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Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently of the others, even when the particles are separated by a large distance—instead, a quantum state must be described for the system as a whole.

To me, the important part of this extract from Quantum Entanglement: Wikipedia is the phrase pairs or groups.

I might well be getting bogged down in circular reasoning, or plain old semantics, but my question is:

Is quantum entanglement, based on this definition above, or a better one if you know it, a property inherent to a particle, (that is not revealed until it decays and needs to comply with various quantum numbers) or, because entanglement only occurs after the decay, can it be considered a process?

My point here is analogous to the change in energy level of a electron when it absorbs a quantum of radiation, it produces an unstoppable, indivisible event. My source for this assertion is Bohm's 60 year old basic primer, (Quantum Mechanics, so I could be basing my question on out of date information).

To me, this chain of events is not an inherent property of an electron, (it is not, directly at least, listed in the Standard Model). It is a process of emitting radiation.

If I am confused by my ignorance, or indulging in hair splitting, then my apologies. If the answer is, how do we categorize an as yet not understood phenomenon, then that's something I will obviously just have to accept.

This related question Entanglement, a subjective or objective property, says it is an objective property, but I am not asking precisely the same question,at least, I don't believe I am.

There are plenty more related questions on this topic, and I will delete this post if it is not asked properly, not thought through sufficiently or already answered.

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    $\begingroup$ Entanglement is a property of a quantum state, in the same sense that being even is a property of an integer. More precisely, given a vector space $H$ and a decomposition of that vector space as a tensor product, any given vector in $H$ either is or is not entangled. $\endgroup$
    – WillO
    Aug 2, 2017 at 19:59
  • $\begingroup$ I've made it an answer. Thanks for letting me know this helped. $\endgroup$
    – WillO
    Aug 2, 2017 at 22:41

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Entanglement is a property of a quantum state, in the same sense that being even is a property of an integer. More precisely, given a vector space $H$ and a decomposition of that vector space as a tensor product, any given vector in $H$ either is or is not entangled.

In particular: If $H$ is given in the form $H=H_1\otimes H_2$, then a vector in $H$ is unentangled (by definition) if and only if it is of the form $h_1\otimes h_2$, and entangled if and only if it is not unentangled

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  • $\begingroup$ I think you are right but it could be more complete. What makes those two disjoint cases entangled or not? Clearly you u dears tand what does from your comments, is there a simple (or not so simple but accurate) way to state it? In know it has to do with the probability distributions or states descriptions, it'd be nice to see it. $\endgroup$
    – Bob Bee
    Aug 3, 2017 at 5:02
  • $\begingroup$ @BobBee: If $H$ is given in the form $H=H_1\otimes H_2$, then a vector in $H$ is unentangled (by definition) if and only if it is of the form $h_1\otimes h_2$, and entangled if and only if it is not unentangled. $\endgroup$
    – WillO
    Aug 3, 2017 at 5:04
  • $\begingroup$ yes, thanks. Maybe include it in the answer, it makes it explicit. $\endgroup$
    – Bob Bee
    Aug 3, 2017 at 5:06
  • $\begingroup$ @BobBee: Okay, doing so. $\endgroup$
    – WillO
    Aug 3, 2017 at 5:32
  • $\begingroup$ Apologies for the delay in accepting, my L. Sussskind's book on the topic temporarily lost. $\endgroup$
    – user163104
    Aug 6, 2017 at 17:04
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Entanglement is in my opinion an attempt to describe in words quantum mechanical solutions for a system.

Take the calculation of the trajectory of a rocket in Newtonian gravitation. The rocket and the earth are "entangled" in this trajectory. Suppose a second rocket intercepts the first. Then three objects are "entangled" in the solution.

Take an electron and a proton in the quantum mechanical potential problem. The solution is a wavefunction which "entangles" the electron with the proton. One electron and a proton neutron are "entangled" in deuterium. At every time t, the probability of finding one of them at (r,theta,phi) is tied up with the probabilities of the other two.

The word "entanglement" acquired importance when studying information transfer. Simple quantum numbers which constrain wave functions , like spin, are carried by the particles participating.

Take the Higgs to gamma gamma. One can measure one gamma and if its spin projection is +1, immediately the spin of the other one is constrained , in this measurement, to be -1 , because the Higgs has spin 0. It is the present mathematics model of the quantum mechanical underlying state of nature.

To answer the title , it is a model of the quantum mechanical behavior of particles, and in this sense a process.

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  • $\begingroup$ "At every time t, the probability of finding one of them at (r,theta,phi) is tied up with the probabilities of the other two." But this is not what entanglement means. The probability that it will be sunny at 2PM on June 30, 2099 is "tied up" with the probability that it will be sunny at 3PM on that same day---that is, the two events are not independent. They do, however, still have a joint probability distribution, whereas entanglement generally refers to situations where (for at least some combinations of events) no joint probability distribution exists. $\endgroup$
    – WillO
    Aug 3, 2017 at 3:47
  • $\begingroup$ If there is no joint probability distribution, they have decohered and are no longer entangled, by cons truction. To decohere they have to interact with an outside particle, which means the spin detected in the Higgs example, may have changed from the original entangled one. $\endgroup$
    – anna v
    Aug 3, 2017 at 3:53
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    $\begingroup$ "If there is no joint probability distribution, they have decohered and are no longer entangled". This is the exact opposite of the truth. Consider the four events "Particle 1 has spin up in direction 0", "Particle 1 has spin up in direction $\pi/6$", "Particle 2 has spin up in direction 0" and "Particle 2 ha s spin up in direction $\pi/6$". Assume the particles are in an (entangled) Bell state and try writing down a joint probability distribution for those four events. The whole point of Bell's theorem is that you can't. But they certainly haven't decohered. $\endgroup$
    – WillO
    Aug 3, 2017 at 4:30
  • $\begingroup$ (If the particles decohere into a completely unentangled state, THEN those four events will have a joint probability distribution.) $\endgroup$
    – WillO
    Aug 3, 2017 at 4:33
  • $\begingroup$ @WillO experimentally the only way one can impose solutions in quantum mechanical systems is through boundary condition on wavefunctions, i.e. ultimately probability distributions. Your example has no meaning without the explicit boundary conditions. One has to solve quantum mechanical differential equations to get the probabilities for the states, one cannot set up the states and handwave probabilities $\endgroup$
    – anna v
    Aug 3, 2017 at 5:14

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