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Aug
9
comment Why does nonlinearity in quantum mechanics lead to superluminal signaling?
So linearity implies no cloning implies no signalling (if we assume that signalling with cloning is the only way one could potentially signal). This means that signalling implies nonlinearity. If I understand the question though, the OP wants to know how/why nonlinearity implies signalling.
Jul
12
comment Difference between Eulerian and Lagrangian formulation of Fluid Dynamics
See also: en.wikipedia.org/wiki/Material_derivative
Jul
12
comment Difference between Eulerian and Lagrangian formulation of Fluid Dynamics
Force is not $\frac{\partial (m v)}{\partial t}$, it is $\frac{d(mv)}{d t}$. Expand the derivative in terms of partial derivatives and you will get the same equation in both cases.
Jul
5
comment The derivation of fractional equations
Forces proportional to velocity, such as friction for example, can be described by putting fractional derivatives in the Lagrangian.
Jun
28
comment Can isotropic states have bound entanglement?
The states you write here are called Werner states. There do exist Werner states that are single-copy undistillable and NPT in a certain region, but general distillability conditions are unknown as far as I know. See for example arxiv.org/abs/1003.4337. Somebody else might be able to tell you more.
Jun
28
comment Can the entangelement of basis vectors increase under local operations?
Everything you write here is true, but you may have misunderstood the question (maybe OP can clarify). He's not asking if $E(\rho') < E(\rho)$, but whether a single component of $\rho'$ can have a greater entanglement than a single component of $\rho$. Imagine that $\rho$ is pure and you are doing probabilistic single-copy entanglement distillation. You can write the output as a mixed state, with one of the components having greater $E$, but the output state as a whole having less entanglement, so satisfying the LOCC requirements.
Jun
28
answered Can the entangelement of basis vectors increase under local operations?
Jun
26
answered Do the states forming an orthonormal basis have the same amount of entanglement?
Jun
22
comment Time dilation problem ($\gamma$ and $u$ are unknown)
Express time for the passenger in terms of $\gamma$ and $u$. Express $\gamma$ in terms of $u$ and insert back into the time for passenger. Then solve for $u$. It shouldn't be too difficult from there on.
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...