Physics of Quantum Entanglement

[UltrafastPED]

I learned the principles of quantum physics and the basic mathematical techniques quite some time ago. The only discussion of quantum entanglement concerned the EPR paper. There have been many advances in the field since that time, including the somewhat mysterious phenomenon of quantum teleportation.

My background is primarily optics, ultrafast laser applications, ultrahigh vacuum systems, photo-electron beams, electron microscopy, some materials science, grown carbon nanotubes ... designing and building systems, plus a lot of industrial applications.

I understand the process for generating entangled photons by means of down conversion, though it is a very inefficient process. In this case the initial photon is replaced by a pair while conserving total energy and momentum. The entanglement process occurs when the two photons are "created".

My current understanding of the physics of quantum entanglement is that the entangled quantum particles must share a superposition of states.

Question #0: Is it true that every set of quantum entangled particles must be in a superposition of states?

Question #1: is the act of particle creation the only way to create entangled pairs?
Question #1.a: what other ways have been demonstrated?
Question #1.b: what limits the efficiency of the entanglement "process"?

Question #2: Is it possible to entangle dissimilar particles - e.g., a neutron and a photon?

In the EPR paper only conserved properties were entangled. But there are many quantum observables; each observable corresponds to a definite quantum state - many are discrete, but others are continuous. Some represent conserved quantities, others may not.

Question #3: Is every quantum property capable of being entangled?

It may be convenient to lock this thread, and then I will ask the individual questions one at a time, referring back to this as a common starting point for my continuing education.

 

[atyy]

Question #0: Is it true that every set of quantum entangled particles must be in a superposition of states?

An old definition of an entangled state is that it cannot be written as a product state in any basis. By this definition, it must be a superposition of product states in every basis. A basis-independent measure of this type of entanglement is the entanglement entropy, which is the von Neumann entropy of the reduced density matrix of one of the subsystems.
http://en.wikipedia.org/wiki/Entropy_of_entanglement

However, there are other questions like do we really need two particles to have entanglement? And it seems from those ideas that one can define entanglement in a basis dependent way.
http://arxiv.org/abs/quant-ph/0507189
http://arxiv.org/abs/1302.3509

Question #1: is the act of particle creation the only way to create entangled pairs?
Question #1.a: what other ways have been demonstrated?
Question #1.b: what limits the efficiency of the entanglement "process"

One can entangle two particles by having them interact. For example, the ground state of many condensed matter systems are entangled.
http://arxiv.org/abs/cond-mat/0701055
http://arxiv.org/abs/0808.3773

There are some limitations on entanglement, for example, entangelement must be "monogamous". http://www.quantiki.org/wiki/Monogamy_of_entanglement

There are also some bounds on entangling rates depending on the interaction.
http://arxiv.org/abs/0704.0964
http://arxiv.org/abs/1304.5931

Question #2: Is it possible to entangle dissimilar particles - e.g., a neutron and a photon?

In principle, yes, if you can get them to interact in the right way.

 

[Nugatory]

Question #0: Is it true that every set of quantum entangled particles must be in a superposition of states?

Yes, but that's not saying much when you consider that any pure state is a superposition in some basis. For example, "spin up" is not a superposition in the up/down basis, but it is a superposition in the left/right basis - it's the same state either way.

Question #1: is the act of particle creation the only way to create entangled pairs?
Question #1.a: what other ways have been demonstrated?
Question #1.b: what limits the efficiency of the entanglement "process"?

1) No. For example, if I collide two particles in a way that could change the angular momentum of either individual particle, conservation of angular momentum requires that they they be entangled until I measure the angular momentum of one of them. Similar considerations will apply in any other interaction that produces two related measurable quantities.

Question #2: Is it possible to entangle dissimilar particles - e.g., a neutron and a photon?

Yes, in principle. In practice, I'm not sure what interaction could produce such a state.

Question #3: Is every quantum property capable of being entangled?

Yes. A quantum system, even one that contains multiple particles (the easy entanglement examples all use two particles) is always represented by a single wave function. Entanglement is what happens when we choose to think of that one wave function as describing multiple independent particles.

Consider, for example, an ordinary six-sided die like craps players throw... It is clear that the die is a single (classical) object, but if I choose to consider the values on the various sides as independent measurable quantities, I will find that these values are entangled - if I observe the value on one face to be N I know that the value on the other face will be 7-N. This would be very weird if I insist in thinking of each face of the die as an independent object, but makes sense if I think in terms of a single six-sided object instead of six independent objects.