Exploring the Mysterious Phenomenon of Quantum Entanglement

[Ubern0va]

My question is in the title please do your best to put this into terms that a novice could understand. I sure am no expert :)

Thanx

 

[misogynisticfeminist]

Hmmm, how about when two particles interact with each other, they now share a common wavefunction. This common wavefunction basically indicates that they now share equal probability of position and momentum. And basically taking a measurement on one particle would collapse the shared wavefunction.

Am i right on this one?

 

[marlon]

This is incorrect in my opinion. Entanglement between two particles means that the wavefunction describing the two particles cannot be separated. I mean, it cannot be factored out into a part for particle one and a part for particle two. basically this means that when some measurement on particle one is performed, the wavefunction will change and this change is directly "noticed" by the other particle. The mean consequence of this is the fact that facts and info are known on particle 2 by performing a measurement on particle 1.

Entanglement can also occur between some apparatus and a particle. For example the entanglement between a 0/1 detector and a particle in the which way experiment. Via the entanglement we know that when the detector (which we measure...by looking at the output) gives a 1 the particle passed along the way which is connected to the detector. When the detector gives a zero, we know that the particle went the other way. if entanglement was not here, the two wavefunctions could be separated yielding the independence between the apparatus and the particle. We would not get any info on which way the particle went.

More exotic applications are QIT, Quantum information Technology or Theory where bits are replaced by qubits. These qubits have three states in their wavefunctions : 1, 0 and 1 and 0 at the same time. What you should never do (although you can) is measure a qubit directly because this superposition will be broken and because of orthogonality we can never get the "1 and 0 at the same time"-state. Via indirect measurements we CAN extract info from qubits. The most famous application is the Deutsch-problem where we want to try to check whether a function is balanced or not by making a single measurement. Classically this is impossible, yet in QIT we can do this since the system will evolve into a wavefunction where the input of the function and their outputs are entangelled. Now, via indirect measurements we can find an answer to the question at hand thanks to this socalled massive quantumparallelism. If you were too measure this state anyway you would get one output for a certain input. Ofcourse this is no different then the classical way. The problem here is that all the other info is lost because the superposition of the wavefunction has been broken by the measurement. This is why we need to find INDIRECT ways to extract info from such a quantum state.

regards
marlon

 

[jvangael]

Deutch problem

Hi Marlon,

I think you are mistaken here. There is no entanglement involved in detuch's algorithm. The start states for the algorithm are unentangled and the end state is:

$((-1)^{f(0)}|0> + (-1)^{f(1)}|1>)(|0>-|1>)$

So there is no entanglement involved here. Grover and Shor's algorithm do use entanglement.

Jurgen

 

[marlon]

Hi, Jurgen,

I agree with your remark. I just wanted to point out some applications of quantum information theory. I never wanted to say that entanglement was used in Deutsch's problem. Thanks for your clarification.

studeert gij aan de unief van Leuven ? ikzelve doe nu burgerlijk ir natuurkunde in Gent. Met wat zijt gij bezig?

marlon

 

[Ubern0va]

I think you guys are getting a little off topic here.

 

[marlon]

How ?
we were just clarifying things,...as a matter of fact you should be happy because this clarification was meant to help YOU out...

:)

regards
marlon

 

[marlon]

http://www.theory.caltech.edu/~preskill/ph219/

here you will find everything on QIT. i studied this subject from Preskill's course and i can highly recommend it to you...

regards
marlon

ps : click on lecture notes...and let the adventure begin...

 

[Ubern0va]

Sorry to have upset you in any way Marlon, its just that it seems to me like you guys were getting more and more into insignificant aspects rather than outlining the theory itself. To be honest, debates amongst yourselves don't help me one bit. Sorry to be so blunt about it but that's the way it is. Thanks for the link however. :-)

Do you have any more on the topic of string theory. I tried www.superstringtheory.com however their basic section is a bit too basic and the advanced section is too advanced. What I'm looking for is a solid explanation with theoretical specifics rather than mathematical. Maybe I'm asking for too much, I really don't know, but no place I've found has been able to deliver this.

Thx in advance for any further assistance.

 

[s3nn0c]

Due to my poor English I can't help you too much, but there is a beautiful explanation of entanglement in noncommutative geometry (NCG). In this theory we have a kind of fibres over the whole spacetime (I hope I use correct words here...). Entangled particles, which are in different places in spacetime, have a direct access to the same fibre. Because information about their states is in this fibre, they can share it no matter how far they are in spacetime.

Please correct me if I'm wrong (or translate this into English ;-) ).

 

[jackle]

This may be horribly over simple, but I always think of entanglement as the situation where measuring one particle has an immediate influence on another.

In my understanding, a particle is also entangled with itself in the sense that if you measure it's momentum you have an effect on it's position.

 

[bruce2g]

This may be horribly over simple, but I always think of entanglement as the situation where measuring one particle has an immediate influence on another.

In my understanding, a particle is also entangled with itself in the sense that if you measure it's momentum you have an effect on it's position.

As I understand it, entanglement means that when you measure a certain property of one object, and also measure that property (or a related property) of the entangled object, they have a well defined statistical relationship which cannot be explained by anything that could have existed before the measurements were taken. That "the relationship cannot be explained by anything that could have existed before the measurements were taken" is the essence of Bell's theorem, and this was demonstrated by Clauser and Aspect.

It has not been shown that measuring one particle has an "immediate" influence on the other. The relationship is manifest when the particles are measured, even if they are measured at different times. So, the effect is not necessarily immediate. This is especially important in the "erasure" experiments, where you manipulate one particle without measuring it: you can mark which slit an entangled photon went through with a quarter wave plate, or you can mark the spin of an entangled electron with a Stern-Gerlach magnet. These manipulations can be erased by recombining the beams before they are measured, so nothing "really counts" until measurement occurs.

So, the real definition of entanglement is this: if you measure both entangled particles, the measures will show a special relationship: this relationship turns out to require some sort of "spooky action at a distance" in order to work. It cannot be a function of the measurements performed on each object separately: the relationship requires the measurement of both objects in order for it to work.

I hope this has not been too obscure.

Bruce

 

[vanesch]

This may be horribly over simple, but I always think of entanglement as the situation where measuring one particle has an immediate influence on another.

As I tried to outline, this view is possible, but not necessary. I think the simplest way of defining entanglement is that you can define two subsystems (for instance, due to a large spatial separation, such as 2 different particles, or due to different properties (such as spin and position) ), and that the state of the system does not factorize into a product of states of the subsystems.

Subsystems have a precise definition in quantum theory: a system S has two subsystems 1 and 2 if the state space of S is the direct product space of H1 and H2, H1 and H2 describing the state space of the individual subsystems.

cheers,
Patrick.

 

[vanesch]

This may be horribly over simple, but I always think of entanglement as the situation where measuring one particle has an immediate influence on another.

As I tried to outline, this view is possible, but not necessary. I think the simplest way of defining entanglement is that you can define two subsystems (for instance, due to a large spatial separation, such as 2 different particles, or due to different properties (such as spin and position) ), and that the state of the system does not factorize into a product of states of the subsystems.

Subsystems have a precise definition in quantum theory: a system S has two subsystems 1 and 2 if the state space of S is the direct product space of H1 and H2, H1 and H2 describing the state space of the individual subsystems.

cheers,
Patrick.

 

[marlon]

Sorry to have upset you in any way Marlon, its just that it seems to me like you guys were getting more and more into insignificant aspects rather than outlining the theory itself. To be honest, debates amongst yourselves don't help me one bit. Sorry to be so blunt about it but that's the way it is. Thanks for the link however. :-)

Do you have any more on the topic of string theory. I tried www.superstringtheory.com however their basic section is a bit too basic and the advanced section is too advanced. What I'm looking for is a solid explanation with theoretical specifics rather than mathematical. Maybe I'm asking for too much, I really don't know, but no place I've found has been able to deliver this.

Thx in advance for any further assistance.

Hi, here are some sites on string theory : i especially recommend the first one.

http://tena4.vub.ac.be/beyondstringtheory/mtheory.html
http://www.sukidog.com/jpierre/strings/why.htm

marlon

 

[jackle]

This may be horribly over simple, but I always think of entanglement as the situation where measuring one particle has an immediate influence on another.

In my understanding, a particle is also entangled with itself in the sense that if you measure it's momentum you have an effect on it's position.

Of course, the phrase 'immediately' means 'simultaneous' and this is relative according to relativity, so I concede that it is a poor word to use.

 

[Mike2]

According to string theory there are extra small dimensions throughout spacetime. This means that distant points in the universe are connected by very small distance through these extra small dimensions. So I wonder if the instant communication seemingly required by entanglement isn't some sort of communication through these extra dimensions.

 

[Ubern0va]

Wow, what progress since I last posted. Thanks so much you guys; For the links and new "lingo" especially (Marlon and s3nn0c)!