From Qubit to Secret Key Rate: The Foundational Concepts of Quantum You Need

You will run into the same seven concepts again and again across my posts on QKD and satellite quantum communication. I am writing them down once here, as a reference point for everything that follows.

Qubit

A classical bit can only be 0 or 1. A qubit works differently: it can exist in a superposition, written as |ψ⟩ = α|0⟩ + β|1⟩, where α and β are complex probability amplitudes. A qubit only settles into 0 or 1 at the moment of measurement. Before that, it genuinely occupies both states at once in a mathematical sense, not merely “unknown but already decided” the way a coin under your palm would be.

Superposition

Superposition is exactly the linear combination of basis states described above. With n qubits, you can represent a superposition of 2ⁿ states at once, and this is the source of the quantum parallelism that algorithms like Shor’s and Grover’s exploit. One point trips people up often: superposition does not mean 2ⁿ computations for free. Reading out a result is still constrained by measurement, so designing a genuinely useful quantum algorithm is a hard problem in its own right, not a simple consequence of having more states available.

Entanglement

When two qubits are entangled, measuring one instantly determines the state of the other, no matter how far apart they are. This is not faster-than-light communication. There is no way to force a measurement outcome to encode a chosen message, so relativity is never violated. What entanglement produces is a non-local correlation that classical mechanics cannot reproduce, and that correlation underlies protocols like BBM92, as well as future distributed quantum networks.

No-Cloning Theorem

This is a rigorous mathematical result: you cannot create an exact copy of a qubit in an unknown state without destroying the original. Why does this matter for QKD? An eavesdropper, conventionally called Eve, cannot secretly copy a key-carrying photon to analyze later. Any attempt to measure or copy it disturbs the original state, and that disturbance leaves a trace that can be detected.

Quantum Key Distribution

QKD is a protocol that lets two parties, conventionally Alice and Bob, generate a shared encryption key whose security rests on quantum physics rather than computational hardness. The best-known protocol, BB84, works like this: Alice sends photons encoded in randomly chosen polarization bases, Bob measures using his own randomly chosen basis, and the two then publicly compare which bases matched, without revealing any measurement outcomes, keeping only the portion of the key where their choices agree.

Quantum Bit Error Rate

QBER is the error rate in the raw key, estimated by publicly comparing a small sample. Channel noise always produces a nonzero baseline QBER. But if Eve is eavesdropping, her own measurement disturbs the quantum state further, pushing QBER abnormally high. This is QKD’s built-in eavesdropping detector: it requires no extra assumptions about what the attacker is capable of.

Secret Key Rate

After discarding the compromised or erroneous portion of the key, through error correction and privacy amplification, what remains is a genuinely usable secret key. SKR is the rate at which this key is produced, measured in bits per second. It depends directly on channel loss and QBER, making it the single most useful number when judging whether a QKD link, satellite or otherwise, is actually viable.

These seven ideas are enough to follow the rest of what I write here: satellite and FSO infrastructure, PQC versus QKD, and channel modeling for the tropics.