Genady

From Rieffel, Eleanor G.; Polak, Wolfgang H.. Quantum Computing: A Gentle Introduction: Which states are superpositions with respect to the standard basis, and which are not? For each state that is a superposition, give a basis with respect to which it is not a superposition. a. |+〉 b. 1/√2 (|+〉 + |−〉) c. 1/√2 (|+〉 − |−〉) d. √3/2 |+〉 − 1/2 |−〉 e. 1/√2 (|i〉 − |−i〉) f. 1/√2 (|0〉 − |1〉) *Definitions: |+〉 = 1/√2 (|0〉 + |1〉) |−〉 = 1/√2 (|0〉 − |1〉) |i〉 = 1/√2 (|0〉 + i|1〉) |−i〉 = 1/√2 (|0〉 −i|1〉) My answers: a. superposition; basis: |+〉, |−〉 b. not a superposition c. not a superposition d. superposition; basis: √3/2 |+〉 − 1/2 |−〉, 1/2 |+〉 + √3/2 |−〉 e. not a superposition f. superposition; basis: |+〉, |−〉 Agree?

Sorry, I forgot to say where the exercise came from: Rieffel, Eleanor G.; Polak, Wolfgang H. Quantum Computing: A Gentle Introduction.

Which pairs of expressions for quantum states represent the same state? For those pairs that represent different states, describe a measurement for which the probabilities of the two outcomes differ for the two states and give these probabilities. (My answers in red.) a. |0〉 and −|0〉 same b. |1〉 and i|1〉 same c. 1/√2 (|0〉 + |1〉) and 1/√2 (−|0〉 + i|1〉) different; measure 1/√2 (|0〉 + |1〉); probabilities 1 and 0 d. 1/√2 (|0〉 + |1〉) and 1/√2 (|0〉 − |1〉) different; measure 1/√2 (|0〉 + |1〉); probabilities 1 and 0 e. 1/√2 (|0〉 − |1〉) and 1/√2 (|1〉 − |0〉) same f. 1/√2 (|0〉 + i|1〉) and 1/√2 (i|1〉 − |0〉) different; measure 1/√2 (|0〉 + i|1〉); probabilities 1 and 0 g. 1/√2 (|+〉 + |−〉) and |0〉 same h. 1/√2 (|i〉 − |−i〉) and |1〉 same i. 1/√2 (|i〉 + |−i〉) and 1/√2 (|−〉 + |+〉) same j. 1/√2 (|0〉 + eiπ/4 |1〉) and 1/√2 (e−iπ/4 |0〉 + |1〉) same *Definitions: |+〉 = 1/√2 (|0〉 + |1〉) |−〉 = 1/√2 (|0〉 − |1〉) |i〉 = 1/√2 (|0〉 + i|1〉) |−i〉 = 1/√2 (|0〉 −i|1〉) [Rieffel, Eleanor G.; Polak, Wolfgang H.. Quantum Computing: A Gentle Introduction. The MIT Press.] Is everything OK?

Only the relative angles matter, don't they? A and C are orthogonal, and B is at the angle θ to A. Yes, this is what they mean, I am sure.

Let the direction |v〉 of polaroid B’s preferred axis be given as a function of θ, |v〉 = cosθ|→〉 + sinθ|↑〉 and suppose that the polaroids A and C remain horizontally and vertically polarized as shown. What fraction of photons reach the screen? Assume that each photon generated by the laser pointer has random polarization. My answer is 1/2*cos2θ*sin2θ. Any objections?

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Thank you. This goes towards EV. I do, so this goes towards EV. This needs to be considered. Thank you.

Does it matter that our air temp is around 27-320C year around?

Almost all my trips are quite short, 2-5 miles each. I guess, battery recharge time would not be an issue in this case. How else would EV and IC cars compare in such use?

Not counting some overseas municipalities.

It works the other way around as well: Area as a fuel consumption.

What does it mean? How do the moving electrons appear?

Another example, Hubble parameter in cosmology. Its units are speed per distance, which is 1/time, which is units of frequency. It does not make the Hubble parameter a frequency of anything. Even if one expresses it in Hz.

It is an amazing achievement. Did they see anything unexpected?

So far, it's obvious.

It looked so to me, as well.

I don't think so. For example, in any universe, one could pick a unit of time and then define a unit of distance as the distance which is covered by light in that unit of time. In these units, the speed of light is 1. E.g., 1 year for time and 1 light-year for distance: c = 1 lyr/year = 1. The same works for other units, such as defining degree temperature to make the Boltzmann constant equal to 1, etc. It could be the cause if we discover that these two numbers have to be equal because of some dynamic symmetry, for example. You might not call it a cause in such case, but it could be the only value that allows solution of an equation. Simply put, my hypothesis is that the parameter values cannot be different, like the value of number pi cannot be different.

AFAIK, gravitons would be real particles in gravitational radiation, i.e., gravitational waves. But gravitational waves originate outside of the black hole's horizons, so the OP question does not apply.

Black hole can be, in principle, charged. A charged nonrotating black hole creates a static electric field outside its event horizon.

I don't think so.

Graviton would not need to escape from inside the event horizon. Gravitational field is present outside of it, and graviton is a quantum of that field.

I'd like to know the Janus' explanation, but my guess is that to decelerate at the end, you need to accelerate that deceleration fuel in the beginning. So, you'd need about 8 kg of fuel per kg of payload for the deceleration at the end, but much more than that at the beginning.

This part is not (and was not, since I've heard about this hypothesis first time) clear to me. Populations in biology are finite in size and limited by available resources, which is the cause of competition and natural selection. I don't see this kind of selection in this hypothesis.

Yes.

This is the only number of dimensions that makes equal the numbers of independent rotations and independent boosts, for example.