How are bits encrypted into quantum states using photon polarization in QKD?
Quantum Key Distribution (QKD) is a cryptographic technique that utilizes the principles of quantum mechanics to securely distribute encryption keys between two parties. One of the key components of QKD is the encoding of classical bits into quantum states using photon polarization. In this process, the quantum states are manipulated to represent the classical bits, and these encoded photons are then transmitted over a communication channel.
To understand how bits are encrypted into quantum states using photon polarization in QKD, let's consider the underlying principles. In quantum mechanics, the polarization of a photon refers to the orientation of its electric field oscillations. It can be described using different bases, such as the rectilinear basis (horizontal and vertical) or the diagonal basis (45° and 135°).
To encode a classical bit (0 or 1) into a quantum state, we can use the rectilinear basis. For example, let's say we want to encode a bit 0. In this case, we can choose to encode it as a horizontally polarized photon. Conversely, for bit 1, we can encode it as a vertically polarized photon. Therefore, the classical bits are mapped to specific polarization states.
In QKD, the sender (Alice) prepares a stream of photons with randomly chosen polarizations corresponding to the classical bits she wants to transmit. For example, if Alice wants to send the bit sequence 0101, she would prepare a stream of photons with horizontally polarized, vertically polarized, horizontally polarized, and vertically polarized photons, respectively.
Next, Alice sends these encoded photons to the receiver (Bob) through a quantum channel, which could be an optical fiber or free space. During transmission, the photons may interact with the environment, leading to disturbances or potential eavesdropping attempts. However, the laws of quantum mechanics ensure that any eavesdropping attempts can be detected by Alice and Bob.
Upon receiving the photons, Bob measures their polarization using a basis of his choice. He can choose either the rectilinear basis (horizontal/vertical) or the diagonal basis (45°/135°). The choice of basis is important for the subsequent key generation process.
After Bob measures the polarization of each photon, he informs Alice about the basis he used for each measurement. Alice, in turn, reveals the basis she used to encode each photon. Both Alice and Bob discard the measurement results where they used different bases. This is known as the sifting process.
Once the sifting process is complete, Alice and Bob are left with a subset of photons that were measured in the same basis. These photons form the basis for the subsequent key generation process. By comparing a random subset of their measurement results, Alice and Bob can estimate the error rate caused by noise and potential eavesdropping.
To ensure the security of the generated key, Alice and Bob perform an information reconciliation process, where they use error correction codes to correct for errors. This process allows them to obtain a final shared secret key that is secure against eavesdropping attempts.
Bits are encrypted into quantum states using photon polarization in QKD by mapping the classical bits to specific polarization states. The sender (Alice) prepares photons with randomly chosen polarizations corresponding to the classical bits and transmits them to the receiver (Bob). Bob measures the polarization of the received photons using a basis of his choice. Both Alice and Bob then perform the sifting process to discard measurement results where different bases were used. The remaining photons are used for key generation, error estimation, and subsequent information reconciliation to obtain a secure shared key.
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