You can’t travel faster than the speed of light (we are assuming). If we consider teleportation of this kind to be travel then you can travel at the speed of light (plus some time to map yourself beforehand and reassemble a new you (or another you)). You can also travel close to the speed of light using the old fashioned method of moving really fast, so time-wise the teleportation system is only a little faster. Physical travel and teleportation each have their hazards, but with teleportation at least you get do-overs if something goes wrong.
It might destroy the instance of your body here, but what makes you say that kills you? It seems to me that if I walk out of the receiver just fine, then rumors of my death are greatly exaggerated.
The trick would be to aim that “stream of photons” precisely enough that it gets to Alpha Centauri.
Think of it this way.
Imagine that somehow a perfect copy of you is made without destroying the original.
Now I have Chronos and Copy-Chronos which in all ways is identical to Chronos.
I walk up and say something went wrong and I have to kill Chronos so Copy-Chronos can get on with his day.
You’d be ok with me killing you since your perfect copy will carry on?
How can you make such definitive statements about a fictional technology?
I say it WON’T kill you.
There is an additional sticky-wicket, of a practical nature. If you point a powerful pin-point laser at α-Centauri, that tiny point of light will spread as it travels, until, when it reaches the receiver, it is billions of miles across (and thus, proportionally weaker).
From α-Centauri, the Earth itself is less than one arc-second (1/3600°) from the Sun at its furthest. The sun itself spews something like 15Pw of various wavelengths of light on the Earth. This means that the signal of you must overcome a rather large amount of noise in order to be decoded.
Thus, you will have to buffer your signal with an absurd amount of ECC in order for it to be properly decoded. I am going to venture that the signal of you would take approximately one lifetime to transmit and receive. You corporeal form would probably be long gone before they could reconstruct your simulacrum over there.
(Granted, there are band gaps in the solar radiation that you could slide your signal into, but that is still not going to make it any stronger when it gets there.)
What if both versions are kept unconscious throughout the process. If an accidental duplicate is made, the two versions are shuffled randomly in the chamber, and one is destroyed. Nobody knows which one was destroyed. The Chronos that was destroyed has no awareness of the event. And the Chronos that is kept just remembers falling asleep and waking up again.
So far as both Chronos himself and the outside world are concerned, this is indistinguishable from any other night where he falls asleep, loses consciousness, and then wakes up again.
Is it really still meaningful to say that Chronos might have died overnight?
You just need to learn to think like a dinosaur.
I’m not a physicist but I suspect that the uncertainty principle would stop you from scanning all of the information needed for that kind of teleportation.
No, in that situation, it must be settled by cage match fight to the death.
Point is, if the transport mechanism kills you in the process, then it doesn’t really kill you, but instead, you walk out of the end point, a tough feat for someone that just got killed. The idea is that the scanning beam for such a thing would have to have such high energies that it would essentially vaporize you as it scanned you. I always fan waved the star trek transporters as starting with a low resolution targeting beam that makes sure everything is lined up, and ensures there is room for you at the target. Then you are hit with high intensity gamma rays that vaporize you instantly, and leave the impression of where everything goes holographically on the shield, then the shield is transported to the destination, and reverse the process, recreating a 3d object from the hologram.
If you are able to be making copies, then there are two of him. If one gets killed, then the other is not any more dead. I may not personally appreciate being the copy that gets a bullet to the head, but the copy of me that gets to live is fine. At this point, though, you are just murdering people for bureaucratic reasons, not because that is how it has to happen by the laws of the technology you are using. I would be against such laws, if a cloned copy is viable, then it should get to keep living.
Put it a slightly different way, the earth is about to blow up, and you can copy yourself into a transmitter that will send you to Mars (a colonized, safe mars to receive you). After the copy is made and transmitted, the original you dies in the cataclysm that destroys the planet we all know and love. When you step out of the transmat at the other end, are you going to feel alive?
You’d be correct if it was fictional technology but alas it is real. We are a looong way off from teleporting people (if ever) but in principle it is doable. As it happens this means of teleportation destroys the original. (bolding below mine)
Mars me will feel alive. Earth me will feel the agony and terror of dying in a cataclysm. It is small consolation to earth me that there is a Mars me who is safe and happy.
My “je ne sais quoi.” Almost by definition.
From an observer’s perspective all we see is Chronos leave the room.
But imagine your setup with a little spin.
I take Chronos and Copy-Chronos into a room. I tell them I am going to give them a sleeping pill and during the night I will kill one of them and dispose of the body. The other gets to leave and live their life and as a practical matter Chronos and Copy-Chronos are the same so the world just sees an alive and well Chronos.
I am willing to bet they would both be uneasy with that setup.
All your test did was hide from them the reality of what happened. But if we see that reality then it is a scary prospect to get teleported.
I think I’ll pass. 
Don’t ever sleep. When you sleep, you die, and though when you get up in the morning, you are alive, that’s a small consolation to the previous night’s you that gave up his life so that morning you can live.
But, really, you would not feel any better about knowing that, even though your personal existence is coming to an end, your thoughts, memories, and personality; your legacy really, will continue to live on?
Would you feel this way to the point of not bothering to step into the transmitter, to give cloned you a new chance at life?
Let’s look at something simpler–an old-fashoned mechanical pocket watch. Let’s say that you have a device for scanning the entire volume of the watch in high detail. Let’s also say that you have a very fancy 3D printer that can print in all sorts of metal, glass, grease, semiprecious gems, and anything else found in the watch. Great, you can make a perfect copy of the watch. But can you make that copy in such a way that the new copy never stops ticking and continues to work and keep time as it is being built? I’m guessing that is a big “no.”
Humans have multiple orders of magnitude more moving parts than a pocket watch. Life is a process, not a state. The idea that you can rebuild a living creature on the fly is silly fantasy that will never step outside of fiction.
If I am about to die anyway I’d step into the transmitter.
But I would have reservations doing it if all I wanted to do was go check out Mars for the weekend.
Strange definition of “real” you have. I say another way of scanning will be invented that doesn’t kill you. In principle, it’s doable.
I think allowing both to become conscious changes the game somewhat, because they will immediately begin to diverge. But let’s set aside that point.
It seems to me that you are begging the question. What is “the reality of what has happened”? If “Chronos” is information, then duplicating that information does not create a second Chronos; and erasing one of two identical copies does not “kill” anyone.
And if consciousness is somehow critical in the “count” of how many Chronoses exist, what happens normally every night when he falls asleep and loses consciousness? Does he die every night?