How far are we away from technology that would allow us to send an unmanned probe...

We could do it now if we wanted to. It requires the use of nuclear pulse propulsion (dropping small tactical nuclear weapons behind a spacecraft to propel it forward). Some preliminary research done in the fifties suggested we could have a working prototype within a few years' development which could reach 1.5% of the speed of light. It was known as Project Orion, and could concieveably reach Alpha Centauri within about 50 years.
http://en.wikipedia.org/wiki/Project_Orion_%28nuclear_propulsion%29

With sufficient funding, a massive Orion spacecraft could be built as a full colony ship, however that would require a suitable target for colonization. Orion's engineers felt it could be done with a few decades of work.

Another project known as Project Longshot could, if funding was given, be built within a few decades and reach Alpha Centauri B within a century. It uses inertial confinement fusion for power coupled to a conventional fission reactor.
http://en.wikipedia.org/wiki/Project_Longshot
 
Voyager is on the way, It was the fictional Vger of the the First Star Trek movie. Launched in the early 70's, it will get there eventually.
 
Centuries if not millenia. It takes nearly a decade to get to Pluto. We are mindbogglingly far away from Alpha Centauri even if it is our "closest" neighbor. You need to accept that space is big and no matter what science fiction tells you, it's not easy to colonize or explore. It'd likely take centuries for our probe to reach the system either way.

EDIT: Orion's a great idea in theory, its just that very little research has been done into it since it was canceled. However, he does have a good point if NASA was serious about it and it turned out to be work. Its still never been tested and proven. It's just a theory.

EDIT 2: Also, I just realized that it's not a very logical thing to do unless we had plans on more than sending it there. We would never even know if it even got there let alone receive information.
 
we could do that now. it would cost trillions of dollars and take thousands of years to get there, but we could do it, if we wanted to. I guess that's not the sort of thing you're talking about, though. maybe you have in mind something more like say, a 50 year trip costing "only" a few billion dollars, typical cost of a mars probe or something like that. give it a couple of centuries, I guess... and that's all this is, a guess... bearing in mind that certain crystal ball gazers a hundred years ago imagined that our primary mode of transportation would be... zepellins. it ain't easy to predict this sort of thing!
 
Centuries. And even with advanced technology that would allow a craft to carry enough fuel and accelerate to 10% light speed (19,000 miles per second), that would still be at least a 50 year trip plus the 4.3 years to send information back to us via radio.
 
Well, strictly speaking we could do that right now.

In fact, NASA has already sent 5 probes completely out of the solar system. Look up the following:

http://en.wikipedia.org/wiki/Voyager_program
http://en.wikipedia.org/wiki/Pioneer_10

So there is no reason why we could not design a suitable trajectory to send a probe to A cent.

The only problem is that with the best current technology, it will take around 150,000 years to get there! But if your purpose is simply to send a human artifact to another star, you will have succeeded. Check this:
http://en.wikipedia.org/wiki/Voyager_golden_record

Apart from such missions, it is conceivable that if enough budget was available we might build something like this:

http://en.wikipedia.org/wiki/Project_Daedalus

It would use a more exotic form of propulsion such as ion drive, or if we were desperate enough nuclear rocket technology is available. The transit time could possibly be reduced to several thousand years. If the probe send back signals of what it found, it is remotely possible that whatever species takes over from humans might be able to receive the signals in (say) 20,000 years time.

Cheers!
 
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