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9

You cut off the sentence that tells you what the numbers mean. "All uncertainties define a 90% credible interval". Crudely speaking, it means that there is a 90% probability of the parameters lying in the quoted range, with the most likely estimate being the headline number. It doesn't really make sense to translate these into Gaussian sigmas (it would be ...


4

The phase ambiguity is a bit worse than you think. There is a global phase ambiguity in $|\Psi⟩$, for sure, but if the state $$ |\Psi⟩=\sum_n c_n |\alpha_n⟩ \tag 1 $$ is all you have around, then there is also a phase ambiguity in the phase of each individual $c_n$. This is because if you change $|\alpha_n⟩$ to $|\alpha'_n⟩=e^{i\theta_n}|\alpha_n⟩$, the ...


3

In theory there is no lower limit on the amount of energy that must be exchanged to make a measurement, at least directly. But you are constrained by Landauer's principle when you initialize the memory you need to record the measurement. Effectively the measurement is the replication of information about the measured system's state in the measurement system'...


3

This is done in several papers, e.g. here: http://cds.cern.ch/record/546624/files/0204052.pdf The relevant portion is Lemma 1. Given a state $\rho$ with covariance matrix in block form $$ \gamma_{\rho}=\begin{pmatrix}{} A & B \\ B^T & C \end{pmatrix} $$ the covariance matrix after a measurement after a projection onto the pure Gaussian state with ...


2

[Note: answer completely updated] Based on your SEM picture and the further explanation in the comments, it seems that your system looks like this: You have materials A and B that form the thermocouple pair, a bead of mixture "AB" as a junction. The bead is embedded in and fused with a substrate material "C". A further complication is that there is a ...


2

The least count of the watch used for the measurement of time period is $0.01$ s This information is just telling you to round off to the second decimal place, as you correctly did. The sample mean is $\mu = 0.56$ and the sample standard deviation is $\sigma = 0.02$. The answer the text is referring to is $$\frac \sigma \mu = 0.0357 = 3.57 \%$$ But I ...


2

I think you are confusing systematic and random errors. Your experimental results can give you no idea about the systematic error. For example it might be that your timing device is calibrated incorrectly and when the correct time is 1.00 seconds then your timing device gives a reading of 1.10 seconds; when the correct time is 2.00 seconds the timing device ...


1

As explained in the comments, for a given MC event, the errors $\delta x$ and $\delta y$ for the two reconstruction methods A1 and A2 are uncorrelated. Therefore, no extra information is gained by using both reconstructions. We should just use the better one. Now, what does "better" mean. As stated in the OP, for both reconstructions, the distributions of $\...



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