Continuing from an overview of BB84, this entry discusses several ways in which BB84 can be realised.

Fig. 1 shows an experimental setup built by IBM [NC10, Box 12.7], where

• 🧔 Bob generates strong coherent states $|\alpha\rangle$ using a 1.3 μm (near infrared wavelength) diode laser and transmits the states to 👩 Alice 10 km away via an optical fibre.
• 👩 Alice attenuates the states to generate approximately a single photon, and subsequently polarises the photon to one of $|0\rangle$, $|1\rangle$, $|+\rangle$ and $|-\rangle$.
• 👩 Alice returns the photon to 🧔 Bob, who measures it using a polarisation analyser in a random basis (either rectilinear or diagonal).

For the setup in Fig. 1,

• The reason for making the photons traverse the optical fibre twice (from Bob to Alice then back to Bob) is to automatically compensate for asymmetry and fluctuations of the medium.
• The polarisation controller (“Pol Cont” in Fig. 1) is for correcting polarisation drifts in the quantum channel [Sud10, p. 111].
• The Faraday rotator (“Faraday Rot” in Fig. 1) effects polarisation through the Faraday (rotation) effect; watch demonstration on YouTube.
• The classical channel of wavelength 1.55 μm is carried over the same optical fibre. Multiplexing of the quantum and classical channels is achieved through the wavelength (division) multiplexers (“WM” in Fig. 1).
• The polarising beamsplitter (also called polarization beamsplitter, or “PBS” in Fig. 1) plays a crucial role, but let us first look at Thorlabs’ Quantum Cryptography Analogy Demonstration Kit (part number EDU-QCRY1), because the accompanying manual [Tho20] is rich with practical information rarely found elsewhere.

Fig. 2 shows a minimalist block diagram for EDU-QCRY1, while Fig. 3 shows a photo of a physical setup realising the block diagram.

Let us study the functions of the PBS in this context:

• For Alice to send a $|0\rangle$ to Bob, a half-wave plate (HWP, also called λ/2 plate, labelled as “Polarization Rotator” in Fig. 4) is physically rotated to 0°.

  To send a $|1\rangle$, the HWP is physically rotated by 45° to achieve a polarisation rotation of 90°.

  In general, for linearly polarised light, polarisation is rotated by a value twice as large as the rotation of the HWP.

• On Bob’s side, a horizontally polarised photon ($|0\rangle$) passes through the PBS, while a vertically polarised photon ($|1\rangle$) gets reflected, as shown:

  Thus, a single-photon detector is needed to detect each state.

• To support both the rectilinear basis (0° and 90°) and diagonal basis (-45° and 45°), the setup in Fig. 4 is extended to the setup in Fig. 6, where Alice’s polarisation rotator now support four angles in total ($|0\rangle$, $|1\rangle$, $|+\rangle$, $|-\rangle$), and Bob gets a polarisation rotator that supports two angles (one for each basis).

  Note Bob still needs only two photon detectors, one for each basis state of the selected basis.

• Eve can be emulated by simply 1️⃣ duplicating the setup for Bob (for intercepting Alice’s photons), and 2️⃣ duplicating the setup for Alice (for “replaying” measured states to Bob); as shown in Fig. 2.

In recent years, satellite-based experiments on BB84 and extensions of BB84 (e.g., decoy-state BB84) had been conducted [LCPP22].

Compared to free space, polarisation is harder to preserve over commercial optical fibres [GK05, Fig. 11.7]. An alternative approach to polarisation is using an interferometer, such as a Mach-Zehnder interferometer; see Fig. 7 and [HIP+21, Sec. 3.2].

References