It is possible to define speeds that exceed the speed of light in vacuum-this doesn't mean anything by itself, however. It must be shown that a physical process occurs at that speed. It's not possible to assign a definite value to the speed with which entangled states exchange anything, so it's not possible to assign any meaning to the statement that this speed exceeds the speed of light. 

It doesn't make sense to appeal to relativity, when working within non-relativistic quantum mechanics. Quantum mechanics is a non-local description of physical effects, since states can be entangled and what this means is well-defined. This property doesn't have any classical description, so cannot be described by classical variables at all-whereas there do exist quantum states that do have a classical limit, where they can be described by classical variables.

So the only issue was, do such states, that do not have a classical limit, have physical consequences-and the answer, experimentally, turns out to be Yes. 

To describe ``action at a distance'' locally requires introducing a field. For quantum mechanics such a field turns out to have very particular properties. However it does not reduce the problem to the solution of the classical equations of motion, which ``hidden variables'' might be expected to lead to.

The equations of classical and quantum mechanics are invariant under time reversal-that's a consequence of unitarity in quantum mechanics and it's straightforward to prove that t -t is equivalent to UU+ valid since the Hamiltonian is hermitian.

No, because the light cone structure in non-relativistic quantum mechanics doesn't have anything to do with the light cone structure of Minkowski spacetime-so they don't violate any assumptions of non-relativistic quantum mechanics.  And experiments done with entangled states show that, indeed, the effects predicted by non-relativistic quantum mechanics are consistently found. So no relativistic effects are involved.

It is possible to define speeds that exceed the speed of light in vacuum-this doesn't mean anything by itself, however. It must be shown that a physical process occurs at that speed. It's not possible to assign a definite value to the speed with which entangled states exchange anything, so it's not possible to assign any meaning to the statement that this speed exceeds the speed of light. 

The ambiguous word is ``achieve''-one can write expressions that have the dimensions of velocity, within any given framework-that doesn't mean that something moves at that value, within that framework.   In a hollow  waveguide the phase velocity is strictly greater than the speed of light in vacuum-but nothing physical moves at that speed. In quantum mechanics, an energy eigenstate has a sharp value of energy-but the velocity has a continuous distribution of values. It's not possible to associate any particular value to the velocity of such a state: in a bound state the energy is the sum of two non-commuting operators, so it's not possible to assign a definite value to either its position or its velocity (and a free particle can't be defined as a momentum eigenstate, or a position eigenstate, because such states aren't normalizable-so it can't have a definite value of energy, in an unbounded domain-the origin of all the uncertainty principles). 

However, once more: non-relativistic quantum mechanics doesn't define any special velocity, like the speed of light. If one does try to produce a velocity eigenstate, however, it will be a superposition of position eigenstates, so it can't be associated to any object, with a well-defined  position. 

http://arxiv.org/abs/1508.05949

http://www.physics-astronomy.org/2018/04/breaking-researchers-at-cern-break.html?m=1 The above link clearly proves particles can exceed the speed of light , but less than 500000km/s. Maybe they are ghost particles like tachyons.