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2

Why the outcome after the controlled-phase and Hadamrad is equal to: $$\alpha |++\rangle + \beta |--\rangle = (|0\rangle \otimes H|\psi\rangle+|1\rangle \otimes XH|\psi\rangle)/\sqrt{2}$$ Let us label the qubits $A$ and $B$ for clarity. The initial state for circuit (11) is $$|\psi_A \rangle \otimes |+_B\rangle = \left( \alpha |0_A\rangle + \beta ... 0 What you say is true. If you are dealing with pure counting statistics and a constant source then the uncertainty in the countrate determined from the average of 10 measurements ought to be the same as the uncertainty derived from a measurement that is 10 times as long. So what could be gained? Firstly you get to test whether the statistics are Poissonian ... 1 Use the wave equation (\frac{1}{\epsilon \epsilon_0 \mu \mu_0} \vec{\nabla}^2 - \frac{\partial^2}{\partial t^2}) A = 0 and its solution, i. e. plane waves A = A_0 \exp(\imath ( \omega t - \vec{k} \vec{x})) with ||\vec{k}|| = \frac{\omega}{\sqrt{\epsilon \epsilon_0 \mu \mu_0}}. In words: The bit you already knew was that the (real part of the) wavector, ... 1 The imaginary part of the permittivity is a measure of the loss in the system. In some literature you will see reference to the "loss tangent" - this is in essence the ratio of the real and imaginary parts of the dielectric constant. The simplest way to measure this is to put the sample of interest in a cavity (for example, make it the dielectric of a ... 4 First make a parallel plate capacitor with plates of area A and spacing d. Fill the space between the plates with the dielectric whose complex permittivity \epsilon(\omega) you wish to measure. The formula for this capacitance is a complex function of frequency because the permittivity is a complex function of frequency.$$ ...

1

The displacement of 7.44° is clearly wrong. It is inconceivable that a torsion pendulum with a period of around 50 - 100 seconds could be displaced by such a large amount through the attraction of a couple of 2 kg masses. I have to conclude that other factors (air currents?), not gravity, were the cause of the displacement you observed. You really need to ...

0

I like your question because it puzzled me a lot when I started to learn electronics. Here is the answer. Just imagine a wire. There is a voltage V applied to its ends. What is the voltage at every section of the wire? If it is uniform wire, every meter of wire causes the same amount of voltage drop. Say, you divide the wire into n sections so that there is ...

0

I think we can divide most potential solutions into 3 broad categories depending on what sort of reference is used: Some property inherent to your body or brain: As mentioned in rob's answer, the most obvious is probably to use one of several second counting methods, or a song, drum beat or similar that you have experience performing at a fixed pace. Some ...

1

If your hypothetical stranded astronaut is able to use her own head-to-sole height as a length reference, I would expect her to count seconds by muttering "mississippi one, mississippi two, mississippi three" the way she has been doing since playground days. If your astronaut is a musician she might recall a piece of music for which she knows the ...

1

You've stated that you'd recreate an SI length unit $\text{m}$ (meter) from knowledge of your own height. So you've got a reasonably accurate ruler. Create a small angle pendulum with length $L$. Use this clock to measure the speed of light (in vacuum). Call this $c_p$ (measured with the planet's pendulum period). The ratio of $c$ (measured in SI units ...

1

Might not be the cheapest option, but this has the functionality you need. First a get a silicon photodiode, http://www.osioptoelectronics.com/standard-products/silicon-photodiodes.aspx Then get a blue light pass filter, http://opticalfiltershop.com/product-category/edge-filter/short-wave-pass-filters/ Now you make a circuit with a 1k resistor and connect ...

1

Please keep in mind one is talking of electromagnetic waves. Take the analogy of visible light projected from the location of your WIFI transmitter. Light impinging on objects is either absorbed (energy removed from the wavefront) or reflected. There exist shadows, less light behind somebody etc. So in general energy is absorbed from an electromagnetic ...

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The question how much receivers could receive a radio wave depends from the circumstances. Supposing that the farest away located receiver could receive the signal and this happens in a direct way without reflections from walls and all other receivers do not shadow each other, then YES, all receivers get signals. This happens because you are working with ...

4

Post measurement you want the eigenspaces to be orthogonal (and to have the projection onto the eigenspace to be entangled with a state of the measurement device). So you want the different eigenspaces to be orthogonal. And you want to be able to evolve to a post measurement state that has the right kinds of states. So really it is about the kinds of end ...

1

1) If all the eigenvalues of an operator are real, then it is Hermitian. You can see this by writing the operator (call it A) in the eigenvector basis. Then A has all real eigenvalues along its diagonal and zeros everywhere else. Therefore, $A^\dagger = A$ which means it is Hermitian. 2) Many of the operators that we call "observables" are the generators ...

3

The measurement of C-14 can be accurate. The interpretation of the measurement, in terms of the presumed age of the sample, is the thing that is subject to careful calibration. The assumption of carbon dating is that the ratio of C12/C13/C14 in the sample had some known value at the time the organism was alive. "Known" does not mean "constant over all ...

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