What is B92 Protocol in Quantum Cryptocraphy?

The B92 protocol is a quantum key distribution (QKD) protocol developed by Charles Bennett in 1992 as a simpler alternative to the earlier BB84 protocol. The aim of B92 was to make quantum key exchange less complex than BB84. It is considered a “minimal protocol” for quantum key generation because it uses only two non-orthogonal states for encoding.

Principles of B92

Unlike BB84, which uses four quantum states (two conjugate bases), the B92 protocol employs only two non-orthogonal quantum states to encode bits. These two states are typically chosen to be two non-orthogonal polarizations of a single photon. For instance, Alice might use a horizontally polarized photon (→) to represent the value 0 and a diagonally polarized photon with +45° () to represent the value 1. Alternatively, the protocol can use polarizations of 90 degrees and 135 degrees. In a more general form, Alice uses states from the set |0⟩, |1⟩, where |0⟩ and |1⟩ are the two non-orthogonal states. For example, |0⟩ and cos θ|0⟩-sin θ|1⟩can be used. A specific example uses phase angles in a Mach-Zehnder interferometer: (φA, φB) = (0, 3π/2) for 0-bits and (φA, φB) = (π/2, π) for 1-bits.

The security of the B92 protocol depends on the principle that non-orthogonal quantum states cannot be perfectly distinguished by any measurement. This means that any eavesdropper (Eve) trying to differentiate between Alice’s two encoding states will certainly introduce errors that can be detected by Alice and Bob.

How Does B92 Protocol Work?

The B92 protocol, for generating a key of length n, generally involves the following steps:

Preparation and Quantum Transmission Phase:

• Alice and Bob both make two private random binary sequences of length m, where m is greater than or equal to n.
• Alice turns her first set of random bits into a set of photons. There are two types of non-orthogonal polarizations that she can use to send a bit 0. These are |0⟩ and horizontally polarized photons. She uses the other non-orthogonal polarization (like |1⟩ or a +45° diagonally polarized photon) to send a bit 1. Her second random bit sequence tells her which polarization to use for each bit.
• Alice sends these photons to Bob one at a time through a quantum link. Bob knows when the photons were sent and can tell if there were any losses.

Measurement Phase:

• Bob has a second set of random bits as well. He picks one of two measurement bases for each photon that comes in based on this pattern. He picked two measurement bases so that one doesn’t align with any of Alice’s encoding states and the other doesn’t align with either of Alice’s encoding states. For instance, Bob might measure in the range of |0⟩ to |1⟩ if Alice sends them.
• If Alice sent |0⟩ and Bob measures in the |0⟩ base, he will never find it, which means his test was a “no.” If he measures in the |1⟩ base, he might find it with a chance, which would result in a random result. In the same way, if Alice sent |1⟩ and Bob measures in the |0⟩ basis, he might get a random result.
• If he measures in the |1⟩ basis, he will never find it.The measures Bob takes for each photon he receives are written down and kept hidden.

Basic Key Extraction Phase:

• Bob announces publicly, over a classical channel, the sequence of measurement bases he used for each received photon, but not the measurement outcomes.
• Alice then tells Bob, through the classical channel, in which case his chosen measurement basis would have yielded a definite outcome (a ‘no’ detection) if there were no noise or eavesdropping. Specifically, if Alice sent |0⟩ and Bob measured in the basis orthogonal to it (|0⟩ ), or if Alice sent |1⟩ and Bob measured in the basis orthogonal to it (|1⟩ ), a detection should ideally not occur.
• Bob takes the bits corresponding to the cases where his test (measurement in the basis orthogonal to one of Alice’s states) passed without a detection as part of the raw key. He reports the positions of these bits to Alice via the public channel.
• For example, if Alice sent |1⟩ and Bob measured in the |0⟩ basis and got no detection, this event indicates that Alice likely sent a ‘1’ (represented by |1⟩), and this bit is added to the raw key.

Error Estimation and Reconciliation:

• Alice and Bob have a raw key after the basic key extraction. They need to figure out how often this key is wrong, which could be because of noise in the quantum channel or someone listening in.
• They can do this by comparing a small group of their raw key bits with everyone. They move on to the next step if the mistake rate is less than a certain level. A lot of errors means that someone is probably trying to listen in, so they might decide to throw away the key and start the process over.

Privacy Amplification:

Even I might have learned some things about the key, even if the mistake rate is reasonable. Privacy amplification uses a hash function on the resolved key to make the final key shorter and safer. This reduces Eve’s information to a very small level.

Advantages of B92 Protocol

• Ease of use: BB92 only uses two quantum states for encoding, which could make the tools needed easier to build than for BB84, which uses four states.
• It is sometimes called the “minimal protocol” for QKD because it uses the fewest non-orthogonal states possible.

Disadvantages of B92 Protocol

• Lower Efficiency: The basic B92 protocol’s efficiency is one of its main flaws. There are many photons that were sent, but they don’t add up to the end key because Bob’s measurement choice wasn’t in line with Alice’s sent state. The basic B92 procedure has been shown to have an effective transfer rate of 25%. This means that 75% of the measurements are thrown away, which results in a very low key rate.
• Security Considerations in Noisy Channels: The B92 protocol is completely safe in a perfect lossy channel, but its safety in noisy channels needs to be carefully looked at. For example, if the original qubit error rate in the channel is higher than 0.5, it’s hard to tell if someone is listening in by just looking at the error rate. If the original qubit error is less than 0.5, however, any spying that raises the noise rate above this level can be found.

Changes and improvements

Several changes have been suggested to the basic B92 protocol to make it work better. One way to do this is to use Pulse Position Modulation (PPM). Each optical pulse in PPM can stand for more than one bit by recording the polarization (horizontal or +45° diagonal) in a certain time slot within a frame of several slots. Then Bob uses the + or ò base to measure, and a finding in a certain polarization and time slot is equal to a multi-bit value. This makes it possible for a higher key rate than with the basic approach.

Security of B92

Fundamental ideas of quantum physics, like how we can’t exactly tell the difference between non-orthogonal quantum states and how trying to measure an unknown quantum state causes chaos, are what make the B92 protocol safe. If someone tries to listen in on the conversation by detecting and measuring the photons, they will always mess up the connections between Alice’s sent bits and Bob’s received bits. If Alice and Bob notice that their shared key is making a lot of mistakes, they can tell that someone is listening in.
There are formal security proofs for the B92 protocol that show it is completely safe from all quantum mechanical threats, as long as certain conditions are met, like having a source that sends out single photons. Photon sources that aren’t perfect could make the security less safe, but self-checking sources and other ideas have been put forward to reduce these risks.

Implementation of B92

Different physical methods can be used to execute the B92 protocol, but polarised photons are often used. A Mach-Zehnder interferometer is another useful tool. In this one, Alice and Bob manage phase modulators to store and measure the quantum states. The chance of finding a photon at Bob’s detector relies on the phase differences that Alice and Bob set. This lets them make a secret key using the phase differences that match their random bits.

B92 Compared to the BB84 protocol

Although B92 is simpler in terms of the amount of quantum states it uses, it is not as efficient in its basic form as BB84, which is a big problem. Even though BB84’s use of two conjugate bases makes it a little more difficult to understand, it has a higher potential maximum efficiency. In order to close this productivity gap, changes and improvements are being made to B92, such as the use of PPM. Both methods are important to quantum cryptography and have been shown to work in the real world.

To sum up, the B92 algorithm uses the properties of non-orthogonal quantum states to make quantum key distribution more theoretically elegant and easier. Even though its basic form isn’t very efficient, improvements and changes are still making it an important protocol for the ongoing development of safe quantum communication technologies.