In the previous post, we discussed about the concepts of quantum encryption and black holes. We also talked about how we do cryptography in the subatomic world. This blog post is a continuation of that discussion. As the title suggests, the overarching theme is the relationship between quantum encryption and black holes. Let’s continue talking about it then. Although quantum encryption looks extremely robust in theory, how practical is it? What do we know about its security and how is it related to black holes? We know that nothing can escape from black holes, so we need a way to understand more about the black holes.
Is this completely secure?
Unfortunately, this security isn’t absolutely secure! It is possible for an eavesdropper to find out what the key is. With a certain number of quantum bits (called qubits) from the key, which might contain a few bits, the message can be decoded. Until a person acquires a threshold number of bits, though, the information in the message is locked. We can make the amount of information in the message or the key arbitrarily small right before it unlocks.
Ordinarily, to make a quantum key completely secure, one would have to use a key that is as big as the message. But that’s not very practical! Hence the encryption schemes 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 short key allows patterns to show up that a decoder can crack. Modern encryption is much more sophisticated, but the principle is similar. However, a new paper by Frederic Dupuis and his co-authors showed that one can still get good security even with a relatively short key in quantum communications.
What does quantum encryption have to do with black holes?
Now that we understand what black holes are and how quantum encryption is done, let’s see how they are related. The key concept that relates quantum encryption and black holes is “information”. A group of researchers, lead by Dupius, showed that it’s possible to encode large messages with relatively small quantum encryption keys. These keys are made up of subatomic particles or photons. But the result implies something else i.e. if someone could pull out information that is quantum encrypted in a message, the same thing should work in nature as well.
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. One of the fundamental pieces of quantum information theory is that such information can’t be destroyed. This actually reminds us a little bit about the law of conservation of energy! Black holes suck up matter and emit a small amount of radiation. This is called Hawking radiation, named after the famous physicist, Stephen Hawking, who first came up with 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. The equation that relates mass and energy is probably one of the most famous equations in the world i.e. E = mc², given by Albert Einstein.
Where is the information about the black hole?
Before proceeding, we need to ask ourselves a simple question: Where does a black hole’s mass come from? It has to come 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, many physicists thought there wasn’t any way to decipher that information, because the black hole would have “scrambled” it. Scrambling is actually a concept in communication where a message is encoded to make it unintelligible to an unequipped receiver. The decoding process would be like trying to reconstruct an intricate glass sculpture that had been broken down to dust. More recently, physicists have changed their minds. The information is there, but one just needs to figure out how to decode it.
That’s where proofs like these come in. This is the proof we referred to earlier where we can encode a message with a relatively small key. 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. If it is possible to encode large messages with small keys, thereby 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. We can only say that such a decoding process exists, but we cannot say whether it is easy to perform or whether the decoding might happen naturally.
For example, to gather information about a spoon dropped into a black hole last week, one might need to have started gathering photons from the spoon back when it was formed. Not exactly a trivial process! But that would be the only way to get enough information to do the decoding. The proof and the direction in which it’s heading is a very interesting piece of work. This kind of work links the very large world of our universe with the very small world of subatomic particles. It looks very promising and can potentially unlock so many things about our understanding of the universe. Let’s see where it goes!