Compare and contrast different Quantum Key Distribution (QKD) protocols, such as BB84 and E91.

Quantum Key Distribution (QKD) protocols are at the forefront of secure communication, leveraging the principles of quantum mechanics to create unbreakable encryption keys. Two prominent QKD protocols, BB84 (Bennett-Brassard 1984) and E91 (Ekert 1991), differ in their approaches while achieving the same goal of secure key distribution. Below, I'll compare and contrast these two QKD protocols:

BB84 Protocol:

1. Basis of Security:
- BB84 relies on the principle of quantum indeterminacy. It uses the properties of quantum bits (qubits) to detect any eavesdropping attempts during key distribution.

2. Encoding and Measurement:
- Alice, the sender, randomly encodes each qubit in one of two bases (rectilinear or diagonal). She transmits the qubits to Bob.
- Bob randomly chooses one of the two bases to measure each received qubit.
- If Bob chooses the correct basis (matching Alice's), he will obtain the correct measurement result. Otherwise, he has a 50% chance of measuring incorrectly.

3. Key Distillation:
- Alice and Bob publicly compare which bases they used for encoding and measurement. They discard qubits measured in the mismatched bases.
- The remaining qubits form a raw key, which is further processed to create the final shared key using error correction and privacy amplification techniques.

E91 Protocol:

1. Basis of Security:
- E91 protocol is based on quantum entanglement, exploiting the phenomenon of quantum correlations between particles.

2. Entanglement Creation:
- Alice generates pairs of entangled particles (typically photons) and sends one particle from each pair to Bob.
- The entangled particles are prepared in such a way that their measurement results are correlated, even when measured far apart.

3. Measurement and Key Distillation:
- Alice and Bob measure their respective particles using randomly chosen bases.
- They publicly disclose their chosen bases and keep the measurement results private.
- A subset of the measurement results, obtained with matching bases, forms the shared key. Error correction may be applied if needed.

Comparison:

1. Security Basis:
- BB84 relies on quantum uncertainty and the no-cloning theorem, while E91 relies on quantum entanglement. Both exploit distinct quantum phenomena for security.

2. Complexity:
- E91 is more complex as it involves the generation and distribution of entangled particles, which require advanced experimental setups. BB84 is conceptually simpler.

3. Efficiency:
- BB84 is generally more efficient in terms of key generation rate because it doesn't require entanglement generation and is less susceptible to noise and loss.

4. Eavesdropping Detection:
- Both protocols can detect eavesdropping attempts. BB84 does this by comparing measurement bases, while E91 relies on the violation of Bell inequalities to detect non-classical correlations that indicate eavesdropping.

5. Applicability:
- BB84 is widely implemented and more practical for real-world applications, making it the basis for many commercial QKD systems.
- E91 is more suited for fundamental experiments in quantum entanglement.

In summary, BB84 and E91 are both QKD protocols, but they differ in their underlying principles, complexity, and practicality. BB84 is widely used in practical QKD implementations due to its simplicity and efficiency, while E91 is more suitable for experimental settings exploring the nuances of quantum entanglement. Both protocols, however, share the common goal of secure key distribution using the principles of quantum mechanics.