Day-23 Quantum Cryptography — Quantum Key Distribution and Secure Communication
Note - Some possible questions from the article and Video are:
- What is quantum cryptography and what are its advantages over classical cryptography?
- What is entanglement and how does it enable secure quantum communication?
- What is the no-cloning theorem and how does it prevent eavesdropping on quantum communication?
- What is the BB84 protocol and how does it work?
- What are some of the challenges and limitations of implementing quantum communication in real-world scenarios?
- How can atmospheric free space channels or satellites be used for quantum communication?
- What are some of the current and future applications of quantum communication?
Quantum Key Distribution (BB84) and Secure Quantum Communication
Quantum key distribution (QKD) is a method of securely transmitting a secret key between two parties, Alice and Bob, using quantum mechanics principles. The key can then be used for encrypting and decrypting messages using a one-time pad or other classical cryptographic schemes. QKD guarantees the security of the key against any eavesdropper, Eve, who might try to intercept or copy the quantum signals. QKD can detect the presence of Eve by measuring the error rate in the key bits.
One of the most famous QKD protocols is the BB84 protocol, proposed by Bennett and Brassard in 1984¹. The BB84 protocol works as follows:
- Alice prepares a random string of bits, A, and another random string of bits, B, that determines the basis for encoding each bit. She uses two non-orthogonal bases, such as the computational basis {|0>, |1>} and the Hadamard basis {|+>, |->}, where |+> = (|0> + |1>)/sqrt(2) and |-> = (|0> - |1>)/sqrt(2). She encodes each bit of A as a qubit according to the following rule: if B[i] = 0, she uses the computational basis; if B[i] = 1, she uses the Hadamard basis. For example, if A = 0110 and B = 1011, she encodes A as |+>|1>|->|->.
- Alice sends the qubits to Bob over a quantum channel. Eve may try to intercept or measure the qubits, but she does not know the basis used by Alice. If she guesses the wrong basis, she will disturb the qubit state with probability 1/2 and introduce errors in the key.
- Bob receives the qubits and measures them in a random basis, chosen independently for each qubit. He obtains a string of bits, C. He does not know which bits are correct and which are wrong, since he does not know Alice's basis.
- Alice and Bob communicate over a public classical channel. Alice announces her basis string B, and Bob announces his basis string D. They compare their bases and keep only the bits where they used the same basis. For example, if B = 1011 and D = 1100, they keep only the second bit of A and C. They discard the rest of the bits.
- Alice and Bob perform error correction and privacy amplification to reduce the error rate and increase the security of their key. Error correction involves exchanging some parity information over the public channel to detect and correct errors in their key bits. Privacy amplification involves applying a hash function to their key bits to reduce their length and eliminate any information that Eve may have gained from eavesdropping.
The BB84 protocol is mathematically secure under two assumptions: (1) the quantum channel is authenticated, meaning that Eve cannot modify or inject any qubits; and (2) the quantum states used by Alice are non-orthogonal, meaning that Eve cannot clone or distinguish them perfectly without knowing the basis.
The security proof of the BB84 protocol relies on two main concepts: (1) the no-cloning theorem, which states that it is impossible to create an identical copy of an unknown quantum state; and (2) the Holevo bound, which limits the amount of information that Eve can gain from measuring a quantum system.
The no-cloning theorem implies that Eve cannot intercept and resend the qubits without introducing errors in Bob's measurements. If she tries to measure the qubits herself, she will disturb their state with probability 1/2 if she guesses the wrong basis. This will increase the error rate in Alice and Bob's key bits.
The Holevo bound implies that Eve cannot gain more information from measuring a quantum system than from knowing its classical description. In other words, Eve's information gain is bounded by Shannon's entropy of Alice's qubits. This means that Alice and Bob can reduce Eve's information by applying privacy amplification techniques, such as hashing or extracting random subsets of their key bits.
The BB84 protocol is one of the simplest and most widely used QKD protocols. It has been implemented in various physical platforms, such as photons, atoms, or ions. It has also been extended and modified to improve its performance and robustness against different types of attacks.
Conclusion
I hope that it helped you to understand QKD and BB84. If you want to learn more about QKD and BB84, you can check out some of these resources and follow me on medium and LinkedIn:
Reference
(1) BB84 - Wikipedia. https://en.wikipedia.org/wiki/BB84.
(2) BB84 - Wikipedia. https://en.wikipedia.org/wiki/BB84.
(3) Quantum Key Distribution and BB84 Protocol | Quantum Untangled - Medium. https://medium.com/quantum-untangled/quantum-key-distribution-and-bb84-protocol-6f03cc6263c5.
(4) Quantum Key Distribution: Modeling and Simulation through BB84 ... - MDPI. https://www.mdpi.com/1424-8220/22/16/6284.
(5) Quantum Key Distribution - QKD - Washington University in St. Louis. https://www.cse.wustl.edu/~jain/cse571-07/ftp/quantum/.
(6) 1 Quantum cryptography: BB84 quantum key distribution. http://www.qi.damtp.cam.ac.uk/files/PartIIQIC/QIC-6.pdf.
