Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Geezer on 19/09/2009 04:43:43
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Quantum communication methods are supposed to be "unsnoopable" because, if I understand how it works (which I probably don't), any attempt to copy the information immediately banjaxes the transmission so it becomes obvious that someone is eavesdropping. Essentially, you can't tap into a quantum transmission as if it was a telephone line.
So, what would happen if I cut the "cable" and plugged it into a box that terminates the communication and converts it into a regular electronic communication. Then I make a copy of the transmission by electronic means for future analysis and finally, retransmit a quantum datastream to the destination that is identical to the original I received.
I doubt if the destination would be any the wiser. Whadyathink?
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Quantum communication methods are supposed to be "unsnoopable" because, if I understand how it works (which I probably don't), any attempt to copy the information immediately banjaxes the transmission so it becomes obvious that someone is eavesdropping. Essentially, you can't tap into a quantum transmission as if it was a telephone line.
So, what would happen if I cut the "cable" and plugged it into a box that terminates the communication and converts it into a regular electronic communication. Then I make a copy of the transmission by electronic means for future analysis and finally, retransmit a quantum datastream to the destination that is identical to the original I received.
I doubt if the destination would be any the wiser. Whadyathink?
Well, nowadays we have managed to probe spacetime and their essential ingredients without disturbing the wave function... so we can actually snoop on reality without it acting as though all possibilities have been deflated.
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http://www.physorg.com/news155386974.html
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The problem is that the quantum state has more possibilities in it than the classical signal. The incoming quantum bit might have a 50% chance of being 0 and a 50% chance of being 1. If you measure it classically, it has to either be a 0 or a 1. When you resend it, you have no way of knowing how "mixed" the quantum state should be between 0 and 1, so you can't perfectly reconstruct the quantum bit. This is known more technically as the no-cloning theorem of quantum mechanics, which says that you can't make a perfect copy of a quantum state, since you can't perfectly measure everything about it at once.
Well, nowadays we have managed to probe spacetime and their essential ingredients without disturbing the wave function... so we can actually snoop on reality without it acting as though all possibilities have been deflated.
We have? Do you have a source for that?
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Right above.
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The problem is that the quantum state has more possibilities in it than the classical signal. The incoming quantum bit might have a 50% chance of being 0 and a 50% chance of being 1. If you measure it classically, it has to either be a 0 or a 1. When you resend it, you have no way of knowing how "mixed" the quantum state should be between 0 and 1, so you can't perfectly reconstruct the quantum bit. This is known more technically as the no-cloning theorem of quantum mechanics, which says that you can't make a perfect copy of a quantum state, since you can't perfectly measure everything about it at once.
Well, nowadays we have managed to probe spacetime and their essential ingredients without disturbing the wave function... so we can actually snoop on reality without it acting as though all possibilities have been deflated.
We have? Do you have a source for that?
Ah ha! Thanks. I thought it might be rather too easy!
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It's not that easy, but we can probe reality, as given in the link. The implications are amazing though, because it shows that Bohr and Einstein where partially right, but not wrong either, even though their views seemed to hold different supremacies.
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http://www.physorg.com/news155386974.html
Interesting. This is about quantum weak measurements. As I understand it, instead of taking one big measurement which changes the quantum state a lot, you take a lot of little measurements of similarly produced states, each of which only changes the state a little, and then add up all your little measurements to infer something about the states in general. This probably isn't applicable to snooping on a signal that's using quantum cryptography, since the sender would probably have to send similar states over and over again until the snooper had taken enough weak measurements.
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http://www.physorg.com/news155386974.html
Interesting. This is about quantum weak measurements. As I understand it, instead of taking one big measurement which changes the quantum state a lot, you take a lot of little measurements of similarly produced states, each of which only changes the state a little, and then add up all your little measurements to infer something about the states in general. This probably isn't applicable to snooping on a signal that's using quantum cryptography, since the sender would probably have to send similar states over and over again until the snooper had taken enough weak measurements.
According to definition, ''snooping'' is ''To pry into the private affairs of others, especially by prowling about.''
In a sense, we are prying on reality by prowling, or by analogy looking in without too much disturbance.
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It's not that easy, but we can probe reality, as given in the link. The implications are amazing though, because it shows that Bohr and Einstein where partially right, but not wrong either, even though their views seemed to hold different supremacies.
Just to clarify, I was saying the snooper I originally proposed is rather too "easy", not to mention useless!
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The problem is that the quantum state has more possibilities in it than the classical signal. The incoming quantum bit might have a 50% chance of being 0 and a 50% chance of being 1. If you measure it classically, it has to either be a 0 or a 1. When you resend it, you have no way of knowing how "mixed" the quantum state should be between 0 and 1, so you can't perfectly reconstruct the quantum bit. This is known more technically as the no-cloning theorem of quantum mechanics, which says that you can't make a perfect copy of a quantum state, since you can't perfectly measure everything about it at once.
jp
As usual, I'm confused. I (think I) understand the no-cloning theorem. But I'm struggling to understand how the "transmitter" could know what the transmission actually contained. I don't think the transmitter is allowed to examine the content of its transmission.
If that is true, how does the transmitter really know what it transmitted? If the contents of the transmission are ambiguous to the transmitter there can be no validation of the transmission.
Help! (I am confident I am missing things here.)
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What transmission is the person talking about? Information signalling?
Because if it is it seems faulty, for the information signalling would need to move at superluminal speeds, that is unless some one incorporates a field in which there are signals which are real, but equally nothing physical.
Either way, today we work with non-locality; an attempt in itself to reconcile these extraordinary quantum entangled facts.
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Here's a brief description of how one scheme of quantum encryption actually works. Hopefully that helps.
Alice sends a bunch of quantum bits (qubits) to Bob. These qubits are binary information encoded in one of four ways. Either they're encoded as spin up/down (up being 1 and down being 0) or they're encoded in left/right (left being 1 and right being 0). (The choice of 1 and 0 is arbitrary once you've chosen either up/down or left/right.) Alice flips a coin each time she sends a qubit of data to determine if she sends up/down or left/right.
Now here's the tricky part with these up/down left/right states. Bob has to choose whether to align his measurements with up/down or left/right. If he chooses the right alignment, he can tell exactly what Alice sent, i.e. measuring an up with up/down always gives up. If Bob chooses the wrong alignment, however, he will measure incorrectly, getting each incorrect state 50% of the time, i.e. if Bob measures an up state with left/right, he'll get left 50% of the time and right 50% of the time. So what Bob actually does is randomly align his detector.
After Bob is done measuring, he calls Alice up on the phone (this, by the way, is why "faster-than-light" communication fails here), and Alice tells Bob which states were up/down and which were left/right. This doesn't actually give an eavesdropper any useful information, since the states have already been measured and thrown out. Bob then knows the 50% of cases where he improperly aligned his detector are garbage and discards them. The remaining 50% of measurements are proper results.
Now here's the trick to making it eavesdropper proof. Let's say Eve the eavesdropper is catching qubits along the way. She has no way of knowing if her measurement is properly aligned or not, so if she sees an up, she doesn't know if it's an actually up, or a left or a right. Since measuring an up forces it to become an up (one of the rules of quantum mechanics), she has a choice of either sending an up along to Bob, or creating and sending a left or right. If Eve guesses right, she won't be caught, but what if she guesses wrong?
Let's say she sends a left when it was actually an up. If that qubit is one of the 50% that Bob didn't discard when talking to Alice, Bob knows that his measurement of it should be 100% accurate (because he and Alice agreed that they sent and measured with up/down alignment). But since Bob is actually measuring a left from Eve, he has a 50% chance of measuring up and 50% of measuring down. So all Alice has to do is encode a bunch of extra qubits in her data that don't contain the encrypted information. Bob has discarded 50% of them, but she finds those he didn't discard and tells him (over the phone), "By the way, bits x,y,z,... are extra data and should have values of A,B,C,..." Bob then checks his measured values for those qubits. If he finds errors, then he knows someone has tampered with the qubits along the way. If not, he trusts that the remaining qubits are safe.
You've probably noticed that all of this has to do with probabilities. So if Eve gets really lucky and happens to send out exact copies of the original states, she won't be detected. The chance of this happening can be made arbitrarily small by sending more of those extra qubits.
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jp,
Thanks very much for taking time to explain. The mist is clearing a bit now! I'll go over your explanation a few more times I'm sure.
Geez
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Here's a brief description of how one scheme of quantum encryption actually works. Hopefully that helps.
Alice sends a bunch of quantum bits (qubits) to Bob. These qubits are binary information encoded in one of four ways. Either they're encoded as spin up/down (up being 1 and down being 0) or they're encoded in left/right (left being 1 and right being 0). (The choice of 1 and 0 is arbitrary once you've chosen either up/down or left/right.) Alice flips a coin each time she sends a qubit of data to determine if she sends up/down or left/right.
Now here's the tricky part with these up/down left/right states. Bob has to choose whether to align his measurements with up/down or left/right. If he chooses the right alignment, he can tell exactly what Alice sent, i.e. measuring an up with up/down always gives up. If Bob chooses the wrong alignment, however, he will measure incorrectly, getting each incorrect state 50% of the time, i.e. if Bob measures an up state with left/right, he'll get left 50% of the time and right 50% of the time. So what Bob actually does is randomly align his detector.
After Bob is done measuring, he calls Alice up on the phone (this, by the way, is why "faster-than-light" communication fails here), and Alice tells Bob which states were up/down and which were left/right. This doesn't actually give an eavesdropper any useful information, since the states have already been measured and thrown out. Bob then knows the 50% of cases where he improperly aligned his detector are garbage and discards them. The remaining 50% of measurements are proper results.
Now here's the trick to making it eavesdropper proof. Let's say Eve the eavesdropper is catching qubits along the way. She has no way of knowing if her measurement is properly aligned or not, so if she sees an up, she doesn't know if it's an actually up, or a left or a right. Since measuring an up forces it to become an up (one of the rules of quantum mechanics), she has a choice of either sending an up along to Bob, or creating and sending a left or right. If Eve guesses right, she won't be caught, but what if she guesses wrong?
Let's say she sends a left when it was actually an up. If that qubit is one of the 50% that Bob didn't discard when talking to Alice, Bob knows that his measurement of it should be 100% accurate (because he and Alice agreed that they sent and measured with up/down alignment). But since Bob is actually measuring a left from Eve, he has a 50% chance of measuring up and 50% of measuring down. So all Alice has to do is encode a bunch of extra qubits in her data that don't contain the encrypted information. Bob has discarded 50% of them, but she finds those he didn't discard and tells him (over the phone), "By the way, bits x,y,z,... are extra data and should have values of A,B,C,..." Bob then checks his measured values for those qubits. If he finds errors, then he knows someone has tampered with the qubits along the way. If not, he trusts that the remaining qubits are safe.
You've probably noticed that all of this has to do with probabilities. So if Eve gets really lucky and happens to send out exact copies of the original states, she won't be detected. The chance of this happening can be made arbitrarily small by sending more of those extra qubits.
I had to do some reading into this, and it seems to rely on the wave function.
And entangled particles, so i understand what relation they have now.