Thanks for the post. I have another silly question though - which I'm sure others are asking themselves. If you have particle A and particle B, entangled in spin say, then when you measure A the entangled state collapses, you get the spin for A, and you know what the spin for B will measure. OK so far?
Silly question is, if we haven't measured anything yet, how do we know there is some 'spooky action at a distance'? Maybe particle A's spin was ALWAYS up, and B's was ALWAYS down, you just didn't know it until you measured it? What led us to this idea of superposition in the first place?
Well, that's the complicated part:-) The short version is that you can derive an inequality for the measurement statistics which cannot be violated if the spins already have a defined value and which is violated by quantum mechanics (and experiment).
But maybe the best illustration is the "GHZ paradox": Here you have three entangled particles, and the nice thing is that you don't need much statistics.
Your source emits those three entangled particles, and each one is sent to a different person. Each one can choose to measure one of two observables, called X and Y (for spins, they would actually be the measurements of spin in x and y direction), and will get a result of either 1 or -1. After the measurement they can exchange their results and compare them (and of course also do calculations with them). Now you get the following results:
For each individual measurement you get either +1 or -1 with 50% probability each (i.e. single-site measurement results are completely random).
If you measure X at one particle and Y on the other two, the product of all three numbers are always 1.
If you measure X on all three particles, the product of the results is always -1.
OK, now let's assume the values already exist prior to measurement. Let's call the predetermined value for the measurement of X on particle 1 X1, the predetermined value for Y measurement on particle 1 Y1, etc. Of course since at creation time, it isn't yet decided whether X or Y is measured on any particle, all Xi and Yi would have to have values at the same time.
From the second bullet, we know that for the hypothetical predetermined results we need to have have X1*Y2*Y3=1, Y1*X2*Y3=1 and Y1*Y2*X3=1 (because otherwise we would sometimes measure -1 for any of XYY, YXY, YYX). Now nobody hinders us to multiply all three terms together (after all, we assume they are predetermined), which gives (X1*Y2*Y3)*(Y1*X2*Y3)*(Y1*Y2*X3)=1*1*1=1. On the other hand, in the product, each of the three predetermined Y results (Y1, Y2 and Y3) occurs twice, and since 1*1=(-1)*(-1)=1, we have (X1*Y2*Y3)*(Y1*X2*Y3)*(Y1*Y2*X3)=X1*X2*X3. So we just have derived that X1*X2*X3=1. But as we see from the third bullet above, we get X1*X2*X3=-1. And we get that always. Which directly contradicts the result just derived under the assumption that the values are predetermined.
If all you want to do is to efficiently transmit information, quantum mechanics doesn't give you anything. However I don't see how you want to compute by "pumping information through the frequency spectrum".
The nice thing about html5 is that it's plaintext, and thereby can't be exploited - only the parsers can.
JavaScript is a programming language. Just because the code is delivered in source form, it doesn't mean there cannot be security holes. And Flash exploits are actually Flash player exploits. However, the following still remains true:
And the nice thing of these parsers - which we also call Browsers - is that you can choose, and secure them yourself.
Well, it depends on what you mean with "understand correctly":-) If you mean "correctly interpret the wrong claims of the article" then yes, you understand correctly. However if you mean "correctly understand how quantum mechanics really works" then no, you don't.
Say you have a pair of maximally entangled qubits. Now if you measure one qubit, you get a random result, and you also know the state of the other qubit (because the entangled state tells you which state of the other qubit goes with the one of yours you just determined, for example, there's a state where the other qubit always gets the opposite value). However, the one who has the other qubit cannot distinguish if you actually have measured, because if you haven't measured, he'll just get a random value, and if you have measured, he'll get the opposite of your random value, which of course is a random value. Only after he gets to know what you measured (through conventional communication channels) he can compare the values and determine that they are indeed opposite.
If entanglement isn't that important, how do you explain one-way quantum computing? There you prepare an entangled state at the beginning (which contains no information about the problem you want to solve, except that it has to be large enough) and then do nothing but measurements to do the quantum calculation.
Well, it's a bit more than a percentage, but you're right, superpositions on single qubits are not really exciting. However, the point is that the number of states of two qubits is more than you'd get by giving a state to each qubit individually (those "extra" states are called entangled).
More exactly, a single qubit can be described by 2 real parameters. Without entanglement, n qubits would be described by 2n real parameters (2 for each single qubit). However, actually n qubits are described by 2^(n+1)-2 real parameters. As you see, the number of real parameters in the state grows exponentially instead of linearly in the number of qubits. And that's where the power of the quantum computer comes from.
You don't really need a free will of the experimenters. All you need is a deterministic cause in the past light cone of each measurement which is not also in the past light cone of the other measurement. It's easy to see that such events always exist.
Yes, but "there's a signal that propogates at infinite speed and yet can't be used for communication" is a road you really don't want to go down.
You're right in that I don't. Others don't mind, however, or at least they consider that the lesser evil compared to giving up a classical reality.
Also it could in principle still be an extremely high, but finite speed (it just has to be high enough that we don't hit the "non-correlation window" with significant probability in our experiments). That would, of course, imply a change to quantum mechanics (and also to relativity, because it would mean a detectable absolute frame of reference). Again, it's nothing I consider attractive, but it's not ruled out by our experiments (provided that finite speed is large enough).
Sure, such a quantum computer, if built, could process, say, 10^50 quantum inputs simultaneously. But where does one get the 10^50 inputs?
An equal superposition of the 2^n states of n bits is a completely separable (i.e. non-entangled) state which just has each qubit individually in an equal superposition of 0 and 1. Since no entanglement is involved, that state is almost trivial to create. It's the processing afterwards which is complicated.
Even with the best and fastest computer you'll not get weather prediction accurate to the second. That's because weather is a chaotic system, and you'd need an insane amount of measurement data to be that accurate (and probably would have to predict human behaviour as well!)
The set of problems you can in principle solve with a quantum computer is exactly the same as you can solve with classical computers. The best proof of this is that you can simulate a quantum computer with a classical computer (and vice versa). However, as far as we know you cannot simulate a quantum computer on a classical computer in polynomial time.
You cannot get the power of a large quantum computer by repeatedly running a small quantum computer, because you cannot store intermediate quantum results in classical memory. However, real applications will probably always be combinations of classical and quantum computers, because for a lot of problems quantum computers don't have an advantage over classical computers, so it would be wasteful to do those parts a classical computer can do well on a quantum computer instead. As an example, when running Shor's algorithm, you'll use a classical computer to multiply the factor candidates to see if you already got the correct factors; while a quantum computer could do it, it would just be wasteful.
"This shared state means that a change applied to one entangled object is instantly reflected by its correlated fellows"
Why, oh why, is this nonsense repeated again and again. If you change one entangled particle, you do not change the other. For example, if you have two spins entangled in a way so that if one is measured "up" the other is measured "down" and vice versa, and you turn the one spin around (without measuring it) then you'll have an entangled state where if you measure the first spin "up" the other one is also measured "up", just as you'd expect. As long as you don't measure, there's no "spooky action at a distance" but only local changes. The "spooky action at a distance" happens at measurement (which BTW destroys the entanglement), and it's all but a given that there's indeed an action at a distance (you only need it if you want a certain type of interpretation, where basically "under the hood" the system behaves completely classical, but we don't see it because there are so-called hidden variables which we cannot determine). The point is that in an entangled state the correlation is all which is defined, and the result of local measurements are completely undefined (OK, strictly speaking this is only true for maximally entangled states, for others there's less correlation and more local information; it's basically a trade-off between the two). Now when you measure the spin of one of the particles, the value of the spin gets a defined (but random) value (up or down, in the direction you measure), and also the value of the spin of the other particle gets a defined value, which is determined by the entangled state and the result you got for the first particle, i.e. if the entangled state was "both particles have opposite, but otherwise undefined spin" then after measurement, the particles will have opposite, well-defined spin. However, since the result is random, if you have the other particle, you cannot see any difference whether the first particle has been measured or not; he will get a random result either way. Only if he gets told the measurement result of the first particle, he can predict (or, if he already measured, compare) his measurement result.
Oh, and yes, I'm working in the field of entanglement, so I know what I'm speaking about.
But I absolutely like the following statement from the article:
"Hang on, what's quantum entanglement when it's at home? I was afraid you were going to ask."
Slashdot Mirror
And the item goes to ... Anonymous Coward! :-)
Thanks for the post. I have another silly question though - which I'm sure others are asking themselves. If you have particle A and particle B, entangled in spin say, then when you measure A the entangled state collapses, you get the spin for A, and you know what the spin for B will measure. OK so far?
Silly question is, if we haven't measured anything yet, how do we know there is some 'spooky action at a distance'? Maybe particle A's spin was ALWAYS up, and B's was ALWAYS down, you just didn't know it until you measured it? What led us to this idea of superposition in the first place?
Well, that's the complicated part :-) The short version is that you can derive an inequality for the measurement statistics which cannot be violated if the spins already have a defined value and which is violated by quantum mechanics (and experiment).
But maybe the best illustration is the "GHZ paradox": Here you have three entangled particles, and the nice thing is that you don't need much statistics.
Your source emits those three entangled particles, and each one is sent to a different person. Each one can choose to measure one of two observables, called X and Y (for spins, they would actually be the measurements of spin in x and y direction), and will get a result of either 1 or -1. After the measurement they can exchange their results and compare them (and of course also do calculations with them). Now you get the following results:
OK, now let's assume the values already exist prior to measurement. Let's call the predetermined value for the measurement of X on particle 1 X1, the predetermined value for Y measurement on particle 1 Y1, etc. Of course since at creation time, it isn't yet decided whether X or Y is measured on any particle, all Xi and Yi would have to have values at the same time.
From the second bullet, we know that for the hypothetical predetermined results we need to have have X1*Y2*Y3=1, Y1*X2*Y3=1 and Y1*Y2*X3=1 (because otherwise we would sometimes measure -1 for any of XYY, YXY, YYX). Now nobody hinders us to multiply all three terms together (after all, we assume they are predetermined), which gives (X1*Y2*Y3)*(Y1*X2*Y3)*(Y1*Y2*X3)=1*1*1=1. On the other hand, in the product, each of the three predetermined Y results (Y1, Y2 and Y3) occurs twice, and since 1*1=(-1)*(-1)=1, we have (X1*Y2*Y3)*(Y1*X2*Y3)*(Y1*Y2*X3)=X1*X2*X3. So we just have derived that X1*X2*X3=1. But as we see from the third bullet above, we get X1*X2*X3=-1. And we get that always. Which directly contradicts the result just derived under the assumption that the values are predetermined.
let me ask, how do i NEVER get this add-on?
Simple: By not installing it.
If all you want to do is to efficiently transmit information, quantum mechanics doesn't give you anything. However I don't see how you want to compute by "pumping information through the frequency spectrum".
JavaScript is a programming language. Just because the code is delivered in source form, it doesn't mean there cannot be security holes. And Flash exploits are actually Flash player exploits.
However, the following still remains true:
Yeah, they want him to know the person to sue if anything goes wrong with quantum computing.
Well, it depends on what you mean with "understand correctly" :-)
If you mean "correctly interpret the wrong claims of the article" then yes, you understand correctly. However if you mean "correctly understand how quantum mechanics really works" then no, you don't.
Say you have a pair of maximally entangled qubits. Now if you measure one qubit, you get a random result, and you also know the state of the other qubit (because the entangled state tells you which state of the other qubit goes with the one of yours you just determined, for example, there's a state where the other qubit always gets the opposite value). However, the one who has the other qubit cannot distinguish if you actually have measured, because if you haven't measured, he'll just get a random value, and if you have measured, he'll get the opposite of your random value, which of course is a random value. Only after he gets to know what you measured (through conventional communication channels) he can compare the values and determine that they are indeed opposite.
If entanglement isn't that important, how do you explain one-way quantum computing? There you prepare an entangled state at the beginning (which contains no information about the problem you want to solve, except that it has to be large enough) and then do nothing but measurements to do the quantum calculation.
Well, it's a bit more than a percentage, but you're right, superpositions on single qubits are not really exciting. However, the point is that the number of states of two qubits is more than you'd get by giving a state to each qubit individually (those "extra" states are called entangled).
More exactly, a single qubit can be described by 2 real parameters. Without entanglement, n qubits would be described by 2n real parameters (2 for each single qubit). However, actually n qubits are described by 2^(n+1)-2 real parameters. As you see, the number of real parameters in the state grows exponentially instead of linearly in the number of qubits. And that's where the power of the quantum computer comes from.
Because the uncertainty relation would enable them to create money out of nothing, if they only give it back quickly enough. :-)
You don't really need a free will of the experimenters. All you need is a deterministic cause in the past light cone of each measurement which is not also in the past light cone of the other measurement. It's easy to see that such events always exist.
Yes. Ever heard of the butterfly effect?
You're right in that I don't. Others don't mind, however, or at least they consider that the lesser evil compared to giving up a classical reality.
Also it could in principle still be an extremely high, but finite speed (it just has to be high enough that we don't hit the "non-correlation window" with significant probability in our experiments). That would, of course, imply a change to quantum mechanics (and also to relativity, because it would mean a detectable absolute frame of reference). Again, it's nothing I consider attractive, but it's not ruled out by our experiments (provided that finite speed is large enough).
With just as many nukes pointing to the US, I'd not be so sure.
Hell, if Hitler had just had better weather there's a good chance you'd all be speaking German right now. Those of you that survived, that is.
If he hadn't killed that butterfly as a five year old ...
no, no, no
the prank is you release 3 sharks with the numbers 1, 2 and 4 on them and watch while everybody searches for the one with the number 3 on it...
But that one is easy: You just have to look for the laser.
Jehova! Jehova! Jehova!
So what if you compare Jehova to Hitler? Will Godwin get stoned?
An equal superposition of the 2^n states of n bits is a completely separable (i.e. non-entangled) state which just has each qubit individually in an equal superposition of 0 and 1. Since no entanglement is involved, that state is almost trivial to create. It's the processing afterwards which is complicated.
What Bell's theorem disproves is local hidden variables. Non-local hidden variables are perfectly possible, as Bohmian mechanics proves.
Even with the best and fastest computer you'll not get weather prediction accurate to the second. That's because weather is a chaotic system, and you'd need an insane amount of measurement data to be that accurate (and probably would have to predict human behaviour as well!)
The set of problems you can in principle solve with a quantum computer is exactly the same as you can solve with classical computers. The best proof of this is that you can simulate a quantum computer with a classical computer (and vice versa). However, as far as we know you cannot simulate a quantum computer on a classical computer in polynomial time.
You cannot get the power of a large quantum computer by repeatedly running a small quantum computer, because you cannot store intermediate quantum results in classical memory. However, real applications will probably always be combinations of classical and quantum computers, because for a lot of problems quantum computers don't have an advantage over classical computers, so it would be wasteful to do those parts a classical computer can do well on a quantum computer instead. As an example, when running Shor's algorithm, you'll use a classical computer to multiply the factor candidates to see if you already got the correct factors; while a quantum computer could do it, it would just be wasteful.
The pages are entangled.
From the article:
"This shared state means that a change applied to one entangled object is instantly reflected by its correlated fellows"
Why, oh why, is this nonsense repeated again and again. If you change one entangled particle, you do not change the other. For example, if you have two spins entangled in a way so that if one is measured "up" the other is measured "down" and vice versa, and you turn the one spin around (without measuring it) then you'll have an entangled state where if you measure the first spin "up" the other one is also measured "up", just as you'd expect. As long as you don't measure, there's no "spooky action at a distance" but only local changes. The "spooky action at a distance" happens at measurement (which BTW destroys the entanglement), and it's all but a given that there's indeed an action at a distance (you only need it if you want a certain type of interpretation, where basically "under the hood" the system behaves completely classical, but we don't see it because there are so-called hidden variables which we cannot determine). The point is that in an entangled state the correlation is all which is defined, and the result of local measurements are completely undefined (OK, strictly speaking this is only true for maximally entangled states, for others there's less correlation and more local information; it's basically a trade-off between the two). Now when you measure the spin of one of the particles, the value of the spin gets a defined (but random) value (up or down, in the direction you measure), and also the value of the spin of the other particle gets a defined value, which is determined by the entangled state and the result you got for the first particle, i.e. if the entangled state was "both particles have opposite, but otherwise undefined spin" then after measurement, the particles will have opposite, well-defined spin. However, since the result is random, if you have the other particle, you cannot see any difference whether the first particle has been measured or not; he will get a random result either way. Only if he gets told the measurement result of the first particle, he can predict (or, if he already measured, compare) his measurement result.
Oh, and yes, I'm working in the field of entanglement, so I know what I'm speaking about.
But I absolutely like the following statement from the article:
"Hang on, what's quantum entanglement when it's at home?
I was afraid you were going to ask."
I hope the above explanation is understandable ...
Too many people have dirty feet anyway. It will only be an advantage if those feet get in contact with water. :-)