# EPR Experiments¶

## The problem¶

In 1935, Einstein, Podolsky and Rosen 1 analysed in a *Gedankenexperiment*
the situation of two entangled particles, that, although there were separated
by a large distance, would be strongly correlated. This lead to a paradox,
because, depending on the choice between alternative measurements on one of the particle,
the second entangled particle could be simultaneously affected, i.e. the outcome of a
measurement on this second particle would be then known in advance.
The result of the measurement on the first particle would be random,
but the outcome of the second particle not any more.

The *randomness* on one side, and the *simultaneous* change in behavior of the second
particle, lead Einstein to consider Quantum Mechanics as an “incomplete” theory:
“God does not play dice with the universe” 2 . In Einstein’s mind, and this is one of the messages of the paper by EPR, it wasn’t satisfactory that Quantum Mechanics
didn’t provide an explanation behind this randomness, and the nonlocality shown in the EPR experiment was also a matter of discontent.
It was necessary to search for a deterministic theory that was behind these phenomena.
This yet unknown theory could be described using hidden variables, and aimed to preserve locality. Furthermore this story relied on the belief that, even if a measurement wasn’t performed, the measured quantity was always existing, what is described by “realism”.

In 1964, John Bell imagined a particular kind of experimental settings and derived an inequality involving measurement outcomes, that would allow to test the validity of either Quantum Mechanics or a hidden variable theory. Elements to understand and interpret these inequality are given in Bell Inequalities.

## Experimental validation¶

linear polarization correlation of the photons emitted in a radiative atomic cascade of calcium, [12], [10]

Type-II noncollinear phase matching in parametric down conversion, a violation of Bell’s inequality by over 100 standard deviations in less than 5 min, [73]

15 years after Aspect’s experiment: “for the first time fully enforce the condition of locality”, with type-II parametric down conversion, [132]

detection loophole: [61], [45], [120], see also [M3]

closing freedom-of-choice loophole: [27]

- 1
A. Einstein, B. Podolsky, and N. Rosen. Can quantum-mechanical description of physical reality be considered complete?

*Phys. Rev.*, 47:777–780, May 1935. URL: https://journals.aps.org/pr/pdf/10.1103/PhysRev.47.777, doi:10.1103/PhysRev.47.777.- 2
Albert Einstein. Letter to Max Born, 1926. In

*Born-Einstein Letters, 1916-1955*. Palgrave Macmillan US, 2005. URL: https://www.springer.com/de/book/9781403944962.