What Can a Beam Splitter Teach Us About Quantum Technology?

Eve’s Dropped Out

Eve, once the most feared eavesdropper in the cyber world, is outmatched. The rise of Quantum Key Distribution (QKD) and Post-Quantum Cryptography (PQC) has rendered her old tricks obsolete, leaving her with frustration and despair. Her old methods of intercepting and decoding secret communications, which once worked flawlessly, fail miserably against the quantum world.

Determined not to be outdone by this new technology, Eve has no choice but to become the master of quantum technologies herself. But as she delves into quantum science, she feels overwhelmed: “Quantum mechanics, superposition, entanglement, the list is endless! Where can I start? “

A Simple Start: The Beam Splitter

One day, as Eve broke into a quantum lab, her eyes landed on a piece of equipment so small that at first sight, it appeared useless to her. It is a beam splitter, a simple, fundamental optical component. Eve picks it up, inspecting the small cube, and noticing its reflective surfaces.

“Can this teach me anything about quantum technology?” she says.

A beam splitter, she learns, is a basic device that splits a beam of light into two separate paths. Half of the light is transmitted through, and the other half is reflected off at a 90-degree angle. It’s a simple concept, one she can easily grasp, but in the quantum realm, this device opens the door to profound discoveries.

Quantum Random Number Generation (QRNG)

Eve’s first lesson in quantum technology with the beam splitter is in Quantum Random Number Generation (QRNG). She learns that when a single photon (light’s smallest, indivisible unit) hits the beam splitter, the photon can either be reflected or transmitted with a 50 percent chance. Furthermore, until a measurement is done, there is no way to know which path was taken. Using the randomness associated with the photon path, one can create a quantum random number generator.

Figure 1: Optical setup for QRNG [1]. The photon has a 50 percent chance of ending up at a given detector. By associating a 0 and 1 bit when the corresponding detector clicks, a sequence of random numbers is created.

Unlike classical Pseudorandom Number Generators (PRNGs), which use deterministic algorithms to produce sequences of numbers that only appear random, QRNGs are truly random. The randomness comes from the inherent unpredictability of quantum processes, not from an algorithm.

Eve finally understands why her old methods of guessing and brute-forcing random numbers couldn’t break modern cryptographic systems. PRNGs, although complex, remain predictable if you know enough about them. QRNG, on the other hand, provides a level of randomness that is impossible to predict, making cryptographic systems based on QRNG far more secure.

Entanglement with a Single Photon and a Vacuum State

But the beam splitter has more to teach her.

“The single photon has a 50 percent chance to end up in one of the two paths, so nothing gets out of the other one”, she recalls. “And if I do not see anything getting out of one path, I know for sure that my photon got out from the other one: the outputs are perfectly correlated!”.

Formally, as Eve discovers, we say that the quantum state describing this system is entangled. Indeed, considering the so-called vacuum state at the second input port of the beam splitter, the state describing both the one photon state and the vacuum state incident on the beam splitter is entangled: measuring what happens at one detector tells us what will be measured at the other.

By simply understanding how a beam splitter works, Eve has gained insight into some of the most groundbreaking concepts in quantum technology. Her mind now wonders, what about sending two photons, or three, or more, to the beam splitter?

Further reading:

[1] Random number generation white paper, What is the Q in QRNG? ID Quantique, May 2020.

To learn more about the quantum mechanics of a beam splitter, see Chapter 6 of Introductory Quantum Optics, Gerry & Knight.