CS260 Study Guide
Unit 9: Quantum Key Distribution
9a. Explain photon polarization
- What is a photon?
- What is wave polarization?
- What is photon polarization?
It is well-known that light can be described as an electromagnetic field exhibiting wave properties such as interference, refraction, and diffraction. The plane wave description of electromagnetic waves, such as light, allows the amplitude to be polarized along a certain direction. Birefringent materials cause a wave velocity to be dependent upon the direction of propagation. They can be used to control the polarization orientation. The smallest indivisible quantum packet of light is known as a photon implying that light can exhibit both wave-like and particle-like properties depending upon what property is being measured. A photon can be created when an electron orbiting an atomic nucleus drops from a higher energy level to a lower energy. The difference in energy between the two levels dictates the frequency of the electromagnetic radiation given off by the energy level transition. Finally, since waves can be polarized, so can photons. Photon polarization means that photons possess a polarization orientation. When the intensity of a light beam is reduced to a single photon, it retains the properties of the original wave. You should be familiar with wave-like and particle-like properties of photons as they are central to quantum communications concepts.
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9b. Describe the security of quantum communications
- What are some relevant properties of quantum objects?
- How can photons be used in quantum communications?
- What is the Heisenberg uncertainty principle?
The Heisenberg uncertainty principle, which states that we cannot know both the position and speed of a particle, such as a photon or an electron, with perfect accuracy, places limits as to when the simultaneous measurement of observable quantities can take place. For example, in contrast to a classical object such as a baseball, it is impossible to simultaneously measure the position and the momentum of a quantum object such as an electron. The implication is that a measurement of a quantum system cannot take place without affecting the system. This principle lies at the heart of quantum communications since it can be known if an eavesdropper is listening on the channel.
Another important principle is that of probabilistic quantum measurement, where measurement outcomes of a quantum system are inherently probabilistic. Recall that a beam splitter is a material that can separate light waves into two beams, one that is horizontally polarized and one that is vertically polarized. If a single photon polarized at 45 degrees encounters the beam splitter, since the photon is indivisible, it will randomly choose one of the two paths. This means there is a 50-50 chance of the photon emerging from the beam splitter as either horizontally or vertically polarized. You should be aware that quantum measurements can affect the measurement statistics in a way that can reveal the presence of an eavesdropper. This fact is also relevant to quantum communications and especially for developing protocols for quantum key distribution (QKD), the process of applying the quantum properties of photons to distribute keys between two parties.
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9c. Identify features of the BB84 protocol
- What is the BB84 protocol?
- How is QKD performed using the BB84 protocol?
- What key quantum principles are used in the BB84 protocol?
The BB84 protocol is one of the earliest approaches to performing QKD using photon polarization. The quantum principles most central to this protocol are probabilistic quantum measurement and the Heisenberg uncertainty principle. You should be familiar with "bra-ket" notation for describing photon states. For example, |0> or |H> could represent a horizontally polarized photon. In the BB84 protocol, a photon state can be written as
cos š|0> + sin š|1>
where š is the polarization angle.
Using the BB84 protocol, Alice and Bob can create a shared key, which is as follows:
- Alice sends Bob a string of single photons whose polarization is randomly chosen from the set {H,V,45, 135}. The sequence of these polarizations is kept secret.
- Bob makes a measurement of each photon using either an H-V polarizer or a 45-135 polarizer, records the result of the measurement, and keeps these measurements secret.
- Bob publicly announces the type of measurement (H-V or 45-135) made on each photon.
- For each photon, Alice tells Bob which measurement type aligned with the original photon sent.
- Bob and Alice keep the measurements that were aligned and create a binary sequence for the key based upon the measurement (for example, H ā 0, Vā1, 45ā0, 135ā1).
An eavesdropper with measurable probability can be detected because the expected ratio of aligned measurements to misaligned measurements would be altered. If an eavesdropper is detected, then throw out the key.
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9d. Describe the current state of QKD
- What quantum principles beyond those of BB84 can be applied to QKD?
- What are some other protocols that have been proposed?
- Why have these protocols been developed?
Probabilistic measurement and the Heisenberg uncertainty principle are central to secure quantum communications and QKD. Another useful concept is entanglement, where two photons exist in a state where one can always affect the other. For example, assume one photon is in an H state and the other is in a V state. If the states are entangled, this means that, no matter how far apart the photons are, an H measurement of one directly implies a V measurement of the other and vice versa. The E91 (Eckert91) protocol is an approach to QKD that directly applies entangled photons as part of the key verification process between sender and receiver. It is considered to be more robust than the BB84 approach. The COW (Coherent One-Way) protocol is an approach to QKD that applies entanglement so that a receiver does not need to settle photon statistics with the sender. The name one-way implies that the receiver can perform a security check based solely on entanglement statistics. These entanglement protocols were developed to address the security shortcomings of BB84. More sophisticated protocols are on the horizon as this field develops from its embryonic state.
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Unit 9 Vocabulary
This vocabulary list includes terms you will need to know to successfully complete the final exam.
- BB84
- beam splitter
- birefringent
- COW
- E91
- entanglement
- Heisenberg uncertainty principle
- photon polarization
- probabilistic quantum measurement
- quantum key distribution (QKD)