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TheDonk
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How do particles become entangled? I've heard that it's when two particles bump into each other. How is this "bump" defined? What does it mean for 2 particles to bump? Is it based on distance apart, or something else?
So when Bob performs a measurement Alice does not gain any information on her state nor can she tell whether Bob made his measurement. TBut, Bob can conclude in which state Alice's qubit will be in when she measures.
masudr said:Two particles must have interacted. If they have, then two measurements represented by operators A and B must behave like [A, B] = ih and then we have entanglement.
First of all let's explain the idea of quantum "entanglement".TheDonk said:How do particles become entangled?
It sounds like the type of interaction you have in mind is that of a "collision-like" scenario. So, let's use the example of an "elastic collision". Then, with regards to the "bump" itself, there is nothing really special about it. What is special here is that we are dealing with quantum states.I've heard that it's when two particles bump into each other. How is this "bump" defined? What does it mean for 2 particles to bump? Is it based on distance apart, or something else?
alexepascual said:I suspect though, that a collision of two particles may not be the simplest example to study how two particles can become entangled. Wouldn't spin entanglement be easier to understand?
Once they are entangled, can you force the spin of one electron to be up so that the distant electron's spin must be down? That would create instant communication, right?alexepascual said:If you bring both atoms together, they'll form a molecule. But for those alternatives in which both spins are up or both spins are down, it will be impossible to form a molecule because of Pauli's exclusion principle. So, I guess if you were shooting these atoms towards each other, some would "stick" and some would bounce . About the ones that bounce you can say that their spin is mostly pointing in the same direction while you can be sure that those that stuck to form a molecule have their spins pointing in opposite directions. This relationship between the spins is what entanglement is. Now, you can pull the atoms apart and that relationship (if one is up the other is down) will persist, even if the atoms are taken appart a long distance. When I say "one is up, the other one is down" don't take me wrong. Actually they are both in a superposition of "up" and "down". It is just that when you measure spin on one, at that point you collapse the wave function and one of the two states "up" or "down" becomes reality. If you find one atom to be "up" the other one will be down.
This is definitely an oversimplification. In particular, from this simplification, it may appear that the resulting quantum state is merely given by a quantum superposition of the possible classical trajectories. But this is surely not the case! [... However, it is worth noting that for an inverse-square law of force between the two particles, the differential scattering cross section, dσ/dΩ, calculated classically happens to coincide precisely with the quantum-mechanical one (e.g. Rutherford scattering).]... after the particles have gone "bump" and have flown well apart, the wavefunction of the joint system will involve a superposition of the various angles of deflection resulting from each of the possible distances between the two lines of flight consistent with the spread of each particle's initial wavefunction in the xy-plane.
These statements are made only with respect to the phenomenon of "entanglement". On the other hand (as indicated above), the interaction itself is, of course, quantum mechanical – and in that respect, there is certainly something 'special' about the "bump".... with regards to the "bump" itself, there is nothing really special about it.
... there is nothing really 'special' about the "bump" itself.
Are you saying that forcing the spin into a particular state is the same as measuring that state? Or is there just a greater probability of being in a state with an applied force as opposed to knowing for certain after measuring the spin?alexepascual said:Mike:
The spins are entangled as far as what you are going to find if you measure them on both ends. Once you force one spin into another direction, you lost your correlations. As far as I know, no communication is possible using entanglement.
Yes, all honest conversation helps.alexepascual said:As far as I know, measurement is supposed to tell you something about the state of the particle before you influence it by applying any force which might change the state. If you change the state, then you don't know what it was before. If you are going to measure spin, you make the particle go through a Stern-Gerlach apparatus. The Stern-Gerlach apparatus does apply a force to the particle but this force does not change the spin. It is just that those particles with spin "up" go thorugh one channel and those with spin "down" go thorugh the other channel. Typically, you know that the particle went through a certain channel by having it strike some kind of detector. When the particle hits the detector, the state is destroyed. But at least you know what it was just before detection,(or during detection?) which is what you where looking for.
The electromagnetic force is governed by interaction with the photon. For a weak enough magnetic field, some electrons will interact with the photons of the magnetic field, and some will not. And for a series of entangles pairs, we would never know on our end which electron spins were effected by the magnetic field photons and which were not. We would only know that on the average more of them are affected with a stronger magnetic field than with a weaker magnetic field. However, if the pairs remain dependent on the electron spins on our side because they are entangle, then a measurement on their side would reveal and average affected by the magnetic field on our side, right?selfAdjoint said:I don't know what a force strong enough to affect the probability of a spin but too weak to change the spin would be in QM. Spin (around a given axis) only comes in a discrete set of states, so you either leave it in the state it is, that is, you don't interact with it, or less you influence it and then you are operating on the spin state with some operator and the state goes into some set of discrete eigenvalues. It looks to me to be all or nothing.
And therefore yes, if you truly interact with either entangled particle, you collapse the entangled state. Anything that finds out what the spin state of one particle is, disentangles the other particle, if it is still entangled. What you don't know is whether your measured spin of this particle was determined by a prior measurement of the other or not.
I don't know if the spin perspective makes it any easier to understand "how" the particles become entangled; but the spin perspective certainly presents some conceptual advantages. It was Bohm, in 1951, who recast the EPR scenario in just such terms. Then, in 1964, with the Bohmian version in mind, Bell discovered his famous inequality.alexepascual said:I suspect though, that a collision of two particles may not be the simplest example to study how two particles can become entangled. Wouldn't spin entanglement be easier to understand?
Note that in a spin measurement of the above kind, what we have in mind is a Stern-Gerlach device (or the equivalent). For such a physical arrangement, there is no "forcing" of spin to be in any particular direction. However, there is "forcing" of the particle to move either "up" or "down" spatially in relation to the axis n in a manner which correlates with spin. Thus, by detecting the presence of the particle – say particle 1 – in either of these "up" or "down" tracks, a measurement corresponding to the projector P1n,+ or P1n,- (respectively) has been performed.Mike2 said:Once they are entangled, can you force the spin of one electron to be up so that the distant electron's spin must be down? That would create instant communication, right?
By "forcing", it appears to me that you mean some kind of apparatus which will, for example, leave the |+> as it is, but cause the |-> to become a |+>. Can we do this? Sure! ... why not?Once they are entangled, can you force the spin of one electron to be up so that the distant electron's spin must be down?
Indeed, if the "entanglement" phenomenon were such that a direct 'manipulation' of some property particle 1 would induce an (immediate) corresponding change in some property of particle 2, then yes that would be a means for superluminal communication. However, in the above example, we saw that the change "forced" upon particle 1 had no effect upon particle 2.That would create instant communication, right?
Yes, certain properties (and in general, any dynamical properties) of two particles can become entangled. In a complete description of the entanglement, we must not only specify which properties have become entangled, but also in what manner. If we can write down the quantum state for the joint system, then the description is complete (... least from the quantum-mechanical perspective).TheDonk said:Eye_in_the_Sky, your explanation helped, tho I'm still confused.
So certain properties of two particles become entangled? To properly explain 2 entangled particles, it isn't enough to just say they are entangled but you would need to say which properties are entangled. Is this right? What are all the properties that can be entangled? Is there anything else needed to explain how to particles are entangled?
Wouldn't instantaneous communication prove that one object isn't causing the other to change at all? Wouldn't it mean that they ARE the same object? It would be like looking at two sides of the same coin. One object (or what we thought was it's own object) is in a different location than the other, but we would now have shown that location has nothing to do with identity.alexepascual said:...I think a causality argument could also be used against the possibility of "instantaneous communication"
The said process, as seen from within the Hilbert space of that particle, is clearly non-unitary. Nevertheless, there must be some physical arrangement which can bring it about ... but I am not precisely sure what it is, nor how to represent it mathematically.By "forcing", it appears to me that you mean some kind of apparatus which will, for example, leave the |+> as it is, but cause the |-> to become a |+>. Can we do this? Sure! ... why not?
... is definitely wrong! (... because the final state shows a preferred direction which can be identified on the "particle-2 end".)(1/√2)(|+>|-> – |->|+>) → (1/√2)|+>(|-> – |+>)
... is also wrong! (... because such a Hamiltonian implies that the said process, as seen from within the Hilbert space of particle 1, is unitary.)Htotal = (H1 + Hmod) x H2 ,
where Hk is the 'free' Hamiltonian for particle k, and Hmod is the Hamiltonian for the interaction which modifies the status of particle 1.
alexepascual said:About changing the state on one side: let me give you a simple classical example: If we have a set of two cards, one has a 1 written on it and the other one has a 0, and we give them to two different peaple that go to different cities (without knowing what their cards are). We know that when they look at their cards, if the first one has a 0 on it, the other one will have a 1 for sure. That is if nobody changed them. If you have someone changing the zero into a one, then the original correlations don't hold, and, what is more important, the other card didn't magically change to keep the correlation. I know this example is not totally appropriate because is classical (superposition is missing) but except for that, I still think it illustrates this issue very well and the argument can still be used for a quantum system.
I agree that this reasoning would point towards the entangled objects not being the same object but who's to say that the properties are not objects of some type? I think it could still work either way... maybe not tho, because of the next thing you said:alexepascual said:If we were only talking about two entangled particles of the same type, then your idea might make some sense and it would deserve being explored further. On the other hand, remember that what is entangled is not the particles themselves but properties of the particles. Also consider the things that have entangled properties do not have to be of the same type. How would you apply your reasoning in that case?
Let's say we "connect" two objects for instantaneous communication. Then one person flies really fast away towards another star. Unless the people come back to the same frame of reference, there is no agreement on who is older than who. I may be wrong but each person would be able to say they are older than the other person. So if one person starts communicating when will the other person get the info? I don't think they could decide on what instantaneous is, could they? I think we need someone who knows special relativity well to answer this. But if I'm right, this will only enforce the point I quoted you on above.alexepascual said:Think of this: You invent this cute machine that allows you to send instantaneous messages. You send your partner experimentalist to a star a good distance from earth. Then you send a message, which in your frame of reference is received "instantaneously". I another person's frame of reference (someone on a spaceship moving at a great speed in a certain direction) the reception of the message happens before it was sent.
Does this violate causality? Well, thinking again about it maybe not, because if the events are "space related" none of them can be considered to be a cause of the other.
Particles become entangled when they interact with each other and share a quantum state. This can happen through various processes such as collision, interaction with a third particle, or through the influence of a common environment. Once entangled, the particles' states become correlated, meaning that any changes in one particle will affect the other particle, regardless of the distance between them.
Any type of particle that exhibits quantum behavior, such as electrons, photons, atoms, or molecules, can become entangled. The key factor is that they must interact in some way to share a quantum state.
Yes, particles can become entangled without direct interaction. This is known as remote entanglement and can occur when particles are influenced by a common environment or when they are created in a shared quantum state. This type of entanglement has been observed in experiments with photons and ions that are separated by large distances.
Entanglement is a crucial resource in quantum computing. It allows for the creation of qubits, which are the basic units of information in a quantum computer. By manipulating the entangled states of qubits, quantum computers can perform calculations and solve problems much faster than classical computers.
Yes, entanglement can be used for secure communication through a process called quantum key distribution (QKD). In QKD, two parties share entangled particles and use them to generate a secret key that can be used to encrypt and decrypt messages. This method is secure because any attempt to intercept the key will result in a change in the entangled state, alerting the parties of potential eavesdropping.