Surprisingly, the answer is apparently yes, at least according to this paper:

http://www.researchgate.net/publication/225519229_Entanglement_Between_Degrees_of_Freedom_in_a_Single-Particle_System_Revealed_in_Neutron_Interferometry

EDIT: However, there appears to be a terminology problem: some authors define entanglement as an inherently multiparticle phenomenon, see e.g. http://en.wikipedia.org/wiki/Quantum_entanglement

Article Entanglement Between Degrees of Freedom in a Single-Particle...

In general, interference is the manifestation of entanglement. The state is the superposition of two states corresponding to the two paths, and it is an entangled state since detecting the particle at one path instantaneoulsy makes it undetectable at the other path. The interference pattern pictures the correlation. Actually, every mysterious quantum behavior is some form of entanglement.

@Charles Francis, this is not about the describing the terminology but the effect of entanglement on the degree of freedom of same particle.

Dear Rahul,

It seems very much possible as pointed out by Artur. In fact, the multi-partiteness in the entangled systems is only in the nature of our talking about the parts of the single system, which has for some reason become apparently separated in to those parts. It should be treated as the same old system as a whole whose parts have now separated out. Then the answer to your question should be yes.

The parts are said to be entangled if measurement of an observable for one leads to the determination of the value for the other due to their previously having been united in one single system with some definite known value of the observable.

A simple classical physics example of such an interpretational extension of the idea of entanglement could be the interplay between KE and PE of an oscillator given that the total energy is constant. You measure one of them and the other is automatically determined from the known value of the constant total energy.

Regards

Rajat

I don't think we can make that distinction anyway, since the wave function isn't defined in the ordinary space, but in the configuration space, in which may also be included spin and other degrees of freedom. In the traditional setup, there is not two photons, but a single electromagnetic field that is conventionally decomposed into two quanta, such that they are in causally separated regions, which is more interesting with respect to the interpretation, but has nothing more fundamental. This decomposition is quite arbitrary, as shows intensity interferometry. In standard interference experiments, the paths are causally separated too, and exactly the same conceptual difficulties arise.

Whenever there is a tensor product structure, one can meaningfully define notions of entanglement. Usually, this tensor product structure refers to degrees of freedom associated with spatially separate locations, but it does not have to.

Dear Jens,

Separations are not absolute and we can always transform to other frames where the separation will come within the ambit of definition of a single system.

Secondly, as per the current notions of entanglement, the ionised or highly excited H-atom is bi-partite while the bound H-atom is a single system.

What determines singleness and partiteness in case of entanglement ? Is it distance of separation alone (overlapping wave functions, in some sense)? Are there not other entanglement measures?

Is it necessary that the separation must be space-like between the two parts in order for entanglement to be there.

I think Rahul's question can be answered in the affirmative. You have just fallen short of that.

Regards,

Rajat

There are types of entanglement. Single particle state can be entangled and it is called "mode entanglement". Mode entanglement happens in the second quantization picture.

The more commonly used definition of entanglement characterises via the inseparability of the system density operator, hence in the first quantization picture and it is called "particle entanglement". You need more than one particle in this picture.

Depending on your system, you can define "entanglement". After this definition, you should wisely choose your measure. For example, widely used measure of concurrence is a pairwise-correlation measure and hence it measures particle-type entanglement.

EPR type entanglement happens to be in the second quantization, and there measures for this type of entanglement defined through the correlation functions of the field annihilation operators.

If you need references, you can contact me. Most educative paper on single-particle (mode entanglement) for me is:

S. Van Enk, Physical Review A 72, 64306 (2005).

regards,

ümit.

Consider a neutron with spin 1/2 incident on a region of magnetic field, where spin up passes and spin down reflects. Is there entanglement between spin and path?

I would say that anytime you have a Hilbert space that is decomposable as a tensor product then you can introduce a notion of "entanglement". The fact that traditionally entanglement had to deal with multiparticle systems was because in Q.M. multiparticle systems are naturally described by a tensor product. However this is not the only case when this is so, think about the spin and position of a particle, to describe it you use a Hilbert space that is a tensor product of $L^2(C)\otimes C^2$.

So to be more rigours, entanglement is in a sense a measure of correlation between two quantum systems represented by a Hilbert space (and I wouldn't say that they have to be different PHYSICAL systems).