This comment is a bit long, but bear with me, as I hope to give you an enlightening view of entanglement:
EINSTEIN, LOCALITY AND REALISM
Influences cannot travel faster than the speed of light, but particles can be entangled at separate ends of the universe because both sentences are true at the same time, since they are caused by one and the same thing: What constitutes phenomena propagating at the speed of light to us, material observers, means instantaneity for the massless quanta involved.
And it’s kind of tragic that Einstein, who created the EPR paradox to prove that Quantum Mechanics was incomplete (and ended defining entanglement), already had the solution before his eyes. It was hidden in his own theory of Special Relativity, which completely modifies the way space, time and simultaneity would be experienced if we were able to reach the speed of light exactly.
Einstein objected to Quantum Physics using the principles of realism (entities having determined intrinsic properties) and locality (entities being affected only by its immediate surroundings). The problem is that Einstein didn't fully grasp how his own theory redefines those two terms.
Einstein changed how we picture space and time by following the logical consequences of taking the constancy of the speed of light at face value. But he should have pushed forward. If he had followed the logical conclusions of his own theory to its ultimate consequences, he would have realized that the principles of locality and realism are also artifacts of our reference frames, like it happens with our subjective spacetime units, and he would have found that Special Relativity leads to a natural explanation for entanglement.
The key to solve entanglement lies on adjusting two basic assumptions about the meaning of the speed of light, and the nature of particles and interactions. This, in turn, will modify our concepts of locality and realism, explaining entanglement in an intuitive way.
SPECIAL RELATIVITY
Special Relativity states that if we could travel as close to the speed of light as we wanted, we could traverse the whole universe in any unit of time (proper time) we wanted, just by adjusting our speed closer to that of light. Time will tick slower by the time dilation effects caused by our motion, and if we could reach the speed of light exactly, then time will stop ticking altogether. We would experience going nowhere in no time, leaving and arriving at the same time. Emission and detection (and anything in between) would be the same instant blink of existence for us.
This is exactly what the massless quanta (photons, gluons...) and field perturbations that appear to propagate at the speed of light to us are able to pull off. What material observers experience as different spacetime intervals is always "condensed" into single blinks of existence for the massless quanta involved. Any distance, duration or sequence of events we think they covered, lasted or endured gets compressed to a single point and instant of timeless existence for them.
SPEED OF LIGHT MEANS INSTANTANEITY
The moment we introduce space and time to describe how the universe works, we're choosing a particular frame of reference that is only valid for a specific set of material entities. But the objective reality of any massless entity is what it would experience for itself: that "no time elapses", regardless of what any material observer could have to say about it.
So the true nature of any phenomenon that manifest as traveling at the speed of light to us is the instant bridge it represents through spacetime, not the subjective time interval of any material observer. We should stop thinking that massless quanta are entities or processes that propagate at the speed of light through spacetime. They are more like instant connections between different spacetime coordinates that comply with the light speed ratio.
The speed of light is constant and the same for all observers because it's just the incredibly distorted way these instantaneous spacetime connections map onto the observers' subjective frame of reference, so when we observe that the speed of light is involved in some phenomena, we must understand that some form of timelessness, instantaneity or simultaneity is implied.
Then, a massless quantum represents more of an entanglement between emitter and absorber than a particle traveling between them. Any field disturbance we imagine propagating at c through spacetime is, also, the entire emission-flight-detection process we imagine, somehow.
massless quanta experience the time intervals and sequences of events we infer for them, all at once and in no particular order. This means that phenomena that appear to develop at the speed of light to us don't experience our spacetime dimensions, so our "spooky action at a distance" is "action at spooky distance" to them.
ENTANGLEMENT
This explains how entangled photons can show weird correlations, even when their detections appear to be separated by large distances and time spans from our reference frame: It doesn't matter how far apart in opposite directions two entangled photons appear to us, nor what specific sequence of events they seemed to endure for the interval we think they where "flying" out there, nor which one appears to be detected before or after the other because, to themselves, all the spooky spacetime connections we observe are one and the same indivisible ensemble, where the common emission event and all related detections (no matter how scattered through spacetime) form a single instantaneous action/reaction event with no spacetime qualities, as long as the intervals we observe for them keep them related by the speed of light. Each carrier we detect still feels linked to the entanglement event wherever/whenever it gets detected, by virtue of the speed of light.
ENTITIES, PROCESSES AND PROPERTIES
We should modify our notion of locality, as every piece of matter is affected by all the fundamental interactions that reach it at the speed of light at a given moment, regardless of how past or distant the events to which those light-like interactions connect to. If a photon generated 13 billion years ago or at a 13 billion lightyears distance can change the state of a detector here and now, then what "locality" even mean? What are "immediate surroundings" when anything lying on the inner side of the cosmological horizon can affect the observer?
But if the speed of light is key for entanglement, then, how is it possible for some material particles to show entanglement at speeds other than c?
This is where our new understanding of fundamental interactions as instant spacetime connections modifies our idea of realism:
We should stop thinking that each element of reality (matter, forces or spacetime) is composed of different fundamental entities, with different intrinsic properties. Everything is just a pattern of fields or a network of fundamental interactions. In the end, any energy or information exchange, any piece of matter, any property, structure, sequence, entity or process that physically exists in the universe is ultimately made up of the instant but light-like interactions (spacetime relations) that shape them internally and those that communicate them externally. Massless quanta and field perturbations are not little carriers that propagate through spacetime at the speed of light, but more like wormholes or "short circuits" that instantly connect different spacetime coordinates, always complying with the light speed ratio.
So the light-like interactions that unfold each time form a network of instant relations that interconnect spacetime from past to present, stitching reality each time. All the massless carriers we picture as travelling through the universe at the speed of light are, at the same time, the instantaneous entangled connections that create the spacetime structure itself, the information exchanges that hold up reality and make it self-consistent with all its past history automatically. Properties are not "carried" by the particles, or "propagated" between them by massless quanta. The whole universe is recreated before our eyes each and every time by the fundamental interactions that instantly interconnect past states to the present moment through light speed relations. Nothing "evolves" through spacetime. Not even matter. Entities and processes are emergent phenomena that come from the patterns the light-like interactions that develop each time create respecting the restrictions that previous interactions laid out through spacetime.
In this regard, Einstein was wrong about how entities can only be affected by their close environment (incorrect notion of locality), and also wrong about the existence of predefined properties (incorrect notion of realism). But although Quantum Mechanics correctly ditches the notion of locality, it still insist on explaining the world using concepts and mechanisms that change or evolve in time themselves (wavefunction superpositions and collapses, branching many worlds, observer's consciousness...), but no mechanism or concept that changes or evolves in time could ever properly describe the instant nature of the universe, since each interaction that pops into reality is a collapsed wave function that fulfills at once all the requirements for the series of events we imagine it confronted one after the other at the speed of light.
ENTANGLEMENT AS FUNDAMENTAL PRINCIPLE
Everything is made up of these instant spacetime relations, so entanglement is the fundamental principle that drives the universe. It is not that massive particles can display some entangled properties under very specific conditions, it is that entanglement, although hard to observe, underlies every physical property, structure or process existing in the universe. And as said earlier, any energy or information exchange is also an instant action/reaction event, which ensures conservation laws are enforced automatically, no matter what unfolds in spacetime. So entanglement is not a consequence of conservation laws, it is entanglement which supports the existence of conservation laws.
The dual nature of the speed of light as instantaneity in disguise explains entanglement, and from there, all quantum weirdness can be explained. There's no need to call for extra dimensions, parallel worlds, retrocausal waves, superdeterminism or other convoluted spacetime mechanisms, since the massless quanta that shape reality don't know what the measurement problem is, as they know nothing about our space or time dimensions. They have, literally, no time to evolve, and there's no "where" or "when" to change, since the whole process we think takes place is an indivisible "happening" they experience instantly.
