How does the BB84 protocol differ from the six state protocol in terms of the number of bases used for measurement?
The BB84 protocol and the six state protocol are two widely used quantum key distribution (QKD) protocols that ensure secure communication by exploiting the principles of quantum mechanics. While both protocols aim to establish a shared secret key between two parties, they differ in terms of the number of bases used for measurement.
The BB84 protocol, named after its inventors Charles Bennett and Gilles Brassard, utilizes two non-orthogonal bases, typically denoted as rectilinear (|0⟩, |1⟩) and diagonal (|+⟩, |−⟩), for encoding and measuring qubits. In this protocol, the sender randomly chooses one of the two bases for each qubit and prepares it accordingly. The receiver also randomly selects one of the two bases for measurement. If the sender and receiver use the same basis, the measurement outcome will be deterministic. However, if they use different bases, the measurement outcome will be random. By comparing a subset of their measurement outcomes, the sender and receiver can estimate the error rate caused by eavesdropping and discard suspicious bits. The remaining bits can be used as a shared secret key.
On the other hand, the six state protocol, also known as the B92 protocol, was proposed by Artur Ekert. Unlike the BB84 protocol, the six state protocol employs three non-orthogonal bases, denoted as rectilinear (|0⟩, |1⟩), diagonal (|+⟩, |−⟩), and circular (|↺⟩, |↻⟩). The sender randomly chooses one of these three bases for each qubit and prepares it accordingly. Similarly, the receiver also randomly selects one of the three bases for measurement. If the sender and receiver use the same basis, the measurement outcome will be deterministic, while different bases yield random outcomes. By comparing a subset of their measurement outcomes, the sender and receiver can estimate the error rate and establish a secure key.
To summarize, the BB84 protocol uses two non-orthogonal bases (rectilinear and diagonal) for qubit measurement, whereas the six state protocol employs three non-orthogonal bases (rectilinear, diagonal, and circular). The additional circular basis in the six state protocol provides an extra dimension for encoding and measuring qubits, potentially enhancing the security of the protocol.
The BB84 protocol and the six state protocol differ in terms of the number of bases used for measurement. The BB84 protocol uses two non-orthogonal bases, while the six state protocol utilizes three non-orthogonal bases. These differences contribute to the distinct security properties and performance characteristics of each protocol.
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