### Cloning quantum information from the past

##### January 8, 2014

It is theoretically possible for time travelers to copy quantum data from the past, according to three scientists in a recent paper in *Physical Review Letters*.

It all started when David Deutsch, a pioneer of quantum computing and a physicist at Oxford, came up with a simplified model of time travel to deal with the Grandfather paradox*. He solved the paradox originally using a slight change to quantum theory, proposing that you could change the past as long as you did so in a *self-consistent manner*.

“Meaning that, if you kill your grandfather, you do it with only probability one-half,” said *PRL* co-author Mark Wilde, an LSU assistant professor with a joint appointment in the Department of Physics and Astronomy and with the Center for Computation and Technology. “Then, he’s dead with probability one-half, and you are not born with probability one-half, but the opposite is a fair chance. You could have existed with probability one-half to go back and kill your grandfather.”

**No-cloning theorem**

But the Grandfather paradox is not the only complication with time travel. Another problem is the “no-cloning theorem,” or the no “subatomic Xerox-machine” theorem, known since 1982. This theorem, which is related to the fact that one cannot copy quantum data at will, is a consequence of Heisenberg’s Uncertainty Principle, by which one can measure either the position of a particle or its momentum, but not both with unlimited accuracy.

According to the Uncertainty Principle, it is thus impossible to have a subatomic Xerox-machine that would take one particle and spit out two particles with the same position and momentum — because then you would know too much about both particles at once.

“We can always look at a paper, and then copy the words on it. That’s what we call copying classical data,” Wilde said. “But you can’t arbitrarily copy quantum data, unless it takes the special form of classical data. This no-cloning theorem is a fundamental part of quantum mechanics — it helps us reason how to process quantum data. If you can’t copy data, then you have to think of everything in a very different way.”

**Looper**

But what if a Deutschian closed timelike curve *did* allow for copying of quantum data to many different points in space? Deutsch suggested in his paper that it should be possible to violate the fundamental no-cloning theorem of quantum mechanics. Now, Wilde and collaborators at the University of Southern California and the Autonomous University of Barcelona have advanced Deutsch’s 1991 work.

The new approach allows for a particle, or a time traveler, to make multiple loops back in time — something like Bruce Willis’ travels in the Hollywood film “Looper.”

“That is, at certain locations in spacetime, there are wormholes such that, if you jump in, you’ll emerge at some point in the past,” Wilde said. “To the best of our knowledge, these time loops are not ruled out by the laws of physics. But there are strange consequences for quantum information processing if their behavior is dictated by Deutsch’s model.”

A single looping path back in time, a time spiral of sorts, behaving according to Deutsch’s model, for example, would have to allow for a particle entering the loop to remain the same each time it passed through a particular point in time. In other words, the particle would need to maintain self-consistency as it looped back in time.

“In some sense, this already allows for copying of the particle’s data at many different points in space,” Wilde said, “because you are sending the particle back many times. It’s like you have multiple versions of the particle available at the same time. You can then attempt to read out more copies of the particle, but the thing is, if you try to do so as the particle loops back in time, then you change the past.”

To be consistent with Deutsch’s model, which holds that you can only change the past as long as you can do it in a self-consistent manner, Wilde and colleagues had to come up with a solution that would allow for a looping curve back in time, and copying of quantum data based on a time traveling particle, *without* disturbing the past.

“That was the major breakthrough, to figure out what could happen at the beginning of this time loop to enable us to effectively read out many copies of the data without disturbing the past,” Wilde said. “It just worked.”

However, there is still some controversy over interpretations of the new approach, Wilde said. In one instance, the new approach may actually point to problems in Deutsch’s original closed timelike curve model.

“If quantum mechanics gets modified in such a way that we’ve never observed should happen, it may be evidence that we should question Deutsch’s model,” Wilde said. “We really believe that quantum mechanics is true, at this point. And most people believe in a principle called Unitarity in quantum mechanics. But with our new model, we’ve shown that you can essentially violate something that is a direct consequence of Unitarity. To me, this is an indication that something weird is going on with Deutsch’s model. However, there might be some way of modifying the model in such a way that we don’t violate the no-cloning theorem.”

Other researchers argue that Wilde’s approach wouldn’t actually allow for copying quantum data from an unknown particle state entering the time loop because nature would already “know” what the particle looked like, as it had traveled back in time many times before.

** Consequences of being able to copy quantum data from the past**

But whether or not the no-cloning theorem can truly be violated as Wilde’s new approach suggests, the consequences of being able to copy quantum data from the past are significant. Systems for secure Internet communications, for example, will likely soon rely on quantum security protocols that could be broken or “hacked” if Wilde’s looping time travel methods were correct.

“If an adversary, if a malicious person, were to have access to these time loops, then they could break the security of quantum key distribution,” Wilde said. “That’s one way of interpreting it. But it’s a very strong practical implication because the big push of quantum communication is this secure way of communicating. We believe that this is the strongest form of encryption that is out there because it’s based on physical principles.”

Physicists and computer scientists are working on securing critical and sensitive communications using the principles of quantum mechanics. Such encryption is believed to be unbreakable — that is, as long as hackers don’t have access to Wilde’s looping closed timelike curves.

“This ability to copy quantum information freely would turn quantum theory into an effectively classical theory in which, for example, classical data thought to be secured by quantum cryptography would no longer be safe,” Wilde said. “It seems like there should be a revision to Deutsch’s model which would simultaneously resolve the various time travel paradoxes but not lead to such striking consequences for quantum information processing. However, no one yet has offered a model that meets these two requirements. This is the subject of open research.”

* In the Grandfather paradox, a time traveler faces the problem that if he kills his grandfather back in time, then he himself is never born, and consequently is unable to travel through time to kill his grandfather, and so on. Some theorists have used this paradox to argue that it is actually impossible to change the past. The question is, how would you have existed in the first place to go back in time and kill your grandfather?”

**Abstract of Physical Review Letters paper**

We show that it is possible to clone quantum states to arbitrary accuracy in the presence of a Deutschian closed timelike curve (D-CTC), with a fidelity converging to one in the limit as the dimension of the CTC system becomes large—thus resolving an open conjecture [Brun et al., Phys. Rev. Lett. 102, 210402 (2009)]. This result follows from a D-CTC-assisted scheme for producing perfect clones of a quantum state prepared in a known eigenbasis, and the fact that one can reconstruct an approximation of a quantum state from empirical estimates of the probabilities of an informationally complete measurement. Our results imply more generally that every continuous, but otherwise arbitrarily nonlinear map from states to states, can be implemented to arbitrary accuracy with D-CTCs. Furthermore, our results show that Deutsch’s model for closed timelike curves is in fact a classical model, in the sense that two arbitrary, distinct density operators are perfectly distinguishable (in the limit of a large closed timelike curve system); hence, in this model quantum mechanics becomes a classical theory in which each density operator is a distinct point in a classical phase space.

### References:

- Todd A. Brun, Mark M. Wilde, Andreas Winter, Quantum State Cloning Using Deutschian Closed Timelike Curves,
*Physical Review Letters*, DOI: 10.1103/PhysRevLett.111.190401 - Todd A. Brun, Mark M. Wilde, Andreas Winter, Quantum state cloning using Deutschian closed timelike curves,
*arXiv*, 2013, arxiv.org/abs/1306.1795

## comments 16

January 11, 2014by cybervigilante

Time is like a filmstrip. Each frame does not Cause the next one. It just seems to, due to the velocity of the film. Since there is really no causation, the grandfather paradox is perfectly acceptable.

January 10, 2014by timetc

Hold on! all this granfather paradox and linear time streams isnt it nulified if the many worlds theory is corect? kill your grandfather and you have a new world line created where he did not exist. Just like the world line where Hitler won the war because the RAF did not bomb Berlin by accident in 1940

January 10, 2014by Gorden Russell

But the many worlds hypothesis begins with every choice you make now in the present. If you travel back in time to change something, that negates a decision that was made, thereby erasing that choice of a world.

January 8, 2014by nfordkai

Time is not an entity. It is a system of measuring the rate of change of entities. Just like math is not an entity but a system of defining characteristics of things. You cannot travel through a system of measurement; you can only travel through the things being measured.

So when one talks about traveling back (say, 10 years exactly) in time, every particle in the universe would have to revert back to exactly the location, direction of change, etc., that it had at exactly 10 years ago. The laws in our universe do not allow that.

January 8, 2014by J2014A57b

That seems to make sense. On top of that I thought we were dealing with only 6 percent of the universe, you see, like some say my brain—if we change the parameters of things measured by time and known space will we also change those of things we are just learning about and know next to nothing of like dark energy and matter? We may be even changing the state of consciousness itself of which we know so little, even if it is or not embedded in that 94 percent of the universe we almost totally ignore if we really want to think about it. Quantum encryption I hope is safe from this angle at least. Besides Quantum encryption has one gigantic flaw like any encryption- who or what is at either end of what’s encrypted. That would be a hell of a lot easier to compromise.

January 8, 2014by Exovane

Your thinking of Time/Space as a giant pool that must all be changed at once in order to achieve the goal of Teleportation through it. Consider the effect gravity has on the Universe. If you create a point in the universe that has the maximum amount of density possible in a single space, do you shrink the rest of the universe around that object? Only slightly, but yes. What if you could control approximately HOW the universe shrank around the object? Down to energy state of the particles. In effect you have CHANGED the entire universe to whatever state you wanted it to be. Are the calculations incredibly complex and nearly impossible? – yes. But that doesn’t make it any less real.

January 10, 2014by beephatron

People used to think that, but if I start walking, the rest of the universe’s actually changes, very slightly, in my timeframe. If time is a system of measuring, it’s a very fluid and flexible system, that changes drastically depending on the relative velocity of the measurer, and the measured.

January 10, 2014by nfordkai

Time (a system of measuring) is a very fluid and flexible system because it is whatever we define it and agree on it to be, whether it is the speed with which the earth circles the sun or the a rate of radioactive decay. If you travel east, the sun appears to move faster than if you travel west and your “day” becomes shorter. You can even travel back across the international date line where the day becomes “yesterday”, but that does not mean that you are literally travelling back in time to meet yourself, right?

January 11, 2014by beephatron

In absolute time terms you will be younger than everyone else when you get back from your trip, because time moved faster for them than it did for you. How fast time passes for you depends on your velocity. You will believe you travelled into the future. Noone knows if you can travel into the past, or if it even exists.

January 8, 2014by cloudswrest

How about copying some deceased’s biological image from the past, from shortly before he died (or his last neurologically healthy point) and then reinstantiate him in the present. No more need for cryogenic preservation. Just reach back in time and grab a couple snapshots!

January 8, 2014by Gorden Russell

I’ve been talking about that for some time, cloudswrest. You need to scan your loved one’s connectome and take a DNA sample and then bring it all back to clone a new body while installing the old mind.

Years ago I called this a “chron-scanned clone” and I can’t think of anything better to call it now that I’m old.

January 8, 2014by dougw659

If you read Deutsch’s books “The Fabric of Reality” and “The Beginning of Infinity” it will help explain a lot. They are both aimed at ‘non-physicists’, i was able to get through them easily, and have to say there is a lot to like in his theories. Basically, for this issue, what Deustch says (apologies for the layman’s interpretation…) is that there are a huge number (not infinite) of universes where the various states or outcomes of Quantum probability exist, and you can use probability to determine how often specific states occur. So, in the case of the Grandfather killing, in half of the resulting Universes your grandfather would be killed, but in half he would live, perhaps because in those universes you never existed to go back and kill him or maybe you just ‘missed’ when you tried to kill him, etc.

The big idea behind what Deustch proposes is that we have actual real ‘proof’ even today that these other universes exist. That proof can be seen in the interference between multiple quantum state particles (i.e. the photon in the dual-slit experiment is clearly interacting with another photon….so where is that photon?) and in the proven use of quantum computers (as small as that has been to date), where calculations are actually completed using fewer bits that exist in our universe than possible (so where are the bits that perform the calculation?).

January 8, 2014by pablof

Thank you Dougw659 that was very helpful. At least now I have an idea of what the article meant and some reading suggestions! Thanks!

January 10, 2014by beephatron

you could explain wave-particle duality without creating all these universes. It could just be that the psi field randomly coalesces around a point when u measure it like a pool of water forming a dew drop, or some other mundane hidden effect. We just don’t have the tools to come to any conclusions.

.

January 8, 2014by pablof

Since I’m not a physicist I need some help understanding much of this…can someone explain this in layman’s terms?:

“Meaning that, if you kill your grandfather, you do it with only probability one-half, Then, he’s dead with probability one-half, and you are not born with probability one-half, but the opposite is a fair chance. You could have existed with probability one-half to go back and kill your grandfather.”

Thanks

January 8, 2014by Gorden Russell

That’s like the T-shirt with the wanted poster that reads:

“Wanted Schrodinger’s Cat…Dead and Alive”