On Quantum Entanglement
This blog post is intended to provide on overview of a fundamental concept which laid the foundation of quantum computing. With the 2022 Nobel Prize being awarded to the pioneers who proved Quantum Entanglement, understanding it becomes essential for anyone seriously interested in the field. Some familiarity with Quantum Mechanics and the Copenhagen Interpretation would help the reader appreciate the post a lot more. If not, or looking to brush up your knowledge, check out the blogs by Quantum Untangled!
Quantum computing is a paradigm which utilises quantum objects and their properties to carry out computational tasks which may be very time consuming or even impractical for classical computers. Quantum superposition, interference and entanglement are the 3 major properties which are used to achieve the same. Here, in this blog, we talk about quantum entanglement in more detail.
Quantum Entanglement
I’m sure a lot of you reading this blog post have a broad idea about quantum entanglement, which goes something like the following —
Any two quantum objects may become entangled and any change in the state of one particle instantaneously changes the state of its entangled counterpart.
Let us dissect it and understand what does this really mean?
In simplest of forms, entanglement means some kind of correlation.
For a simple example, consider any pair of particles, say A and B. We assume that these are sufficiently small, like electrons, and their lives are directly governed by quantum mechanical properties. If particles A and B are entangled with each other, it means that any change in the state of A or any action on A will affect the state of B. That’s all fine, we observe this in our daily lives. For instance, hitting a billiard ball affects the state of the ball in comes in contact with. But can it happen instantaneously? Without any communication or information transfer? Without contact of the balls? Quantum Entanglement does.
Irrespective of the magnitude of the distance present between the entangled particles, the change is instantaneous or non — local. This is what is puzzling. How can it happen? Does the pair actually contain some hidden information which gets transferred? All this was pondered upon by Einstein and his colleagues.
Einstein, Podolsky and Rosen on Entanglement
Come in Einstein.
He was a realist and believed that the world was governed by local realism —
- local means that any event or action or effect or any change in our vicinity (at arm’s length/in the room/near the building) does not affect something (body/reaction/process) which is far away or sufficiently separated from the former event. By far away we mean that any effect can not be felt in a time lesser than that required by light to travel between the cause and the effect.
- realism means that the world exists even if there is no observer. Means that even if no one is looking at a tree, it must exist. Similarly for quantum particles it means that even though we have not observed the particle, its definite state must exist.
Coming back to entanglement.
According to Einstein, entanglement was something like correlation at origination. Building upon the ideas of local realism, his explanation was that the entangled particles must have emerged as the states which we are observing them right now, instead of any kind of instantaneous change.
According to him the entangled particles must have started off in the same set of states as measured and that no collapse of the state vector had occurred.
Moreover, using these two principles as universal truths, Einstein along with Podolsky and Rosen (EPR), claimed that quantum mechanics might not be complete, even though it was correct. To understand this, we can take an analogy. Think of an apple. A theory says that an apple is a red looking object. While this theory is correct, but it is not complete. An apple is characterised by many properties such as weight, size, sweetness, etc. which are indeed relevant to any human interacting with it. So while saying an apple is red, may be correct, but not complete.
As some of you may know, a very crucial aspect of quantum mechanics is the concept of measurement. Following the Copenhagen Interpretation of Quantum Mechanics, it is widely accepted that the state of a quantum particle is not well defined until it is measured. Measurement itself forces the particle(s) to choose one of the several possible states in which they can collapse. These pioneers conjectured that even though quantum mechanics gave correct results and agreed with experiments, it was not in line with realism. So what were indeed their explanations and what was the quantum mechanical view of particles? Let us see —
An Experimental Setup
Take a pair of particles which are entangled. While not going into the experimental details of creating such entangled pairs, we are assuming we have something like a generator. This device would produce entangled pairs of particles for us to play around with. The physical property which this device deals with is the spin and what is actually entangled is the spin of the pair of particles.
Say that the particles are entangled such that we have perfect anti-correlation. This means that if one of the particle has an up spin (↑) along an axis, the other would necessarily have down spin(↓) across that same axis of measurement. Also assume that we have 2 detectors situated at some distance from the generator, with one on the left and the other on right. Note that the generator and the detectors are located in a straight line. The last assumption we make is that the detectors are synchronised — whenever one detector measures a particle, the other detector simultaneously measures another.
Einstein’s View
Einstein could not accept randomness which is associated with quantum mechanics. Whenever a wave function of a quantum object is measured, he conjectured, randomness isn’t associated with it. According to him, what we had measured was exactly how the state of the particle existed before measuring.
With respect to our experiment it means that the although particles are correlated, the result we obtained at measurement was always present since the time of origination of the particle pair. During the generation of the entangled pair it may have been randomly assigned, but once set it does not fluctuate.
This means a pair with spins ↑↓ remained as ↑↓ after getting generated. Moreover, when we measure the particles we measure a property as it was already set. There is no ‘spookiness’ here (to quote Einstein!).
Quantum Mechanical View
Here things are a bit different. Quantum Mechanics says that we do have anti-correlation, but during the time when the particle pair is not measured, its states are not definite.
Whenever we measure one or both the particles, not only do we get a definite answer, but the answer is defined by the act of measurement itself. Measurement forces the system to choose from one of the possible states. For our simple experimental setup, this means that if we measure one particle as ↑ along an axis, the other one is bound to be measured as ↓ along the same axis. This was the thing which bothered Einstein.
For instance, in the above measurement setup, we did measure particle 1 as ↑. Now, we also simultaneously measured particle 2, and detected it as ↓. Einstein could not get to terms with the fact that measurement of one particle affects the quantum state of the other particle instantaneously. To say in terms of a concept which we just went over in the above post, the interaction is non-local. This problem or rather the mystery about the real nature of entanglement or reality remained a mystery for a long time, as it was really hard to test.
Why was it like this? Well, because it was difficult to test something when testing itself breaks the thing we want to test. Let’s take an analogy to clear that up.
If you measure a particle you get a certain definite value or a result, here ↓ or ↑. But doing so, you have lost the information about the nature of what you’re measuring, what was it like before measuring. Its like saying — Hey! I actually have 3 hands when you’re not looking, but as soon as you look, I only have 2. One of the hand vanishes and you see me as a normal human being. The other person will not have any way to test this. This is because the act of seeing or looking at your hands changes the number of hands itself!
This was all about entanglement where we talked about what it means for particles to be entangled and about two very popular yet contradicting views about the real nature of entanglement. Which one of them was correct? This seemingly difficult question was answered by John Stewart Bell in 1964.
Bell said that it is indeed possible to test the Einstein’s view of entanglement and that is what led to the formulation of the Bell’s Inequality and the experiments trying to prove them. What were the ideas behind these inequalities and experiments which settled the dispute about the nature of reality, once and for all? That’s the story of another blog post!
Till then, keep thinking :)
