How do we define a pure vacuum? How do we define a pure vacuum? Is the definition limited by our own capability of what we understand or know how to measure?
 A: The standard definition, in flat spacetime without cosmological constant, would be the situation where there are no matter particles (electrons, quarks, etc.) and no electric or magnetic field and no excitations of the colour fields (called gluons) etc. To spell it out fully you have to invoke quantum field theory and then the vacuum state is the ground state of the entire set of interacting quantum fields. It is subtle because this does not mean the fields are not there at all. They still have a non-zero value for the mean squared amplitude at any given place. But they have a zero value for the mean amplitude, and there is no lower-energy state available to them. In this situation a particle detector which is at rest or in constant-velocity motion, after being given time to settle to its own ground state, and placed with vacuum surrounding it, will never become excited. So this is an empirical way to state the definition.
However, another (and very different) state may be referred to as a kind of 'vacuum state' in theoretical calculations. This is a state where we first imagine the various fields (electromagnetic, Dirac, Higgs, colour, quark, etc.) did not interact with one another, and we take them one at a time, and consider the case where each such 'bare' field is in its ground state. This is, as I say, a calculational tool and not the state the fields are really in when not excited, because in fact the fields do interact with one another. The true ground state is the one I described in the first paragraph and it takes the interactions into account. (Also, the 'particle detector' mentioned in the first paragraph is a detector of real particles with all their interactions, not the 'bare' particles which are simply a calculational tool.)
Finally, this answer ignores gravitation and a possible further feature called cosmological constant. Those both complicate the situation quite a lot. But those complications only have significant effects in either extreme situations (e.g. early universe or near the horizon of a black hole) or over very long timescales (billions of years).
To return to the empirical definition: if one has a device for detecting all sorts of excitation or particle, and the device never registers any incoming energy, then you have a vacuum.
A: A pure vacuum - within our universe - represents a region of space-time in which absolutely no energy is present. On one hand, we could argue that any region of space-time contains quantum fields. Since these fields are subject to the Heisenberg uncertainty principle, it is difficult to argue that any region of space-time could exist with an energy content of zero.
Additionally, as Kip Thorne, for example, has described. when a black hole is formed, matter is converted into space-time curvature. This implies that space, at least in a curved state. has absorbed energy and thus some form of space-to-energy equivalence exists analogous to the matter-to-energy equivalence described in the equation E equals mc squared. If so, then a space-time vacuum, within our universe,  is - by definition - impossible. Since space-time has energy equivalent or content, any region of space is alternatively, interpretable as an energy-equivalent region, and therefor cannot be a pure vacuum.
Finally, space is apparently continually generating additional space. This process results in the acceleration of the expansion of the universe. The leading explanation for this process is the "cosmological constant" described in Einstein's original Theory of General Relativity. This cosmological constant represents an intrinsic energy of space-time that drives the creation of additional space-time. This implies that space-time must have an intrinsic energy content, and therefor no region of space-time in our universe could possibly exist as a pure vacuum.
the point of this explanation is that the definition of a pure vacuum, is equivalent to the definition of absolutely nothing. including no space-time and thus no conceivable universes.
Perhaps this does not mean that no true pure vacuum exists, but rather that a pure vacuum is where a space-time region (a universe) first appears, and into which this new-born universe subsequently expands.
A: The vacuum is a theoretical concept of a state that does not contain any particles. As such, it can be defined as an eigenstate of the number operator of all particle fields with eigenvalue equal to zero. Physically, the vacuum state only ever exists in a superposition together with other number states. However, one can treat such superpositions as being approximately the vacuum state in cases where it represents the dominate term in the superposition.
