is a mixed state with 50% of |x, 0> and 50% of |y, 0>. After time t due to time evolution, the kets become: |x,t>= e^(-i/h Ht) |x,0> and so on. Is it ok to use these kets instead of the original ket to...

What is the arbitrary density matrix of a mixed state qubit?

Let we have two qubits A and B. First qubit has eigenstates |A0> and |A1>, and second has |B0> and |B1>. Let them be in the entangled state, described with vector c1 * |A0> * |B0> + c2 * |B0> * |B1>| where c1 and c2 are complex numbers with |c1|^2 + |c2|^2 = 1. Then what is density...

A superposition of states such as a_1|\psi_1\rangle+...+a_n|\psi_n\rangle represents a single physical state, a state for which the probability of a measurement finding the system in state |\psi_k\rangle is |a_k|^2. The a_k represent "quantum-type" probabilities. On the other hand the...

Let p1,p2 be two density matrices and M be a real, symmetric matrix. Now, <<p1|[M,p2]>>= <<p1|M*p2>>-<<p1|p2*M>>= Tr{p1*M*p2}-Tr{p1*p2*M}= 2i*Tr{(Im(p1|M*p2))}. Why is it that this works out as simply as (x+iy)-(x-iy)? How is Tr{p1*p2*m}=conjugate(Tr{p1*M*p2})? I can't seem to figure...

(1) How does one obtain the density matrix formalism for quantum fields from the path integral? (2) Suppose I have a box containing interacting particles of different kinds. Is it possible to incorporate into the density matrix formalism both a non-zero temperature T as well as a time t...

Let phi(x) and phi_dagger(x) be field operators which satisfy the appropriate commutation relations. Then is there any analytic approximation for the two particle density matrix given by <phi_dagger(x)phi_dagger(x')phi(x')phi(x)> Thanks!

We have a spin state described by a time-dependent density matrix \rho(t) = \frac{1}{2}\left(\mathbf{1}+\mathbf{r}(t)\cdot \mathbf{\sigma} \right) Initial condition for the motion is \mathbf{r} = \mathbf{r}_0 at t = 0. We are then asked to give a general expression for \rho(t) in terms of...

I'm starting to convince myself that the density matrix is a better way of describing a quantum state than a spinor, even in the case of pure states. But it seems like very few of my textbooks have much to say about density matrices. Any comments? Carl

While reading this article http://citebase.eprints.org/cgi-bin/fulltext?format=application/pdf&identifier=oai%3AarXiv.org%3Aquant-ph%2F9708045 (which is by the way very interesting) i've encountered two unknown terms: "reduced denstiy matrix" --- i have never heard this term before...

Hi I am just doing an undergraduate degree in physics and currently studying a course in the foundations of QM. The problem I want to solve is this: There is an ensemble in a state corresponding to vector (i, 2) A measurement of Sy (with the operator represented by the 2x2 pauli spin...