Glossary

12.1 Quantum key distribution protocols (BB84, E91)

4 min read•july 30, 2024

Quantum key distribution protocols are game-changers in cryptography. They use quantum mechanics to create unbreakable secret keys between two parties. This cutting-edge tech leverages the weirdness of quantum physics to detect eavesdroppers and ensure secure communication.

and are two key QKD protocols. BB84 uses single photons and polarization states, while E91 relies on entangled photon pairs. Both offer unparalleled security, but E91's device-independent nature gives it a unique edge in certain scenarios.

Quantum Key Distribution Principles

Fundamentals of QKD

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  • QKD protocols leverage the principles of quantum mechanics to enable two parties to produce a shared random secret key known only to them, which can then be used to encrypt and decrypt messages
  • QKD is based on the fundamental principle that the act of measuring a quantum system disturbs the system, which can be used to detect attempts
  • Information is encoded into the quantum states of photons, such as their polarization, and transmitted over a quantum channel in QKD
  • The security of QKD relies on the Heisenberg uncertainty principle, which states that certain pairs of physical properties, such as position and momentum, cannot both be measured with perfect accuracy

QKD Protocol Steps

  • QKD protocols typically involve the sender (Alice) preparing and transmitting a sequence of quantum states to the receiver (Bob), who measures the states to obtain a raw key
  • After the quantum transmission, Alice and Bob perform post-processing steps, including sifting, error correction, and privacy amplification, to derive the final secure key
  • Sifting involves Alice and Bob comparing their basis choices and discarding bits corresponding to different bases
  • Error correction uses techniques like the Cascade protocol or low-density parity-check codes to reconcile errors in the sifted keys
  • Privacy amplification, typically using hash functions, reduces any information an eavesdropper might have gained to produce a shorter, secure final key

BB84 vs E91 Protocols

BB84 Protocol

  • The BB84 protocol, proposed by and Gilles Brassard in 1984, is the first and most well-known QKD protocol
  • It uses single photons and two sets of orthogonal polarization states (e.g., horizontal/vertical and diagonal/anti-diagonal) for encoding
  • In BB84, Alice randomly chooses the polarization basis and bit value for each photon, while Bob independently chooses the measurement basis
  • Alice and Bob later compare their basis choices to sift the key, discarding bits corresponding to different bases

E91 Protocol

  • The E91 protocol, proposed by Artur Ekert in 1991, relies on the phenomenon of for key distribution
  • In E91, Alice and Bob share a series of entangled photon pairs and perform measurements on their respective photons using randomly chosen bases
  • They later compare a subset of their measurement results to establish a secure key
  • The E91 protocol has the advantage of being device-independent, meaning its security does not rely on the trustworthiness of the devices used for preparing and measuring the entangled photons
  • Both BB84 and E91 are proven to be unconditionally secure, meaning their security is guaranteed by the laws of quantum mechanics rather than the computational complexity of mathematical problems

Entanglement in E91 Protocol

Quantum Entanglement

  • Quantum entanglement is a phenomenon in which two or more particles are correlated in such a way that the quantum state of each particle cannot be described independently of the others, even when the particles are separated by a large distance
  • In the E91 protocol, Alice and Bob share a series of entangled photon pairs, typically generated by a central source and distributed to them via quantum channels
  • The entangled photon pairs used in E91 are typically in the Bell state, which exhibits perfect correlations in certain measurement bases

Role of Entanglement in E91

  • Alice and Bob perform measurements on their respective photons using randomly chosen bases
  • Due to the properties of entanglement, their measurement results are correlated when they choose the same basis
  • By comparing a subset of their measurement results, Alice and Bob can verify the presence of entanglement and detect any eavesdropping attempts, as measuring one photon of an entangled pair instantly affects the state of the other photon
  • The use of entanglement in E91 allows for device-independent security, as the security relies on the fundamental properties of quantum entanglement rather than the trustworthiness of the devices used

Establishing Secure Keys with QKD

Quantum Transmission

  • The first step in QKD is the quantum transmission, where the sender (Alice) prepares and transmits a sequence of quantum states (e.g., polarized photons) to the receiver (Bob) over a quantum channel
  • Bob measures the received quantum states using randomly chosen bases and records the measurement outcomes, which form his raw key

Post-Processing Steps

  • After the quantum transmission, Alice and Bob perform sifting, where they compare their basis choices over an authenticated classical channel and discard the bits corresponding to different bases, resulting in a sifted key
  • To detect potential eavesdropping, Alice and Bob estimate the quantum bit (QBER) by comparing a randomly chosen subset of their sifted key
  • If the QBER exceeds a certain threshold, they abort the protocol; otherwise, they proceed with error correction and privacy amplification
  • Error correction uses techniques like the Cascade protocol or low-density parity-check codes to reconcile any errors in their sifted keys
  • Privacy amplification, typically using hash functions, reduces any information an eavesdropper might have gained about the key, deriving a shorter, secure final key

Secure Communication

  • Once the final key is established, Alice and Bob can use it for symmetric encryption (e.g., one-time pad or AES) to securely communicate over a classical channel
  • The security of the communication relies on the security of the QKD-generated key, which is guaranteed by the laws of quantum mechanics

Key Terms to Review (17)

BB84: BB84 is a quantum key distribution protocol introduced by Charles Bennett and Gilles Brassard in 1984, which allows two parties to securely share a cryptographic key using the principles of quantum mechanics. This protocol relies on the properties of quantum states and the behavior of photons to ensure that any eavesdropping attempts can be detected, thus providing a high level of security compared to classical key distribution methods.
Bell test experiments: Bell test experiments are a series of tests designed to demonstrate the existence of quantum entanglement and to evaluate the validity of quantum mechanics over classical physics. They involve measurements on pairs of entangled particles, typically photons, and are used to check whether the observed correlations between measurement outcomes can be explained by local hidden variable theories. These experiments have profound implications for our understanding of quantum mechanics and are crucial in applications such as secure communication protocols.
Bell's Theorem: Bell's Theorem is a fundamental result in quantum mechanics that demonstrates the impossibility of local hidden variable theories, showing that the predictions of quantum mechanics cannot be reproduced by any theory that maintains local realism. This theorem establishes a profound connection between quantum entanglement and the nature of reality, indicating that measurements on entangled particles can instantaneously influence each other regardless of the distance separating them.
Charles Bennett: Charles Bennett is a prominent physicist known for his pioneering contributions to the fields of quantum information theory and quantum cryptography. His work laid foundational principles for secure communication methods and the development of heralded single-photon sources and efficient quantum state tomography techniques.
E91: E91 is a quantum key distribution protocol that leverages entanglement to securely share cryptographic keys between two parties. It is based on the principles of quantum mechanics and allows for the detection of eavesdropping attempts, making it a robust method for secure communication. E91 utilizes the concept of Bell states and relies on the correlation between entangled particles to ensure that any interception can be detected by the legitimate users.
Eavesdropping: Eavesdropping refers to the act of secretly listening to the private conversations or communications of others, often with the intent to gain sensitive information. In the context of quantum key distribution protocols, it highlights the vulnerabilities in communication channels and emphasizes the importance of detecting any interference that may compromise the security of transmitted keys.
Error Rate: Error rate refers to the proportion of errors made during the process of communication or data transfer, particularly in the context of information security. In quantum key distribution, the error rate is a critical metric that helps assess the integrity and reliability of the key being exchanged, as it can indicate potential eavesdropping or interference during the transmission.
Gisin et al.: Gisin et al. refers to the influential work of Nicolas Gisin and his colleagues on quantum key distribution (QKD) and its security proofs, particularly regarding the BB84 and E91 protocols. Their research has significantly advanced the understanding of how quantum mechanics can be used for secure communication, highlighting vulnerabilities and the importance of proper security measures against potential eavesdropping.
Key Rate: The key rate in the context of quantum key distribution refers to the maximum rate at which secure keys can be generated between two parties, often denoted as Alice and Bob, while ensuring the integrity and confidentiality of the communication. This rate is influenced by various factors, including the type of quantum key distribution protocol used, the level of noise present in the communication channel, and the efficiency of error correction techniques employed.
Man-in-the-middle attack: A man-in-the-middle attack is a form of cyberattack where an unauthorized third party intercepts and relays messages between two communicating parties, making them believe they are directly communicating with each other. This attack can compromise the confidentiality and integrity of information exchanged between the parties, which is especially critical in secure communications like those used in quantum key distribution protocols. By exploiting weaknesses in these protocols, an attacker can manipulate the key exchange process or even obtain the secret keys.
No-cloning theorem: The no-cloning theorem is a fundamental principle in quantum mechanics that states it is impossible to create an exact copy of an arbitrary unknown quantum state. This concept has far-reaching implications for various aspects of quantum information science and technology, affecting how we understand quantum states, measurements, and entangled systems.
Quantum Entanglement: Quantum entanglement is a phenomenon where two or more quantum systems become linked in such a way that the state of one system cannot be described independently of the state of the other(s), even when the systems are separated by large distances. This unique connection leads to correlations between measurable properties, which challenges classical intuitions about separability and locality.
Quantum Repeaters: Quantum repeaters are devices that enable long-distance quantum communication by overcoming the limitations of distance and loss in quantum channels. They work by using entanglement swapping and purification to extend the range of entangled states, which is crucial for secure information transfer in various quantum technologies. These repeaters play a vital role in applications like quantum key distribution and quantum networks, ensuring that entangled states can be reliably transmitted across significant distances.
Quantum state tomography: Quantum state tomography is a technique used to reconstruct the quantum state of a system based on the outcomes of measurements made on that system. This process provides a complete description of the quantum state, typically represented as a density matrix, and connects various phenomena in quantum optics, such as correlations, interference, and entanglement.
Quantum Superposition: Quantum superposition is a fundamental principle of quantum mechanics where a quantum system can exist simultaneously in multiple states until it is measured. This concept is crucial for understanding how particles like photons and atoms can exhibit behavior that defies classical intuition, allowing them to occupy more than one state at once.
Security Proof: A security proof is a formal verification method used to demonstrate that a cryptographic protocol maintains its security under specified conditions and assumptions. It provides mathematical evidence that the protocol is resilient against potential attacks, ensuring that any information exchanged remains confidential and secure. In the context of quantum key distribution, security proofs are crucial for validating protocols like BB84 and E91, highlighting their ability to withstand eavesdropping and other vulnerabilities.
Single-photon sources: Single-photon sources are devices or systems that emit individual photons on demand, playing a critical role in quantum optics and quantum information science. They enable the production of indistinguishable photons necessary for various applications such as quantum communication, quantum cryptography, and quantum computing. Controlling the emission of single photons is essential for achieving high-performance quantum systems, as it relates to phenomena such as spontaneous emission control, quantum interference, and secure information transfer.
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