822 reputation
214
bio website
location London, United Kingdom
age
visits member for 2 years, 3 months
seen Nov 22 at 23:35

Jun
22
comment Proof for the completeness of eigenfunctions of a self-adjoint operator
Mathematicians have a proof for compact self-adjoint operators on Wikipedia: en.wikipedia.org/wiki/Compact_operator_on_Hilbert_space
Jun
19
comment Is time continuous or discrete?
I just mean that there exist quantum observables corresponding to position, and their outcomes in general form a continuum. Time is another issue.
Jun
13
revised Limits of superdense coding
added 275 characters in body
Jun
13
comment Limits of superdense coding
Notation: $\rho$ is the quantum state in question, $A$ refers to Alice's part of the state, $B$ to Bob's. So $\rho^A = Tr_B(\rho^{AB})$, ie. the state that Alice sees, having no access to Bob's part of the state. $S$ is entropy, $S(\rho) = -Tr[\rho \log_2(\rho)]$, $S(A|B)$ is the conditional entropy, ie $S(\rho^{AB}) - S(\rho^B)$ and $S(\rho || \sigma) = Tr[\rho(\log_2(\rho) - \log_2(\sigma))]$ is the relative entropy of states $\rho$ and $\sigma$. For $N$ I updated the answer as there is not enough space in this comment.
Jun
12
answered Limits of superdense coding
Jun
12
revised Quantum Collapse
added 319 characters in body
Jun
12
answered Quantum Collapse
Jun
7
comment A question about quantum measurement and associating a linear self adjoint operator to it
I don't quite follow what you are saying. In particular, I don't see how you can deduce a basis by being given a single vector.
Jun
7
comment Are scientists missing the point with distant cosmic objects, or is it just me?
Just one comment regarding the time light was created. Saying that light was created five billion years ago and has now reached us is the same as saying that it took five billion years to reach us. So it's logically impossible for light to have been created five billion years ago and it having reached us now, and yet having taken 13 billion years to reach us.
Jun
6
answered A question about quantum measurement and associating a linear self adjoint operator to it
Jun
6
comment Why does this state have a Schmidt rank of 1?
@Trimok You probably mean the state is a separable (rather than pure) state if and only if $ad - bc = 0$. As it's written down, it's always pure...
Jun
5
accepted Why do ice cubes make a cracking sound when placed in fizzy wine (Prosecco)?
Jun
4
awarded  Citizen Patrol
Jun
4
comment Why do ice cubes make a cracking sound when placed in fizzy wine (Prosecco)?
Prosecco was poured into the glass first, once it settled the ice cubes were dropped in.
Jun
4
comment Why do ice cubes make a cracking sound when placed in fizzy wine (Prosecco)?
Not sure if there is anything special about wine, I used Prosecco but it may be that the effect is the same with soda. I imagine that the physics of the phenomenon would tell us if the effect is the same with all carbonated drinks. Thanks for the image.
Jun
4
asked Why do ice cubes make a cracking sound when placed in fizzy wine (Prosecco)?
May
24
comment Is particle entanglement a binary property?
It's the other way around. Entanglement measures are defined so that they are $E(\rho)>0$ if and only if the state $\rho$ is entangled. There are also many measures of entanglement. The form a separable state takes, however, was defined decades before the measures of entanglement were developed. For a nice review I recommend reading arxiv.org/abs/quant-ph/0504163
May
24
answered Is particle entanglement a binary property?
May
24
answered Can a single molecule have a temperature?
May
23
comment How do you come up with a POVM?
That's right. You need to do what's called measurement tomography, which is the same thing as state tomography but instead of engineering the right measurements you engineer the right states to measure. The basic idea is have a set of states that form a complete basis in the Hilbert-Schmidt space of operators, measure them repeatedly and use the resulting expectations to reconstruct the matrix elements. See for example nature.com/nphys/journal/v5/n1/abs/nphys1133.html