I saw a video in which a guy from IBM was explaining (very generally) quantum computing, it's difference with classical computing etc.  The talk was not technical at all, it was intended for a broad audience.  At some point he told that, if we need to represent our position on the planet with only one bit, we could only tell for example if we are on the North or South hemisphere, but with a qubit we could tell exactly where we where.  He did this example to explain the difference in how much information can a bit and a qubit contain and to give a little idea of what a superposition is (I think).  Now, my question:  From what I know a qubit has more than one state, but when I read it I can only have one or zero, so why this example was made? From what I can understand a qubit can hold more information but I can't read it, so basically it's useless.
I've just gotten started with Nielsen and Chuang's text, and I'm a little stuck. They mention that theoretically, it would be possible to store an infinite amount of information in the state of a single qubit. I'm not sure I completely comprehend this.    Here's how I rationalized it: You take all the information you want to store, put it in binary form, and make it the real component of $\alpha $ or $\beta$ (the coefficients of the computational basis states).   Now I'm not sure if I've understood it right, but since it's still fuzzy in my head it would be great to get some kind of ELI5 explanation or possibly a more detailed picture of how this would, even theoretically, be possible.    Apologies if the question doesn't meet standards. I'm new to the forum and would be open to feedback regarding asking questions or answering them.
The number of nonnegative integer triples with sum equal to $12$ How many triples $x,y,z$ satisfy  $x+y+z=12$, where  $x,y,z\ge 0$ are integers? Note that these are not ordered: $ (12,0,0)$ and $(0,12,0)$ are treated as same. Progress I have tried the formula ${13\choose 2}$ to select values of $x$ and $y$ from $0$ to $12$ as  $z$ would keep changing according to $x$ and $y$. (That is, $z=12-x-y$.) The problem is that that certain combinations of $x$ and $y$ would give value of $x+y$ greater than $12$. I can't seem to get around this. Profile Bug - Reputation Summary Not Displaying All Lines How can I identify hardware components in a laptop? I just reinstalled my Windows and now I don't have all the hardware components recognized. I have an  laptop and  website seems to have all the necessary drivers for my model. The problem is that I don't know exactly which components I have. For example, in my laptop video card case the site has available drivers for ATI and Intel chips.   How do I know what are the right drivers for my machine? Rewriting a custom-post-type permalink with taxonomy term? Integrate $\int \frac{25 - x^2}{x^4} \operatorname d\!x$ I think we use trig substitution for this. But I'm not sure where to even begin with this   $$\int \frac{25 - x^2}{x^4} \operatorname d\!x$$ Given a real positive sequence $\{a_n\}$ such that $\sum_{i=1}^n a_i$ converges.  Prove that there exists a real sequence $\{c_n\}$ monotonically increasing to $\infty$ such that $\sum_{i=1}^\infty a_nc_n$ converges.  What I have done:  I have written $$\sum_{i=1}^{N+1}a_ic_i=c_{N+1}\sum_{i=1}^{N+1}a_i-\sum_{i=1}^N(c_{n+1}-c_n)S_n$$  and then try to prove the convergence by the Cauchy criterion. However my evaluation is still not good enough. I'm really stuck. Old post apocalyptic cartoon where the main character has red hair and lives with a nomadic group How can I remove whitespace when declaring an XSL variable? Is it possible to know who voted my question/answer up or down? If not, then is it possible to include this feature? By this feature we can come to know if you are being voted up by question owner or persons giving other answers to same question or just the visitors of that question thread.  Like...  If it is a group of people giving other answers, then your answer is most correct If it is readers of that question, then your answer is more popular I want to do something like String.Format("[{0}, {1}, {2}]", 1, 2, 3) which returns:  [1, 2, 3]   How do I do this in Python? Best way to center a &lt;div&gt; element on a page both vertically and horizontally?  I know that margin-left: auto; margin-right: auto; will center on the horizontal, but what is the best way to do it vertically, too? How can I prove that $\,ax\equiv b\pmod{\! n}\,$ has a unique solution if $\,\gcd(a,n) = 1$?  I suspect that the Bezout identity for $\,\gcd(a,b) = 1$ is the key but I don't see how to proceed. Are Stormtroopers paid or rewarded in any way for their service? How to prove that if A, B, C are submodules of M module then $$ A \cap (B+C) = (A\cap B)+C \iff C \subseteq A $$  Any help would be appreciated! Is globbing a feature of the shell? Counting buffer overlap in QGIS For my thesis I'm modeling the identification of recreation areas.  Therefore, there has been a survey where people were asked to specify where they recreate. They had to indicate this place on a map and give a radius. Now I have to analyse which areas were most visited, and afterwards use the data to give a weighted rating with the travel distance.  So, I use QGIS to Buffer the data points by using the given radius. Now, I want to calculate for every point in the country how many times it was visited.  Any thoughts how to do this in QGIS? Korea: Visa required to go to the city while in transit in Seoul for a Philippine citizen? Hi I'm traveling to Uzbekistan and have 12 hours layover in Seoul via Korean Airlines. Do I need a visa to go out of the airport for sightseeing? I'm a Philippine passport holder. Unable to start XAMPP using sudo in Desktop Entry I am using Ubuntu 18.04. I have installed XAMPP and created a .desktop file to run it.  [Desktop Entry] Type=Application Name=XAMPP Control Panel Version=7.3.0.0 Exec=sudo -i python /opt/lampp/share/xampp-control-panel/xampp-control-panel.py Encoding=UTF-8 Terminal=false Comment=Start and Stop XAMPP Icon=/home/lee/.local/favicon.ico   But, for some reason it won't run. The "Exec" line runs fine on the CL. I have it set to execute. Any ideas? I'm currently working through the book Heisenberg's Quantum Mechanics (Razavy, 2010), and am reading the chapter on classical mechanics. I'm interested in part of their derivative of a generalized Lorentz force via a velocity-dependent potential.   I understand the generalized force   $$F_i = -\frac{\partial V}{\partial x_i} + \frac{d}{dt}\left(\frac{\partial V}{\partial v_i}\right)$$  that they derive from a Lagrangian of the form $L = \frac{1}{2}m|\vec v|^2 - V(\vec r,\vec v,t)$.  However, in the next (critical) step of the derivation, the author cites a theorem from Helmholtz saying      ...according to Helmholtz, for the existence of the Lagrangian, such a generalized force can be at most a linear function of acceleration, and it must satisfy the Helmholtz identities.   The three Helmholtz identities are then listed as:  $$\frac{\partial F_i}{\partial \dot{v_j}} = \frac{\partial F_j}{\partial \dot{v_i}},$$  $$\frac{\partial F_i}{\partial v_j} +  \frac{\partial F_j}{\partial v_i} = \frac{d}{dt}\left(\frac{\partial F_i}{\partial \dot{v_j}} +  \frac{\partial F_j}{\partial \dot{v_i}}\right),$$  $$\frac{\partial F_i}{\partial x_j} -  \frac{\partial F_j}{\partial x_i} = \frac{1}{2}\frac{d}{dt}\left(\frac{\partial F_i}{\partial v_j} - \frac{\partial F_j}{\partial v_i}\right).$$  I'm trying to understand where this theorem comes from. Razavy cited a 1887 paper by Helmholtz. I was able to find , but it is in German, so I could not verify whether or not it proved the theorem. Additionally, I could not find it in any recent literature. I searched online and in Goldstein's Classical Mechanics.   The only similar concept that I can find is in the  where we have three equations known as Helmholtz conditions. Are these two concepts one in the same? If so, how should I interpret the function $\Phi$ and the matrix $g_{ij}$ that appear in the Helmholtz conditions I found online?   If the cited theorem from Razavy does not relate from the inverse Lagrangian problem, could I have some help finding the right direction? How to prove that if $a\equiv b \pmod{kn}$ then $a^k\equiv b^k \pmod{k^2n}$