January 06, 2016

Retrieving information from a black hole using quantum teleportation

Aidan Chatwin-Davies, Adam Jermyn, and Sean Carroll of the California Institute of Technology in Pasadena have found an explicit way to retrieve information from one quantum particle lost in a black hole, using Hawking radiation and the weird concept of quantum teleportation.

Quantum teleportation enables two partners, Alice and Bob, to transfer the delicate quantum state of one particle such as an electron to another. In quantum theory, an electron can spin one way (up), the other way (down), or literally both ways at once. In fact, its state can be described by a point on a globe in which north pole signifies up and the south pole signifies down. Lines of latitude denote different mixtures of up and down, and lines of longitude denote the "phase," or how the up and down parts mesh. However, if Alice tries to measure that state, it will "collapse" one way or the other, up or down, squashing information such as the phase. So she can't measure the state and send the information to Bob, but must transfer it intact.

To do that Alice and Bob can share an additional pair of electrons connected by a special quantum link called entanglement. The state of either particle in the entangled pair is uncertain—it simultaneously points everywhere on the globe—but the states are correlated so that if Alice measures her particle from the pair and finds it spinning, say, up, she'll know instantly that Bob's electron is spinning down. So Alice has two electrons—the one whose state she wants to teleport and her half of the entangled pair. Bob has just the one from the entangled pair.





To perform the teleportation, Alice takes advantage of one more strange property of quantum mechanics: that measurement not only reveals something about a system, it also changes its state. So Alice takes her two unentangled electrons and performs a measurement that "projects" them into an entangled state. That measurement breaks the entanglement between the pair of electrons that she and Bob share. But at the same time, it forces Bob's electron into the state that her to-be-teleported electron was in. It's as if, with the right measurement, Alice squeezes the quantum information from one side of the system to the other.

Chatwin-Davies and colleagues realized that they could teleport the information about the state of an electron out of a black hole, too. Suppose that Alice is floating outside the black hole with her electron. She captures one photon from a pair born from Hawking radiation. Much like an electron, the photon can spin in either of two directions, and it will be entangled with its partner photon that has fallen into the black hole. Next, Alice measures the total angular momentum, or spin, of the black hole—both its magnitude and, roughly speaking, how much it lines up with a particular axis. With those two bits of information in hand, she then tosses in her electron, losing it forever.

But Alice can still recover the information about the state of that electron, the team reports in a paper in press at Physical Review Letters. All she has to do is once again measure the spin and orientation of the black hole. Those measurements then entangle the black hole and the in-falling photon. They also teleport the state of the electron to the photon that Alice captured. Thus, the information from the lost electron is dragged back into the observable universe.

Chatwin-Davies stresses that the scheme is not a plan for a practical experiment. After all, it would require Alice to almost instantly measure the spin of a black hole as massive as the sun to within a single atom's spin. "We like to joke around that Alice is the most advanced scientist in the universe," he says.

The scheme also has major limitations. In particular, as the authors note, it works for one quantum particle, but not for two or more. That's because the recipe exploits the fact that the black hole conserves angular momentum, so that its final spin is equal to its initial spin plus that of the electron. That trick enables Alice to get out exactly two bits of information—the total spin and its projection along one axis—and that's just enough information to specify the latitude and longitude of quantum state of one particle. But it's not nearly enough to recapture all the information trapped in a black hole, which typically forms when a star collapses upon itself.

To really tackle the black hole information problem, theorists would also have to account for the complex states of the black hole's interior, says Stefan Leichenauer, a theorist at the University of California, Berkeley. "Unfortunately, all of the big questions we have about black holes are precisely about these internal workings," he says. "So, this protocol, though interesting in its own right, will probably not teach us much about the black hole information problem in general."

However, delving into the interior of black holes would require a quantum mechanical theory of gravity. Of course, developing such a theory is perhaps the grandest goal in all of theoretical physics, one that has eluded physicists for decades.

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