Can a particle entangle with itself?

[San K]

1. can a single particle entangle with itself?

2. In a single particle, double slit experiment, is there any evidence of the wave-functions entangling with each other?

3. what is the relationship between coherence and entanglement? in case of a single particle

 

[Jazzdude]

1. can a single particle entangle with itself?

2. In a single particle, double slit experiment, is there any evidence of the wave-functions entangling with each other?

3. what is the relationship between coherence and entanglement? in case of a single particle

1. Yes, you can entangle spin and position for example

2. Not entirely sure what you mean, but the particles in flight are not self-entangled.

3. Coherence in a tensor factor space (here: spin, position) depends on the degree of entanglement. Tracing over the other factor space gives you a density matrix that describes the state in the remaining factor space. For a completely entangled system the result is an incoherent, non-pure state.

 

[haael]

From macroscopic view, entanglement is a statistic correlation between different particles. For a single particle, its state is always correlated with itself with probability 100%. From quantum mechanics view, entanglement is synchronization of wavefunction phase. For a single particle, its phase is always synchronized with itself and the phase shift equals zero.

 

[Jazzdude]

From macroscopic view, entanglement is a statistic correlation between different particles.

That's a consequence of entanglement, not a definition. There is classical correlation too which has nothing to do with entanglement.

For a single particle, its state is always correlated with itself with probability 100%.

This statement is wrong in several ways. First, the correlations you refer to above are related to quantum measurements, not to the state vector. And again, you're mistaking correlation for the definition of entanglement.

From quantum mechanics view, entanglement is synchronization of wavefunction phase. For a single particle, its phase is always synchronized with itself and the phase shift equals zero.

Phase has quite little to do with entanglement really, and it's not suitable for defining entanglement either. Entanglement is defined as the inability to factorize a state on tensor factor spaces of the state space. The phase between the single terms is just as well defined whether they're separable or not.

 

[DrChinese]

Not trying to take a side here, though I would point out: A particle detected here cannot be there as well. So in that sense, you can have entanglement from a single particle a two different points in spacetime. It is possible to arrange it so you have a certainty of detecting a particle here or there, with the outcome itself not predetermined*. That is a true superposition, and will act accordingly. You might not be able to do any amazing tricks that way**, but it is nonetheless a form of entanglement if you are sufficiently liberal on the use of the term.

* A beam splitter comes to mind.
** On the other hand, maybe you can.

 

[cryptist]

1. Yes, you can entangle spin and position for example

How this could be? How can one particle's spin be entangled with same particle's poisiton? Can you explain in detail?

 

[vanhees71]

The usual Stern-Gerlach experiment, often used as a very nice example to introduce the basic concepts of quantum theory, provides a state, where spin and position of a single particle are entangled.

The trick is to direct a beam of particles, described by a Schrödinger-wave packet, towards an inhomogeneous magnetic field. The force affecting the particle's trajectory is proportional to the spin component in direction of the magnetic field and thus you can well separate particles in space with different spin components in this direction. In other words, the incoming beam splits into well separated partial beams depending on its spin component. In this way you are (nearly) 100% sure that a particle in one of the partial beams has a certain value of this spin component. That means, the particle's position is entangled with the spin component.

 

[cryptist]

The usual Stern-Gerlach experiment, often used as a very nice example to introduce the basic concepts of quantum theory, provides a state, where spin and position of a single particle are entangled.

The trick is to direct a beam of particles, described by a Schrödinger-wave packet, towards an inhomogeneous magnetic field. The force affecting the particle's trajectory is proportional to the spin component in direction of the magnetic field and thus you can well separate particles in space with different spin components in this direction. In other words, the incoming beam splits into well separated partial beams depending on its spin component. In this way you are (nearly) 100% sure that a particle in one of the partial beams has a certain value of this spin component. That means, the particle's position is entangled with the spin component.

Then doesn't it resolves the measurement problem in double-slit experiment?
Let's say we identify the slit that particle is passed, by measuring electron's spin, (or by measuring the polarization of light) then, spin is entangled with position, when we put the measuring device in front of the slits. Consequently, when we know the spin, we know the position, and it destroys the wave-like uncertainty in position (destroys interference pattern) same as we destroy the information when measuring entangled particles.

I had heard that in double-slit exp., measurement device becomes entangled with particle. Then, that is not true. What's happening is, measurement device creates entanglement between spin and position of the particle. (like BBO crystal creates entangled particles) Right?

 

[San K]

The force affecting the particle's trajectory is proportional to the spin component in direction of the magnetic field and thus you can well separate particles in space with different spin components in this direction. In other words, the incoming beam splits into well separated partial beams depending on its spin component. In this way you are (nearly) 100% sure that a particle in one of the partial beams has a certain value of this spin component. That means, the particle's position is entangled with the spin component.

If it has a certain value, is it not determinate?