Entanglement in double slit experiment

Suppose we send 2 entangled photons through the 2 slit, does measuring the position of one of the photons affect the other particle's wave function or does the other particle still behave as a wave ?

Here are single photons at a time arriving at the slits: Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, ... frames

The "measurement" of each photon is a dot.

Suppose we send 2 entangled photons through the 2 slit, does measuring the position of one of the photons affect the other particle's wave function or does the other particle still behave as a wave ?

As your two entangled photons move with velocity c, they will have to be parallel to each other and close in space, in order to both reach the double slits and go through, and both will materialize as a point on the screen. If there were a polarimeter at the location of the dot , the spin correlation could be registered, but the probability waves are reduced to points after the slits, and appears in the accumulation of points in the interference.

• Interesting , when you say that the wave are reduced to points after the slits are you assuming that if we measure the position after the particle goes through one slit , we are actually affecting the particle in the past meaning that time must be running backwards ? – Miguel Guevara Valencia Jun 6 '18 at 4:08
• Not "after the slits" but "at the screen", the point is the measurement of a single instance in a probability distribution that describes the wavefunction of the photon. The probability distribution appears in the accumulation of single instances . – anna v Jun 6 '18 at 5:27
• Each photon is described by a four dimensional wavefunction which when complex conjugated and multiplied with itself gives the probability distribution in space time for a photon, with the given boundary conitions , here two slits and a "screen" all with fixed geometrical distances. Detecting a photon at z in an x,y point picks up one instance at that z. – anna v Jun 6 '18 at 5:30

There are some interesting research about using entangled twin photons, slits and different detection position to achieve a specific quantum state of the complete Hilbert space. The schematic diagram is shown as the figure below. According to the results, like your prediction, different detection positions of one double-slits system will affect the measuring results of the other system, so that we can control the state of the two-particle system. One of the relevant reference's DOI is 10.1103/PhysRevA.78.012307. Hope it is helpful for you. 