# Quantum entanglement, is it real?

1. Sep 24, 2014

### Saruman

Disclaimer, i'm no scientists, and i know enough to get my self into trouble, however

Every time i hear about quantum or quantum computers or such, and its experimental data, its never proved in my mind that the particles where ever in superposition (if that's the tight terminology).

every now and again i read some science news on quantum teleportation and the experiment they have setup, and they claim by looking at one entangled particle they can tell the state of its entangled photon when spatially separated

i.e. i set up an experiment, someone gives me 2 cards (red and black), i put them face together, spin them around, and separate them, then someone looks at one card, it collapses the wave function and i can instantly tell what the other card is , 1 light year away instantly. no spooky action at a distance

Question : double slit experiment aside (cool stuff), how are these entanglement experiments proving that the entangling of a particle has not preset the states of the particles in opposite states before the separation

I'm sure there is more diligence in these experiments than the above comments give credit however, i really would like to understand from my perspective and believe they hype

Has anyone got a links to an experiment or such that easily shows that 2 particles are actually entangled in superposition and can show categorically, that such is the case, or do i need to undertake a physics degree

2. Sep 24, 2014

### bhobba

Its because that assumption leads to conclusions different to experiment - technically its given the name local realism - and is precisely what experiment shows is wrong:
http://www.drchinese.com/David/EPR_Bell_Aspect.htm

Thanks
Bill

3. Sep 24, 2014

### DrChinese

Welcome to PhysicsForums, Saruman!

Great question, and I will follow up on bhobba's comments. As you might guess, this is not just a generally guess by scientists but follows a rigorous logic. You may or may not be able to follow the reasoning, but it really isn't that hard.

Entangled pairs of photons produce different statistics than unentangled pairs when both are measured at the same angle (say 45 degrees). On average, entangled pairs are 100% predictable as to whether they will match. Unentangled pairs are only 75% predictable. So that is the first indication of a specific physical effect.

The next steps are a bit more complicated, but basically it follows from Bell's Theorem that the superposition the entangled pair is in cannot be equivalent to the red and black card analogy you referred to (which is also known as Bertlmann's Socks). Read at the link bhobba provided (or elsewhere):

EPR
Bell
Aspect

4. Sep 28, 2014

### jfizzix

You don't need a physics degree to understand how we experimentally prove entanglement between pairs of particles. I do research on just this subject, and jargon aside, it's simpler than you might think.

There are a number of ways to tell if a pair of particles are entangled, and they all rely one one basic idea. First, we find some mathematical property that's definitely true for all non-entangled (i.e., separable) systems, Then, when our measurements show that the state of the pair doesn't have this property, we know it must be entangled.

Thing one: Entanglement Witness Observables
For certain entangled states, one can actually come up with certain observables whose measurement outcomes are restricted to a certain range if the state of the pair is separable (not entangled). One example of this for spin-1/2 particles, would be the sum of the products of the spin observables in the x, y, and z-directions;
$\hat{W}=\sigma_{x}^{A}\otimes\sigma_{x}^{B}+\sigma_{y}^{A}\otimes\sigma_{y}^{B}+\sigma_{z}^{A}\otimes\sigma_{z}^{B}$.
Here, if the quantum state of a pair of particles A and B is separable, then the average value of W over many measurements must be between -1 and 1. In practice, one would prepare many such pairs to find this average value. As an example, measuring W on the maximally entangled Bell singlet state would give an average value of -3 for W, way outside the range for separable states.

Thing one and a half: Separability inequalities
There are a number of more general inequalities which have been devised which must hold true for the measurement statistics (of multiple observables) of all non-entangled systems. Violating these inequalities proves the system must have been entangled.

Thing two: EPR-steering inequalities
If the measurement statistics of a pair of particles actually demonstrate the EPR-paradox, then the pair of particles must be entangled. As an example, here's an EPR-steering inequality for position and momentum
$\Delta^{2}(x^{B}|x^{A})\Delta^{2}(p^{B}|p^{A})\geq \frac{\hbar^{2}}{4}$
To do this for say position and momentum, one performs many measurements of the positions and momenta of pairs of particles to obtain a joint measurement probability distribution. From this data, we can see how well measuring the position or momentum of one particle A allows us to predict the measurement outcomes of the corresponding position or momentum of the other particle B. If the positions and momenta are so strongly correlated, that knowing the position or momentum of one would allow us to predict the outcome of measuring the position or momentum of the other to a precision stronger than the uncertainty principle would allow without this extra info, we end up demonstrating the EPR-paradox, and showing that the pair of particles are entangled.

Thing three: Bell Inequalities
Bell inequalities are the strongest witnesses of entanglement that we have. The idea behind them is that they are mathematical consequences of models of local hidden variables. These models of local hidden variables are ones where the measurement correlations between a pair of particles could be "explained" by knowing everything in the past of both particles that could have affected both particles (where we assume that information can travel no faster than light). By violating a Bell inequality, you show not only that the pair of particles must be entangled, but also that the correlations between the pair of particles cannot be explained locally.

Hope this helps:)

Last edited: Sep 28, 2014