# Quantum, cryptography & communication

by Tommaso Demarie & Ewan Munro, co-founders of Entropica Labs and QWA team members.

Welcome to the first entry of QWA’s focus series on Quantum 2.0. As we mentioned in our previous Quantum Revolutions article, we begin by exploring the interplay between communication, cryptography, and quantum mechanics.

### A birthday tale

Entanglement might well be considered the quintessence (or indeed, the *quantessence*) of the second quantum revolution, Quantum 2.0. But what does entanglement actually mean? Let us use an analogy. Imagine two twins, whose Mum is a quantum physicist with a bit of a weird sense of humor. On their birthday, she decides to bestow them a quantum entangled gift, which we will represent using the standard mathematical description for quantum states:

This funky gift is a *superposition *of two toy cars and two apple pies. The twins, who are by now used to the peculiarity of their mother’s presents, each go back to their rooms excited to open — *and observe* — their gift. The first opens his box, and — surprise! It’s a toy car. He rushes back to his sister, who has not opened her box yet, and who — on seeing her brother’s toy car — immediately yells “Yes, a toy car for me too!”.

Entanglement might well be considered the quintessence (or, indeed, thequantessence) of the second quantum revolution, Quantum 2.0.

This captures the idea of entanglement, as a form of correlations. The children know they have the same present, they just don’t know what it is. At the sight of what’s inside her brother’s box, the sister immediately knows what is inside her own box, without even having to open it.

You might be wondering what is *really* so special about what the Mum did. After all, suppose she knows the boxes each contain a toy car, but all the children know is that the boxes contain the same gift. Is it really so surprising that when the children look inside one box, they immediately know what is in the other? Are the correlations in our story so remarkable?

The key point is that the mother gives the children their gifts in quantum superposition. Even she has no prior knowledge of what the children will find when they open the boxes. This is something that makes quantum entanglement different from correlations in the classical world, such as those described in the previous paragraph. We’ll cover the subtler aspects of entanglement in a future article, so do make sure to follow us!

For the purposes of this article, just think of entanglement as correlations in a system of two parts, like a pair of gifts. When asked the same question (open the box), the system gives the same random answer for each part (two toy cars or two pies). Entanglement, however, is more than a party-trick. It is the basic feature of the second quantum revolution, playing the protagonist in the field of quantum communication.

**Communication and cryptography**

Communication is so ingrained in our behaviour that we often forget its role in society. Every day we exchange information with our parents and friends, and with governments and banks. While most of these exchanges happen publicly, there is information we wish — and sometimes require — to conceal from wicked ears. We can take this argument to the extreme, and realise that countless wars have been won by obtaining vital information about the opponents’ decisions and actions. Equally many have been lost by the incapacity to protect the very same information. For millennia, humans have sought novel ways to protect their secret messages. During the same millennia, other humans have made great efforts to decode and read others’ secret messages. These matters are the subject of *cryptography*.

It is believed that the Roman emperor Julius Caesar employed a simple — by today’s standards — cryptographic technique to protect messages of military value. Each letter of the message was replaced by a different one, positioned a fixed number of places up or down the alphabet. Suppose we shift the English alphabet two positions down, we get the following:

*Plain-alphabet: ABCDEFGHIJKLMNOPQRSTUVWXYZShift-alphabet: CDEFGHIJKLMNOPQRSTUVWXYZAB*

The shifted alphabet (a *cypher* in jargon) is now our reference for writing messages: The encoded message “SWCPVWO KU CYGUQOG!” really means “Quantum is awesome!”, as anyone who knows the cypher can easily decode. We can agree this is no more than child’s play. However, the decryption by the Allies of the Nazi’s cypher machines — Enigma — was instrumental in shortening the second world war, saving potentially millions of lives.

How do communication, cryptography, and entanglement relate to each other? Historically, up to the 1970s, cryptographic schemes were still in their infancy. The basic intuition of cryptography is that sender and receiver share a common key. The sender first uses the key to encrypt the message. She then transmits the encrypted message to the receiver, who decrypts it using the same key. The great challenge is — of course — to share the key. Imagine if every time you wanted to log in to your Gmail account, you had to secretly meet a technician from Google to exchange an encryption key. Sounds awful, doesn’t it? The great revolution of cryptography was the invention of public-key schemes. These schemes allow two distant individuals to generate a secret key remotely, in a way which is believed to be secure even if some eavesdropper is listening through the exchange channel.

Briefly, this is how a public-key scheme works. Alice wants to send a secret message to Bob. She informs Bob, who proceeds to generate a private key and a public key. He retains the private key and sends the public key to Alice. This establishes a secure one-way channel between them. Alice uses the public key to encode her message, sends this to Bob, who then decodes it with his private key. A useful analogy is that Bob sends a box with a padlock to Alice, but he retains the padlock key. Alice puts her message inside the box, locks the padlock, and sends it back to Bob, who then opens it with his key. The assumption is the following: Eve, the eavesdropper who has access to their channel, cannot decode Alice’s message because she cannot efficiently recover the private key from the public key.

The best known such public-key scheme is RSA, named after its inventors Rivest, Shamir and Adleman. RSA is widely used for secure communication across the internet (think of you as Alice and your bank as Bob). The problem with RSA? Its security relies on the hardness of finding the prime factors of a large number, a problem that can be efficiently hacked by a quantum computer. Indeed, numerous *classical cryptographic algorithms* in use today can be broken by an adversary who has enough quantum power. Hence, we have a rather troublesome situation. Ideally, we do not want our communication lines to be under threat — even if the threat has not materialised yet. This is where quantum communication comes into play.

### Quantum communication

Quantum communication is the art of transferring information encoded into a quantum state. The standard ingredient for quantum communication are photons. Photons are the basic units of light: they can be easily generated, controlled, and manipulated with off-the-shelf lab equipment. Also, photons interact very weakly with the surrounding environment. This means they can travel very long distances before losing their quantum information, an ideal condition for future global quantum networks.

The quantum states of two (or more) photons can be entangled. In analogy with the birthday quantum gift, this means that they share more-than-classical correlations, which are revealed after observations of their states. Let’s go back to our birthday twins, and let’s call them Alice and Bob - the protagonists of all standard cryptography tales. Alice and Bob wish to communicate privately (a parent-free communication line) and they now have access to quantum devices (most likely sneaked out of their Mother’s lab!). How can they benefit from quantum resources to generate a secret key?

First, Alice prepares a large number of pairs of entangled photon and sends one of each pair to Bob. Each pair is equivalent to the entangled boxes received for their birthday. At this stage, the secret key only exists in the form of correlations between the two distant twins. To extract it, they each measure their photons and record the results.

What happens if their parents intercept the photons and tamper with them before they reach Bob? If they do so, they unavoidably spoil the strength of the entanglement between the twins. The twins can pick up on this by comparing their measurement outcomes. They don’t need a secure channel for this part of the protocol: they can simply shout their results to each other down the hallway between their bedrooms. If they detect a reduction in the correlations they expect to see, they scream together “Mum, Dad, mind your own business!” and start the protocol again. On the other hand, if Alice and Bob are sure that the parents are not listening, they can use the outcomes of the measurements as a shared secret key.

This protocol is called Quantum Key Distribution (QKD), a cornerstone of quantum communication. The original underlying ideas were introduced by Bennet and Brassard in 1984, and later extended by Ekert in 1991. Unlike RSA, QKD is safe against quantum attacks! And its security is guaranteed by the laws of physics: Quantum takes, but Quantum also gives. Indeed, thanks to QKD, it is now possible to envision a specialised branch of the regular internet, a *quantum internet*, where information is exchanged in a quantum-safe fashion between the nodes.

The first large-scale experimental proof of this vision happened in August 2017. Chinese researchers used a satellite, named Micius after a Chinese philosopher, to transmit encrypted messages between Earth and Space. The underlying technology was QKD, and the communication with the satellite was performed with photons. In September, the same satellite was used to establish a secure video call between Beijing and Vienna. Thanks to QKD, the 75-minute call was completely unhackable (assuming the satellite itself to be uncompromised). Jianwei Pan, the leader of this experimental effort, has predicted that we are 10 years away from a global quantum network, where satellites are used to create secure communication channels between any two points on Earth.

Communication and cryptography are tightly bounded, and improvements in the former usually caused improvement in the latter, and vice-versa.

Another potential usage of the quantum internet is for secure delegated quantum information. Assume a large tech company puts a quantum computer on the cloud — akin to what IBM already does with its Quantum Experience. In this setting, privacy becomes an important concern. Since data is stored and manipulated by another company, users might be wary of sharing confidential information. However, if users can produce and send quantum information to the quantum server, they can do something that is impossible classically. They can instruct the server to perform the desired computation, without revealing any information to it, a scheme known as blind quantum computing.

ID Quantique (IDQ), one of the founding members of QWA, was the world’s first company to launch a commercially available QKD system in 2006. Founded in 2001 as a spin-off of the Group of Applied Physics of the University of Geneva, today IDQ is a leader in quantum-safe cryptography solutions. In February 2018, the Korean communication giant SK Telecom announced a US$65 Million investment in IDQ. Their goal is to develop quantum-powered solutions for wireless communication networks. This contributes to validate the importance of quantum communication to build tomorrow’s safest communication infrastructures.

To conclude, we emphasise that communication and cryptography are tightly bound together, and improvements in one usually result in improvements in the other. Our deeper understanding of the properties of quantum systems completely changed the way we think of cryptography. QKD promises unhackable channels, able to protect our most sensitive information from all sorts of ill-intentioned eavesdroppers.

In two weeks we will continue our focus series on Quantum 2.0, by starting to explore the great promises of quantum computation. With these articles, we are still scratching the surface of quantum information theory. Some of the exotic aspects of quantum mechanics that make QKD secure against quantum and classical attacks include *nonlocality*,* no-cloning*,* *and *monogamy of entanglement*. Explaining the subtleties of these concepts goes well beyond the scope of this entry. The challenge we wish to overcome in future is to come up with engaging, but rigorous, explanations, which help to build an intuition without compromising scientific integrity. Stay tuned, the best has yet to come.

QWA is helping to bridge the gap between quantum and business. The go-to for providing suggestions, feedback and questions is our email address info@quantumwa.org.