SPOOKY SIGNALS · GAME 02

Ghost Relay

Facilitator guide · 2 November 2026
Solo or 2–3 people sharing one phone · About 6–10 minutes, plus discussion
Grades 8–10; guided use with younger learners

Play Ghost Relay →

The question to play with

What does the receiver need to recover an unknown state? Six relay missions combine a shared Bell pair, a Bell measurement, a two-bit classical outcome, and conditional corrections. Delayed or faulty message records make the classical channel a resource students must reason about.

Set up the crew

Open the game on a phone, tablet, or computer. No account, installation, or real quantum hardware is required. Download its self-contained HTML file for offline play in a browser that supports local files.
Choose Solo Operator, Two Players, or Three Players. Two players use Sender and Receiver roles; the Receiver also handles the radio. Three players add a Courier to receive the classical frames and choose resends.
Use the covered handoffs. The Sender may see the original measurement records, but must not tell the Receiver values outside the game’s radio. Rotate roles after six deliveries. The original input stays hidden from all players until the replay.
Read the route preview. There are two reliable resend stamps for the entire shift and three stops with missing or flagged information. The correction guide is always available.

Run a delivery

Prepare the resources. The simulator selects a hidden input from six teaching states and starts with one ideal Bell pair already shared between Alice and Bob. It does not model distributing that pair.
Run the Bell step. Alice applies CNOT from the input to her half of the pair, then Hadamard to the input, then measures her two qubits. The original input state and the shared entanglement are consumed. Two random classical bits remain in her measurement log. The particles themselves do not disappear.
Receive the frames. Each click advances an ordinary message frame. Waiting is free and has no reflex timer. The Clocktower mission sends X before Z, so read labels rather than positions.
Handle a fault. An erased bit shows “?”. A flagged bit might be flipped, with its stated probability. Spend one stamp to obtain a reliable copy of that one classical record, or proceed with uncertainty. Resends neither recreate the input nor restore entanglement.
Choose the corrections. Apply X when the X / Flip bit is 1; apply Z when the Z / Sign bit is 1. Leave an operation off for 0. When both are 1, the game applies X then Z. The Receiver can return to the radio before committing.
Commit and replay. Compare the chosen correction pair with the true records. The replay opens the hidden preparation and Bob’s output, distinguishes guesses, and explains resource use.

Z / Sign bit	X / Flip bit	Correction
0	0	Neither
0	1	X
1	0	Z
1	1	X then Z

The six-stop challenge

Stop	Classical channel	Decision
Rooftop Run	Clear	Learn the two labels and correction choices.
Night Ferry	Frames arrive separately	Wait for both or explicitly attempt a guess.
Echo Tunnel	One erased bit	Resend or guess the missing instruction.
Clocktower	X arrives before Z	Use labels rather than memorizing positions.
Fog Bridge	One flagged bit; 25% flip probability	Trust a low-risk frame or use a stamp.
Last Lantern	One flagged bit; 50% flip probability	Use the remaining budget or accept uncertainty.

The faults are in classical message records, not the entangled pair. Their probabilities, the route, and the stamp budget are fictional game mechanics. They are not laboratory benchmarks. Without side information, a missing bit is a fair guess; all Bell outcomes are equally likely regardless of the input.

Score logic and evidence separately

A correct pair of correction choices earns 3 points. Six correct pairs give 18 points and the Star Courier result. A wrong pair gives 0.
A guessed pair can happen to be correct and score, but is labeled uncertain. “Fully checked” requires both records received, no unresolved flags, and the correct correction pair. A correct guessed pair is not reported as a reliable protocol.
Some wrong corrections leave a special input unchanged. For example, Z does not change |0⟩. The simulator may show 100% fidelity for that input while correctly giving 0 correction points. Ask which other input would fail.
Two explanation questions have their own 0–2 score. Keep this separate from mission points, enjoyment, and confidence. A player can use the correction table correctly without understanding teleportation.

Try the Relay Lab

The lab computes exact averages over the Bell outcomes consistent with the message Bob has. It assumes Bob applies the known corrections and guesses 0 for each missing bit.

Select any preparation with No bits. Predict outcomes for X, Y, and Z measurements on Bob’s local state. All have a 50% probability of +1; average fidelity to the input is 50%.
Change the preparation while keeping No bits. Can Alice make Bob read a message from those local statistics? The distribution remains unchanged.
Select Both bits, then change the two measurement bits. The ideal correction recovers each chosen preparation with 100% simulator fidelity.
Try Only X / Flip for |0⟩ and then |+⟩. Why can the missing Z operation be invisible for one input but matter for the other? One special successful case is not a universal method.

Discussion prompts

What was consumed, what remained, and what actually traveled down the classical channel?
Why are two classical bits not a full description of an arbitrary qubit’s amplitudes?
Why does a right guess before the message fail to demonstrate faster-than-light communication?
Where should the two resend stamps be spent? Compare expected risks across repeated shifts, rather than declaring a strategy best after one lucky run.
What can the simulator know about the hidden state that a real receiver cannot infer from a single specimen?

Physics and scope

The core uses normalized complex amplitudes. With the standard |Φ+⟩ shared pair and the measurement order used here, Bob’s conditional state is X^xZ^z|ψ⟩. Applying X for x, then Z for z, recovers the input up to an irrelevant global phase. Each Bell outcome has probability 1/4. Averaging all four conditional states without their classical labels gives I/2 for any pure input, so Bob’s local observations do not reveal a controllable signal.

The game illustrates six preparations: |0⟩, |1⟩, |+⟩, |−⟩, |+i⟩, and |−i⟩. The calculation also supports general pure qubits. Exact simulator fidelity is |⟨ψ|output⟩|²; it is not a physical test a receiver can perform perfectly on one arbitrary unknown qubit. Experimental verification needs appropriate repeated preparations and measurements.

Teleportation transfers a state using prior entanglement and classical communication; it does not transport matter or preserve an intact original copy. This release assumes ideal gates, a perfect Bell pair, and noiseless quantum memory. It excludes entanglement generation, quantum-channel loss, decoherence, repeaters, and real hardware. Only the classical message records have the fictional faults listed above.

Sources

Bennett, C. H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., & Wootters, W. K. (1993). Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Physical Review Letters, 70, 1895–1899. Foundational protocol and resource constraints.
IBM Quantum Learning. Quantum teleportation and superdense coding. Circuit, correction convention, and distinction between exact simulator state knowledge and experimental tomography.