Secure Quantum Communications 101 by Dr. Urbasi
As a community, QuantumComputingIndia is committed to learning through theory and practise and one such enabler is our #FaciltatorSeries where we invite exceptional academicians and Practitioners to share their knowledge with the community. As a part of this ongoing series we had Dr. Urbasi with us last saturday and this is quick log of the knowledge shared by Dr. Urbasi around Qauntum Communications and the state of such research initiatives in India.
Quantum entanglement in the lab using photons
The photon is a type of elementary particle. It is the quantum of the electromagnetic field including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force.
When photons are emitted from the source and they come out in the form of cones, in pairs and that’s why they are called pair photon sources.
For an entangled photon source of this kind, you don’t know if the photon is on this cone or its partner cone. This particular intersection that you can see in the figure where you have the entangled protons is called quantum entanglement.
Entanglement measures and studies of entanglement dynamics
This is the reason it can be said that entanglement is more than the sum of parts
This is how you can create entanglement in the lab using photons .
These form an entangled pair. One is h then the other is v, but you can’t know which ones they are . so we name it the hv plus minus vh state. Ultimately, we can find out the state of the photon through what is called quantum state tomography.
Need for quantum cryptography and how it can affect the RSA encryption method
We are doing things online now more than ever and a growing concern is the security of these transactions. The current communication techniques can be jeopardized by certain advances in quantum computing.
We need to counter classical cryptography with what is called quantum cryptography to overcome these vulnerabilities.
In any communication, what essentially happens is that there is a sender, a receiver and an exchange of a message. This message is encrypted using a key which is available to the receiver who uses it to decrypt the message. If we have an eavesdropper in the middle who can find out the key, the transactional security is jeopardised.
The amount of time it takes to crack a certain problem tells you about what hardness class it belongs to. Quantum cryptography can crack even some of the hardest of the computations in a short, feasible time range.
The unbreakability of the RSA protocol is based on the mathematical complexity of factoring large numbers. The typical RSA is thousand twenty four or four thousand ninety six bits long.
Today’s hard problem can be solved tomorrow using brute force attack so we need new algorithms for classical cryptography or new technology that is future secure.
This brings out the need for quantum cryptography where security is based on laws of nature or laws of physics and not on the mathematical complexity of a problem. These classical encryptions can be broken either by new algorithms on existing devices or by new devices which are getting built at a very fast rate .
How does quantum mechanics protect information?
Measurement disturbs the signals on an average.
If the signals are non orthogonal, the adversary cannot ascertain which one it is.
This helps because the unknown quantum states cannot be cloned by the adversary or the eavesdropper. Quantum correlations can be used to protect information.
The different ways in which quantum key distribution can be done
1.Without using Entanglement (insert image? 31:01) example: BB84 protocol
In this protocol we do not use entanglement but we use the uncertainty principle or the no cloning theorem for non orthogonal states to protect the information.
2.With Entanglement example: E91 protocol
In this we use entanglement to protect the information.
BB84 protocol
The BB-84 protocol is perhaps the most well-known quantum key distribution protocol because it’s the first one it was established in 1984.Orthogonal states are 0 & 90 and 45 & 135 the non-orthogonal states are 45 & 90 or 0 & 135 or 45 & 0.
Let us see how this works: We have a single photon source and two characters namely, Alice and bob.Now the single photon source has emitted a certain photon and this is encoded with the basis information and this is done randomly.Alice does this encoding randomly and selects one of these four possibilities and encodes that on the photon and this is what she stores.Now Bob also has a random selection of bases by which he decodes it and then he measures it,so right now Alice is creating it randomly and bob is measuring it randomly therefore this leads to the case where the decoded message might be incorrect as the measurement is random.
In order to solve this we use a classical channel where Alice and Bob will actually share their basis information and so by sharing it they now know where they had matched and where they had not and this is called Basis Choice Sharing and then finally you have what is called the raw key.
Alice’s operations:
- Prepare single photon different types of sources including weak coherent pulse (WCP) source, spontaneous parametric down conversion (spdc)
- Random selection of polarization bases for each photon between rectilinear and diagonal basis and then record the time stamps.
Bob does the reverse operation that is he does random selection of polarization bases for each photon,records time stamps and polarization state for detected photons
So together alice and bob’s operation send time stamping and bases selection for each photon over classical channel compare this and consider only those events where choices matched and discard the rest. So far Alice and Bob have shared a common set of binary data.
In the beginning we had the raw key. After basis information exchange we have what is called the sifted key now how do we make the key secure? We use a concept called a sacrificial key.
Sacrificial key:Statistical test on a subset of data where the bit values are also announced (not just basis).Compare actual bit values.If they are the same, then one can conclude that the rest of the key follows similar logic and Alice and Bob share the same data.
The ideal situation is when Alice and Bob are able to send these messages on a secure channel by sharing the key but in reality there will be a third person say Eve who will be eavesdropping and this situation where we have a third-party listening in is called as an Attack situation so in order to overcome this we use message authentication and use the concept of seed randomness. In message authentication there is a secret key shared initially between Alice and Bob. This involves hashing and tagging.
Timing is very essential here so do quantum key exchange and immediately after that do authentication therefore by doing this even if Eve manages to break the authentication later it does not matter since the secure key exchange is already done.
Implications of errors:
- Alice and bob do not share the same secret key this will have an adverse effect on the message being transmitted.
- Error is a signature of an adversary trying to intercept signals
- Worst case scenario: All errors due to adversary
So essentially the critical elements to be developed in QKD:
- Quantum source
- QKD simulations
- QKD protocol
- Sifting
- Privacy amplification
- Error correction
- Secure key.
Similarly there is the b92 protocol which is also a prepare and measure protocol so b92 is essentially a modified version of BB84 the only difference here is that instead of using four bases we use two bases.
Need for entanglement:
Let us have 3 characters namely A,B and C.C is emitting these two correlated photons(green and red) towards A and B and till they reach A and B we don’t know for sure whether it’s the red or the green which they are receiving so A asks B “What color did you get?” B says,”No idea”. Then A declares that he has Green and B deduces that his must be Red since A had green.This is the general idea where once we decode at Alice’s end then we can know what Bob has too.
Quantum Entanglement = AB + AB / √2
Entanglement is something which makes things possible which otherwise would not exist; it is like an Orchestra where only when all the instruments are being played together there is a symphony of sounds that make wonderful music. Entanglement is more than the sum of parts it only makes sense when its together; it does not give any meaning when it is written as a separate state; therefore it is like a Quantum Orchestra.
Why is entanglement necessary in quantum key distribution?
We are actually using certain components which we are buying since we can’t make all the elements ourselves and when we buy it from someone we have implicit trust on this manufacturer but how much can we trust our devices? What about security? Vulnerability which may be introduced at the device level itself. Hence we need QKD which is device independent. Entanglement based QKD is the only known route towards device independent QKD and longer distances are also possible through entanglement based swapping repeaters.
Long Distance Quantum Communication:
Quantum Experiments using Satellite Technology (QuEST) is an ongoing project at RRI and India’s first satellite based QKD project where we have a ground station here and we have a ground station somewhere else and we use a satellite as a trusted node to establish a quantum link between these two ground stations.
But why satellites for QKD?
Because there are distance limits for quantum channels. When we are on the ground Alice and Bob are communicating by exchanging a key. The typical distance that you can reach with ground based QKD is around 100 kilometers and demonstrations could happen up to a maximum of 300 kilometers. So what happens when we go beyond that? Beyond this distance it becomes a problem and is not very viable to continue doing this by line of sight and that is why there is a natural limit to ground based free space QKD. You can use fibers but then fibers also have losses. So if you want to go to longer distances you need to do something different and so one of them is trusted repeaters the other is by using satellites.
Quantum Relays,memories and Repeaters:
Like a relay race where the baton is being passed onto the next person until the last person finishes the race. The idea of swapping the baton is used in entanglement and is referred to as entanglement swapping. Let us take an entangled photon source one and an entangled photon source two and this source is creating a pair of entangled photons one and then the second source is creating another pair let’s call it three and four. These entangled photons are apart by a certain distance now we make two and three meet by bell state measurement and by doing this one and four become entangled which means we have actually increased the distance so instead of just one-two and three-four we have one-four which have been entangled. This is called a quantum relay.
Now we cannot take this quantum relay beyond a certain point we need to put in some concept of a memory in between and that is the idea of a quantum repeater so you have a relay plus a memory that will give you the repeater. The idea would be to combine repeaters and satellites together and form the global quantum network or the global quantum internet.
Satellite is a trusted node that exchanges a key with one ground station and then moves to a different one exchanges a key there and then by performing certain operations on the key and we can have the conversation between A and B linked with a quantum key. We can either have the source in the satellite and distribute the two photons between two receivers or we can have the sources on the ground and these are called uplink and downlink.
Outlook of the QuEST project
- Experimental implementation of SPDC based entangled photon source.
- Demonstrate in-lab entanglement-based QKD protocol
- Demonstrated a long distance free-space entanglement-based QKD within campus and test its robustness against atmospheric turbulence.
qkdSim
It is a simulation toolkit for QKD that we have invented at RRI which considers realistic imperfections and its performance analysis. In order to implement a cost effective QKD protocol we have certain requirements
- Quick and precise simulation of physical processes considering realistic experimental imperfection.
- Simulation of single photon source, detection module and the background noise in more details.
- Generalization and applicability to all existing protocols
In order to decide which components to buy we can run a simulation to figure out what is it that we might get as the answer to our key rate as well as the QBER most of the simulation toolkit never bothers about the fact that experiments are not ideal and therefore give results which are not accurate. Our qkdSim considers all the imperfections and essentially fills a gap which is very important for a person who wants to do the experiment or develop this technology and then if I tell you that my key rate is 126kbps a qkdSim is going to predict it in that order. qkdSim helps in quick accommodation and testing of these techniques by enabling simulation of qkd protocols considering physical process models realistic imperfection and experimental non-idealities.
QKD protocol can be broken up into different modules which would be used to simulate and so we have followed the agi-fall software model so you have the waterfall structure where you bring in some agility in some of these modules so that with new imperfections you can just include that without having to change.
In the area of quantum communications we have India’s first project on satellite-based QKD we also have a project on quantum communications using integrated photonics. This is a different domain instead of the long distance which of course is a thrust area we also want to be useful to us common people . If we want to use QKD personally then we will be relying on something which is small and portable and so that is the idea of chip based QKD which we are investigating with our Italian collaborators under this program and we are also working on quantum teleportation under the quantum enabled science and technology program of the department of science and technology.
The UN have a focus group for quantum information technology for networks and are working on development of standards for QKD so that if we claim something whether that is actually meeting a certain global standard or not. Our facilitator Dr. Urbasi, is an invited member of this focus group from India.
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