chrome computing is cool but you know want to be extra awesome a quantum internet in fact if you want the first we'll need the latter and the first step to a quantum Internet is quantum cryptography quantum theory may seem like an obscure subject of questionable relevance to the average person but in fact much of our technological world depends on our understanding of the quantum properties of the subatomic universe and soon perhaps very soon we'll be interacting with the weirdness of quantum mechanics even more directly with the coming of quantum computing and the quantum Internet today we're gonna talk about a latter specifically quantum cryptography and quantum key distribution the foundations of the prospective quantum Internet we may come back to quantum computers in detail but for now just a word on why their Advent will demand a quantum Internet the logic gates of a quantum computer exist in a state of quantum superposition of many simultaneous configurations this allows the iterations of certain types of calculation to be done in parallel and vastly more quickly than a classical computer for example a quantum computer can calculate the prime factors of large numbers extremely quickly this is bad because prime factoring is a cornerstone of internet cryptography for the best description of classical internet cryptography on the internet head to infinite series by comparison and my summary will be pathetic but here it is to send encrypted emails or credit card details to parties need to share a cryptographic key this can be as simple as a number that you need in order to unscramble a message the most secure way to do this would be to meet Ridge on a rainy night and swap the key in advance a so-called private key that's impractical so we use public keys the most widespread example is the RSA protocol choose two prime numbers one of which is very large multiply them together to get an even larger number and broadcast that as your public key anyone can then send you an encrypted message by scrambling the message with the public key using a special one-way function it's a mathematical process that can't be undone with the public key only with its prime factors which only you have all of this works as long as the public key can't be easily factorized back into its two primes this is another type of one-way function it's much much harder to factorize large numbers than it is to create them by multiplication in the first place at least as long as we're limited by classical computing once quantum computers can factorize public keys quickly the entire public key system falls apart there are two levels of snooping that encryption should prevent simple eavesdropping and man-in-the-middle attacks eavesdropping is just someone reading some of your message data without you noticing in an M ITM attack someone fully intercepts and controls a communication stream essentially impersonating both parties to each other the latter is especially dangerous because the attacker could potentially control the sharing of a public key inserting their own key in the middle entire new levels of authentication are required to fix this of course you could just meet under a bridge a metaphorical quantum mechanical bridge which allows the sharing of a secure private key enter quantum key distribution this is a scheme to allow the generation of a shared private key which can be used with a traditional encryption algorithm or as a one-time pad which encrypts each message for a one-time use while qkd doesn't really solve the authentication problem it does make undetected eavesdropping impossible qkd is actually two different schemes at least that we'll look at today each highlights a different fundamental weirdness of quantum mechanics the Heisenberg uncertainty principle and quantum entanglement these will be the keys to unbreakable cryptography of the quantum Internet we'll start with Heisenberg which of course we've done episode on already the uncertainty principle tells us that we cannot sort Aeneas Li know the values of certain pairs of properties for example a particles position and momentum these are so-called complementary or conjugate variables another example is the polarization of a photon a quantum of electromagnetic wave polarization defines the direction that its electric and magnetic fields wave you can either measure vertical versus horizontal polarization or diagonal versus other diagonals polarization rectilinear and diagonal polarization are complementary properties measure one perfectly and you lose all information about the other an unmeasured photon exists in a state of may be vertical may be horizontal a superposition of the two with maybe a preference for one or the other it also exists in a superposition of diagonal States you can measure the state by for example sending the photon through a polarizing filter that act forced the photon to make a choice first which basis rectilinear or diagonal then which actual direction so for example pass a randomly polarized photon through a horizontal polarization filter like a polarized sunglasses lens and the photon will either decide is vertically polarized and be blocked or horizontal and get through run that now horizontally polarized photon through a vertical filter and it'll be blocked because it's vertical polarization component has been measured to be zero in fact he is a quantum experiment you can try at home try this with two polarized sunglasses lenses at 90 degrees you'll see that all like gets blocked now place a third lens in between at 45 degrees bizarrely now some light gets through what did you just do well you just switched between different quantum representations of reality and then back again and so invoked the uncertainty principle see any photon coming out of the first filter has its rectilinear polarization perfectly measured which means is diagonal polarization is completely undefined so when it then reaches that Dane or filter it as a 50/50 chance of passing true then is diagonal polarization is perfectly defined making it's rectilinear polarization undefined so it has a 50/50 chance to traverse that third vertical filter this is the basis of one of the first quantum key distribution algorithms developed in 1984 Wyatt Bennett and Prasad and known as BB 84 and no no astromech droids were named after this key distribution protocol which works like this imagine we have Alice and Bob know Albert and Niels who want to decide on a private key for their messages but they don't emit hope it generates a random string of bits zeros and ones and encodes these bits using photons polarized in a particular basis and uses a randomly chosen basis by the rectilinear or diagonal for each of the photons these bits are then sent over an open channel to Niels who then randomly picks at bases of his own for each photon and projects onto that if he uses the same basis that Albert did he gets the same result ie Albert said to one and Niels also gets a one otherwise he gets a random result Elbert sends a one bird Niels will get a one or a zero with equal probability now over the same public channel they randomly pick a subset of those bits and Albert reveals which basis who used for those photons and what he sent if Niels uses a different basis he ignores the result because he knows it'll be random if he uses the same basis he should get the same answer if he doesn't he knows that something was up and this is where the quantum part becomes useful if someone not Eve Verna intercepted these messages which were after all sent on a public channel and did his own measurements he will have disturbed the system in a way that Albert and Niels could detect that's because Verna like meals can only pick a random basis each time on which to project the photons if he picks the right one the photon state is unchanged otherwise it will protect the photon onto a random state meaning that Niels isn't guaranteed to get the same answer as Albert even though they know that they used the same basis in this way Albert and Niels can detect a man-in-the-middle attack they would know that someone had knocked once they have done this test and verified that the information wasn't intercepted they discard the non matching measurements and keep the rest each translates to a bit 1 or 0 depending on the basis choice rectilinear or diagonal this gives a number that becomes their private key which now only they know it's possible for Verna to get lucky and guess the exact same basis as Albert and so not disturb the state but the chance is 1 in 2 to the power of the number of photons which quickly gets close enough to impossible given that Verner only gets one shot this makes eavesdropping down the channel impossible man in the middle attacks are in principle still possible because Verna could impersonate Albert and Niels from the very start but there are classical authentication methods that can make this very difficult so that's B BA for as one path to a secure quantum Internet another way to generate secure key is using quantum mechanics was developed by Artur Eckert in 1991 it uses a similar choice of quantum basis mechanism but with the added thrill of quantum entanglement in fact it looks for violations of bells inequality here we definitely have to direct you to our full episode on quantum entanglement through the details but the super brief summary create a pair of particles with a quantum property that is correlated between the two for example electrons with opposite spin axes or photons with 90-degree polarizations our choice of measurement direction will set the direction for those spin or polarization axes here's where the entanglement comes in choose an axis or basis on which to measure one of those particles say up down the spin or rectilinear polarization and the other particle will also become measured in that basis it will have the opposite when measured in the same basis but even if measured in a different basis - its entangled partner the results of those measurements will be correlated in a way that depends on the choice of measurement bases at both ends this gives us another way to transmit a secure key this time albert creates a set of entangled particle pairs and transmits one half of those to Niels he then chooses a set of bases to measure his own particles the choice of basis represents a set of this Niels chooses a random set of bases to measure the particles he receives because their entangled the outcome of Albert and Niels measurements should be correlated in a very particular way defined by Bell's Theorem if not then they know that the message was tampered with by someone even if they can't say their name but it was probably that burner dude he must have made some measurement and disentangle the particles on roots if bills theorem is satisfied the entanglement must remain intact no tampering occurred Albert and Niels can create a private key based on the basis choices that happen to match just like with BBA for for now the classical internet is still moderately safe or at least its biggest vulnerability is human stupidity which to be fair will probably be the case with the quantum Internet but come quantum computers even the smartest classical security protocols will be compromised then we'll also need a quantum Internet which we now know how to do in theory with quantum cryptography but it's a different matter to actually build one quantum states and particularly entangled States a notoriously fragile and so it's hard to transmit them across large distances we'll show you how to construct a vast planet spanning network of encrypted quantum states real soon your browsing history may one day depend on it and I assume that history isn't just old