Timeline for Is it possible to write a Density Matrix in the following form?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Jan 22, 2013 at 0:54 | answer | added | Qmechanic♦ | timeline score: 6 | |
| Jan 18, 2013 at 23:05 | answer | added | Mauricio Matera | timeline score: 0 | |
| Jan 18, 2013 at 21:26 | history | edited | Qmechanic♦ | CC BY-SA 3.0 |
retagged; layout;
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| Jan 13, 2013 at 14:22 | comment | added | user17581 | I'm afraid that twistor59 is right, you need the set of kets to be a basis of the abstract space. | |
| Jan 13, 2013 at 8:31 | comment | added | twistor59 | You said that the $|x_l\rangle$ are not necessarily orthonormal, but do they span the (presumably finite dimensional) space? If not, then you can't construct an arbitrary density matrix in this way. | |
| Jan 12, 2013 at 19:41 | history | edited | N. Virgo | CC BY-SA 3.0 |
markup
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| Jan 12, 2013 at 15:46 | comment | added | physics_xyz | I don't think so, because here $\left\{|x_{\ell}>\right\}_{\ell = 1}^{N}$ don't form a basis for space they are just an ensemble. | |
| Jan 12, 2013 at 15:17 | comment | added | Luboš Motl | It's just the diagonalization of the density matrix, a Hermitian matrix, isn't it? $N$ must be chosen to be nothing else than the dimension of the matrix for generic ones, otherwise the $x$-vectors wouldn't be orthogonal to each other. | |
| Jan 12, 2013 at 14:58 | review | First posts | |||
| Jan 12, 2013 at 15:41 | |||||
| Jan 12, 2013 at 14:56 | comment | added | physics_xyz | yeah, that's right but the coefficients of $|x_{\ell}>$ here are all the same and we have factorized them out as $\frac{1}{N}$, besides $|x_{\ell}>$ are normal states! how can it be possible ? | |
| Jan 12, 2013 at 14:48 | comment | added | user17581 | I'm not answering right away because right now I can't think of a way to mathematically prove it (and I'm a lil' bit busy ATM), but I'm sure that to construct a density matrix you don't need the states to be orthogonal to each other. | |
| Jan 12, 2013 at 14:39 | history | asked | physics_xyz | CC BY-SA 3.0 |