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Mathematics Links Quantum Encryption and Black Holes

Mathematics Links Quantum Encryption and Black Holes 1

A proposed mathematical proof that outlines the way information behaves in coded messages may have implications for black holes. The proof suggests that the radiation spit out by black holes may retain information on the dark behemoths.

The research focuses on encoding communications in quantum mechanical systems. But it also connects to a long-standing question for physicists: What happens to all the stuff that falls into a black hole, and is it possible to retrieve any information about the black hole?

A group of researchers from Switzerland and Canada, led by Frédéric Dupuis, showed that it’s possible to encode large messages with relatively small quantum encryption keys, which are keys made up of subatomic particles or photons. But the result implies something else: If someone could pull out information that is encrypted quantum mechanically in a message between two parties, the same feat should work in nature.

Coding with particles

Quantum encryption relies on the idea that any measurement made on subatomic particles changes the particles’ states; quantum mechanics says that these tiny particles are always in a state of uncertainty, until a measurement pushes the particle into one state or another.

The upshot is that subatomic particles can be used as a “foolproof” key that allows only the intended party to decode an encoded message. If anyone tries to decipher the key — by eavesdropping on the message, for instance — the two parties involved would know about it, and could change keys. That’s because any attempt to measure the key would change the information in it.

But this security isn’t absolute; it is possible for an eavesdropper to find out what the key is. With a certain number of quantum bits, or qubits, from the key, which for example might contain a dozen bits, the message can be decoded. Until a person acquires a threshhold number of bits, though, the information in the message is “locked.”

“We can make the amount of information in the [message or the key] right before it unlocks arbitrarily small,” said Jan Florjanczyck, now at the University of Southern California and one of the paper’s co-authors.

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Ordinarily, to make a quantum key completely secure, one would have to use a key that is as big as the message. Since this isn’t practical, encryption schemes all use keys that are smaller than the message itself. For example, in primitive encryption, such as a cipher, the key itself is short, while the message is much longer. (The “pigpen” cipher, for instance, used by children, is 26 characters, each of which substitutes for a letter, while the message itself will be longer).

The short key allows patterns to show up that a decoder can crack. Modern encryption is much more sophisticated, but the principle is similar.

The new paper by Dupuis and his co-authors showed that one can still get good security even with a relatively short key in quantum communications.

Decoding black holes

What does quantum encryption have to do with black holes? The key concept is information.

In quantum encryption, one encodes information in quantum states. Just as one can measure quantum states to decode a message, one can measure quantum states to find out information about an object. And one of the fundamental pieces of quantum information theory is that such information can’t be destroyed.

Black holes suck up matter and emit a small amount of radiation, called Hawking radiation after Stephen Hawking, who first outlined the concept. This radiation takes energy away from a black hole. And with that energy, goes mass, because energy and mass are the same in physics.

But a black hole’s mass comes from all the stuff that has fallen into it. That means the photons emitted as Hawking radiation should carry some information about the black hole, because quantum information can’t be copied or destroyed. For a long time, though, many physicists thought there wasn’t any way to decipher that information, because the black hole had “scrambled” it. The decoding feat would be like trying to reconstruct a building that had been ground to dust. More recently, however, scientists, including Hawking, have changed their minds — the information is there, but one just needs to figure out how to decode it.

That’s where proofs like those by Dupuis and his colleagues come in. If one can “decode” the information contained in the quantum states of photons from a black hole, one can retrieve information about whatever was dropped into the black hole. And if it is possible to encode large messages with small keys, adjusting how much information one needs to unlock the message, it’s also possible to do that with the quantum bits that come out of a black hole.

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“We can only say that such a decoding process exists, not whether it is easy to perform or whether the decoding might happen naturally,” Florjanczyck said.

That is, to gather information about a coffee cup dropped into a black hole last week, for example, one might need to have started gathering photons from the cup back when it formed. That would be the only way to get enough information to do the decoding.

“It’s a very interesting piece of work,” said Wolfgang Tittel, research chair in quantum secured communication at the University of Calgary in Alberta, Canada. “This kind of work links the very large with the very small.”

Original article on LiveScience.


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