In quantum eraser experiments, getting information about one entangled photon decides if the second photon behaves classically or quantum (interfere). Optical lengths for these photons chooses time order of these events, so we can delay the "decision" to happen after what it decides about. But in "standard version" of such delayed choice quantum erasure this decision is made randomly by physics.

I've just found much stronger version - in which we can control this decision affecting earlier events.

Here is a decade old Phys. Rev. A paper about its successful realization and here is simple explanation:

We produce two entangled photons - first spin up, second spin down or oppositely.

Photon s comes through double slit on which there are installed two different quarter wave plates changing polarization to circular in two different ways.

Finally there are two possibilities:

x y R L

y x L R

where columns are: linear polarization of p, initial linear polarization of s, circular polarization of s after going through slit 1, circular polarization of s after going through slit 2.

So if we know only the final circular polarization of s, we still don't know which slit was chosen, so we should get interference. But if we additionally know if p is x or y, we would know which slit was chosen and so interference pattern would disappear.

So let us add polarizer on p path - depending on its rotation we can or cannot get required information - rotating it 45deg we choose between classical and interfering behavior of s ... but depending on optical lengths, this choice can be made later ...

Why we cannot send information back in time this way?

For example placing s detector in the first interference minimum - while brightness of laser is constant, rotating p polarizer should affect the average number of counts of s detector.

What for? For example to construct computer with time loop using many such single bit channels - immediately solving NP hard problems like finding satisfying cryptokeys (used to decrypt doesn't produce noise):

Physics from QFT to GRT is Lagrangian mechanics - finds action optimizing history of field configuration - e.g. closing hypothetical causal time-loops, like solving the problem we gave it.

Ok, the problem is when there is no satisfying input - time paradoxes, so physics would have to lie to break a weakest link of such reason-result loop.

Could it lie? I think it could - there is plenty of thermodynamical degrees of freedom which seems random for us, but if we could create additional constrains like causal time loops, physics could use these degrees of freedom to break a weakest link of such loop.

What is wrong with this picture?