If you have visited our home page, you may have noticed something unusual for a software company’s website: a working quantum simulation. It sends the word “QuanSystem” letter by letter using two real quantum communication protocols, superdense coding and quantum teleportation, and shows what happens to the qubits along the way.
This article explains the ideas behind that simulation in plain language: what a qubit is, what entanglement really means, and what quantum computers are and are not good at today.
Bits and qubits
A classical bit is either 0 or 1. Everything your phone or laptop does is built from enormous numbers of these.
A qubit is different. Its state is described by two amplitudes, one for 0 and one for 1. Amplitudes are complex numbers, so they have both a size and a phase. When you measure the qubit, you get 0 or 1, with probabilities equal to the squared size of each amplitude. After measurement, the qubit is whatever you measured.
Superposition
Before measurement, a qubit can be in a superposition, a combination of 0 and 1 at the same time, such as equal amplitudes for both. It is tempting to say the qubit is “both 0 and 1”, but that undersells the important part: amplitudes can interfere. Like waves, they can add up or cancel out. Quantum algorithms are carefully designed sequences of operations that make wrong answers cancel and right answers reinforce.
The Bloch sphere
A single qubit’s state can be drawn as an arrow, the Bloch vector, pointing to a spot on a sphere. North pole is 0, south pole is 1, and every point in between is a different superposition. Our simulation draws this vector for each qubit. Watch it when qubits become entangled.
Many qubits and the state vector
With two qubits there are four basis states: 00, 01, 10 and 11. The full description, called the state vector, has one complex amplitude for each. Three qubits need eight amplitudes, ten qubits need 1,024, and every extra qubit doubles the count.
That doubling is why large quantum systems are so hard to simulate on ordinary computers. Our simulation uses only two or three qubits, which is small enough to compute exactly in your browser, amplitude by amplitude.
Quantum entanglement explained
When two qubits are entangled, their joint state cannot be described as “qubit A is in this state and qubit B is in that state”. Only the pair has a definite description. The four simplest and most important entangled states are the Bell states:
| Bell state | State | What you see when measuring |
|---|---|---|
| Φ+ (phi plus) | (00 + 11) / √2 | Always equal results |
| Φ− (phi minus) | (00 − 11) / √2 | Always equal results, opposite phase |
| Ψ+ (psi plus) | (01 + 10) / √2 | Always opposite results |
| Ψ− (psi minus) | (01 − 10) / √2 | Always opposite results, opposite phase |
Measure one qubit of a Φ+ pair and you get a random 0 or 1. Measure the other and you get the same value, every time, however far apart they are.
Why the Bloch vector disappears
Here is the surprising part you can see in the simulation. If you look at just one qubit of a Bell pair, by computing its reduced density matrix, its Bloch vector has length zero. It sits in the centre of the sphere. On its own, that qubit is completely random. All the information lives in the correlation between the two qubits, not in either of them.
The simulation also shows concurrence (C), a standard measure of entanglement. It is 0 for unentangled qubits and 1 for a maximally entangled pair like a Bell state.
No faster-than-light messages
Entanglement creates correlations, not communication. Whoever measures first gets a random result and cannot choose it, so nothing they do can send a message to the other side. To use entanglement for communication, you always need an ordinary channel as well. The two protocols below show exactly how.
Superdense coding: two bits in one qubit
Suppose Alice and Bob share a Bell pair in advance, one qubit each. Alice wants to send two classical bits.
- Alice applies one of four operations to her qubit, depending on the two bits.
- She sends her single qubit to Bob.
- Bob now holds both qubits and performs a Bell measurement, which tells him which of the four Bell states he has, and therefore which two bits Alice meant.
| Alice’s bits | Operation on her qubit | Resulting Bell state |
|---|---|---|
| 00 | Nothing (I) | Φ+ |
| 01 | Bit flip (X) | Ψ+ |
| 10 | Phase flip (Z) | Φ− |
| 11 | Both (X then Z) | Ψ− |
This is a common convention. In our simulation, each letter of “QuanSystem” is turned into bits, and those bits travel two at a time, with one qubit carrying two classical bits.
The Holevo bound
Is this cheating? No. The Holevo bound says that one qubit, on its own, can reliably carry at most one classical bit. Superdense coding only reaches two because Alice and Bob shared entanglement beforehand. Count the pre-shared qubit too and the books balance: two qubits, two bits. Entanglement is a resource you can spend, not free bandwidth.
Quantum teleportation: one qubit with two bits
Teleportation runs the trade the other way. Alice has a qubit in an unknown state and wants Bob to have it. They again share a Bell pair, so three qubits are involved.
- Alice performs a Bell measurement on her unknown qubit together with her half of the pair.
- She gets two classical bits and sends them to Bob over an ordinary channel.
- Depending on those bits, Bob applies X, Z, both or neither to his qubit, which now holds exactly the original state.
Three points matter:
- Nothing travels faster than light. Until Bob receives the two classical bits, his qubit is just random noise to him.
- The original is destroyed. Alice’s measurement erases her copy. Quantum mechanics forbids copying an unknown state (the no-cloning theorem), so teleportation moves a state, it does not duplicate it.
- Nothing material moves. What travels is the state, the information, not matter.
In the simulation, two classical bits carry each qubit state across, and the fidelity (F) readout shows how closely Bob’s qubit matches the original. With a perfect channel it is 1.
Noise and decoherence
Real qubits are fragile. Heat, stray fields and imperfect control disturb them, a process called decoherence. Two simple types of error are the bit flip (0 and 1 swap) and the phase flip (the sign between amplitudes changes).
Turn on the noise toggle on our home page and the simulation adds 8% bit-flip and phase-flip noise. Watch the fidelity drop and the concurrence weaken: this is exactly how noise eats away at quantum information. Building large, reliable quantum computers depends on quantum error correction, which spreads one logical qubit across many physical ones.
What quantum computers are good at, and what they are not
Quantum computers are not faster versions of ordinary computers. They are a different tool, useful for specific problems.
| Promising | Not a good fit |
|---|---|
| Simulating molecules and materials, which are quantum systems themselves | Running websites, apps and databases |
| Certain optimisation and sampling problems, still under active research | Everyday business software |
| Factoring large numbers with Shor’s algorithm, once large error-corrected machines exist | Storing large amounts of data |
| Some search problems, with a modest (quadratic) speed-up | Replacing your laptop or the cloud |
Today’s devices are still small and noisy, and most practical advantages remain research goals. One effect is already real, though: because future quantum computers could break today’s public-key encryption, standards for post-quantum cryptography have been published, and organisations are starting to plan their migration.
Why we are called Quantum System
We do not build quantum hardware, and we do not sell quantum computing services. Quantum System is a software development company: we build web platforms, mobile apps, integrations and AI features on ordinary, very real computers.
The name reflects a mindset we try to bring to every project: speed and precision. Quantum mechanics is one of the most precisely tested theories in physics, and quantum computing is about doing more with careful, exact operations. That is how we like to work: short two-week cycles, measurable results, and attention to the details that make systems reliable.
The simulation on our home page is our way of showing that mindset. It is a real state-vector simulation with complex amplitudes, not an animation pretending to be one. If you enjoy that kind of interactive, technically accurate experience, it is also the kind of thing we build for clients through our web development and custom software work.
Try it, then talk to us
Open the live quantum simulation, choose superdense coding or teleportation, toggle the noise, and watch the Bloch vectors vanish as entanglement appears.
And if you have a project that needs the same precision, from an interactive 3D experience to a full platform, request a free quote. You can also email [email protected] or message us on WhatsApp at @quantum.system. The discovery call is free and we reply within one business day.