---
title: "Quantum Teleportation & Swapping Interactive Lab | Sandbox Physics"
description: "If the classical message is blocked, does a teleported quantum state still arrive? No."
canonical_url: "https://sandboxphysics.com/labs/quantum-teleportation/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/quantum-teleportation/"
last_modified: "2026-10-27"
---

Q043 · Entanglement / classical messages

# Quantum Teleportation & Swapping

**If the classical message is blocked, does a teleported quantum state still arrive?** No. Without the two classical bits, the receiver does not know which Bell measurement outcome occurred and cannot pick the right correction. Averaged over the four outcomes, the qubit in hand is completely mixed, whatever the input. With the bits and the correction the state arrives, and the original is used up.

Prepare a state, share a Bell pair and look at all four measurement branches. Block the classical message, then compare fourfold optical coincidence records, delayed-choice grouping, and dense coding with three or four messages. Every failed attempt still counts toward the resources used.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

The ideal protocol uses complete Bell measurements and abstract time steps. The separate optical workbench uses partial Bell projections, schematic nanosecond paths and independent detector loss. The exact classical simulation of a few qubits leaves out vacuum from the source, multipair emission and background counts. Quality given success and yield over all attempts are divided by different totals.

Recorded evidence and resource cost

Simulated trials

## What the receiver measured

Colored bars use trials; gray marks are model predictions. Pointwise 95% Wilson intervals describe verification fractions, not a process certificate or optional-stopping guarantee. Bell fidelity needs all three axes and can fluctuate outside its physical range as a linear sample estimate.

Current verification fraction / 95% range

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Bell fidelity from three measured axes

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Trials / Bell pairs consumed

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Inspect Bell branches and individual trials

Try partial optical detection, delayed choice and dense coding

Optical records · Q043

## Keep the attempts that failed

The apparatus above previews the original protocol with an ideal, complete Bell measurement. This separate optical workbench uses a partial analyzer, missed photons and fixed timing rules. Its counts are simulated pulse records, not a reconstruction of a historical experiment.

Protocol Receiver analyzer (teleport / coding) Single-photon efficiency $0.85$ Pauli channel error probability $0$ Coincidence residual window / ns $3$ Uniform timing half-width / ns $0.5$ Central optical delay / ns $485$

Import saved JSON

Attempts / accepted / failures

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One-input pass fraction or decoding

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Information per attempt / per accepted attempt

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Prepared pairs / transmitted qubits

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### A pulse identity follows every path

$\delta t_i=t_i-t_{i,\mathrm{ref}}$

$\max_i\delta t_i-\min_i\delta t_i\leq W$

The gate uses calibrated path offsets within the same pulse; delayed photons need not arrive simultaneously with earlier detections. All failed pulses stay in the denominator. No cross-pulse matching, dark counts, multipair emission or detector dead time are modeled.

Latest 12 completed pulse records; CSV includes every attempt

| Pulse | Basis / choice | Outcome / message | Pattern | Accepted | Reason |
| --- | --- | --- | --- | --- | --- |

Latest recorded timestamps / ns; a dash is a missed or unused detector

| Pulse | Trigger | Outer / receiver A | Outer B | Central 1 | Central 2 | Choice |
| --- | --- | --- | --- | --- | --- | --- |

Measurement assumptions and primary sources

Polarization basis: horizontal is zero, vertical is one. Bell codes are phase then parity; local encodings act on the travelling member. The original ideal workbench remains independently available above.

$\Phi^{\pm}=\frac{\lvert HH\rangle\pm\lvert VV\rangle}{\sqrt{2}}$

$\Psi^{\pm}=\frac{\lvert HV\rangle\pm\lvert VH\rangle}{\sqrt{2}}$

$(0,1,2,3)\leftrightarrow(\Phi^+,\Psi^+,\Phi^-,\Psi^-)$

The passive analyzer identifies the two opposite-polarization Bell states; equal prior states therefore succeed at most half the time before loss. The delayed-choice version uses a locally rotated analyzer that selects the two same-polarization Bell states and compares the negative branch with HH / VV product outcomes. These are declared ideal polarization projectors with independent threshold-channel efficiency; not a wave-optics or SPDC hardware model.

Three-message coding sends only Psi-plus, Psi-minus and Phi-minus. The analyzer still cannot tell the two Phi signs apart. An extra beam splitter at just one of the original detectors registers the third category with a quarter of the probability, before shared detector losses, following the ideal rate ratio stated by Mattle et al. The noise and timing sliders are teaching parameters, not efficiencies fitted to the 1996 experiment.

- [Calsamiglia & Lütkenhaus (2001)](https://arxiv.org/pdf/quant-ph/0007058)
- [Ma et al. (2012)](https://arxiv.org/pdf/1203.4834)
- [Mattle et al. (1996)](https://courses.grainger.illinois.edu/phys513/sp2019/reading/week9/Dense_coding_Zeilinger1996.pdf)

Physics tutorial

## A quantum resource and an ordinary message

**Background** Before the protocol starts, Alice and Bob already share an entangled pair. Alice uses up her unknown input in a Bell measurement. Bob then uses the two result bits to choose a local correction.

**Why it matters** Keep two viewpoints apart: someone who knows which Bell branch occurred, and the receiver who has not yet been told. Knowing the branch and holding the unsorted local state are different things.

Start with the essentials

- **Focus question**: What changes at Bob when Alice measures, before any message is available?
- **One-sentence intuition**: Each Bell branch needs a different correction. If you ignore the branch, the receiver's state is fully mixed, and it is the same for every input.

### Core mathematical model

#### Prepared input

$$
|\psi\rangle=\cos(\theta/2)|0\rangle+e^{i\varphi}\sin(\theta/2)|1\rangle
$$

The simulator shows the preparation angles for teaching. Someone handed a single unknown state would not be given them.

#### A noisy entangled pair

$$
\rho_{AB}=v|\Phi^+\rangle\langle\Phi^+|+(1-v)I_4/4
$$

The visibility runs from a pure Bell pair to a maximally mixed pair. The noisy pair is a mixture of the four Bell states, which are related by Pauli operations; it is a mixed state, not a pure state with a shorter arrow.

#### Bell measurement branches

$$
|\psi\rangle|\Phi^+\rangle\longmapsto\frac12\sum_{a,b}|ab\rangle X^bZ^a|\psi\rangle
$$

The first bit shown controls the phase correction, and the second controls the bit-flip correction. Each branch occurs with probability one quarter. The correction applies the bit flip first, then the phase flip; the global phase does not matter.

#### Before the classical message

$$
\rho_B=\sum_{a,b}p_{ab}\rho_{B|ab}=I_2/2
$$

Without the branch information or a correction, the receiver's qubit is fully mixed. The branch preview shows what an all-knowing observer would see; Bob has no access to it.

#### Noise limits after correct messages

$$
F_{\mathrm{transfer}}=\frac{1+v}{2},\qquad F_{\mathrm{swap}}=\frac{1+3v^2}{4}
$$

For swapping, the two independently prepared pairs have the same visibility. These limits assume ideal gates, correct messages and no extra noise while the qubits are stored.

#### Measured swapped-pair fidelity

$$
\widehat F_{\Phi^+}=\frac{1+\widehat C_{XX}-\widehat C_{YY}+\widehat C_{ZZ}}4
$$

Each correlation comes from separately prepared trials with both qubits measured along the same Pauli axis, for three axes. The linear estimate is not forced back onto a physical state, so a finite sample can give a value outside the physical range. No joint confidence interval is given.

### Common difficulties

#### How the verifier checks an unknown state

**Typical misconception** The verifier somehow knows an arbitrary unknown state.

**Better mental model** The teaching experiment repeats a known preparation. Its test projects back onto that specific input, so it checks only that input, not the process for every possible state.

#### A colored branch is not a message

**Typical misconception** The colored conditional branch allows instant communication.

**Better mental model** The receiver cannot know the branch label until the classical message arrives. Showing it in the simulator does not send any information.

#### Ideal circuit versus real optics

**Typical misconception** Every optical Bell analyzer succeeds every time.

**Better mental model** This gate-level protocol uses an ideal, complete Bell measurement. Optical collection, partial Bell discrimination, loss and hardware timing are not modeled in it.

### Run the experiment

1. 01

   #### Block the message

   Choose Block the message, acquire the known-input verification and inspect all four branches.

   **What to observe:** The groups sorted by branch differ, but without sorting, the receiver passes the test with probability one half.

2. 02

   #### Use up the entanglement

   Restore the message and acquire again. Then change the input angles.

   **What to observe:** The ideal correction works for every input. Each repetition uses a freshly prepared input and a new Bell pair; nothing is cloned.

3. 03

   #### Let the message arrive too late

   Compare the wait budget with the classical delay.

   **What to observe:** Both are counted in abstract protocol ticks. Bob can correct only after the message arrives. No physical speed is implied, and memory decoherence is not modeled.

4. 04

   #### Swap two pairs

   Choose Swap two pairs, acquire all three axes and inspect the measured fidelity.

   **What to observe:** Given the branch, the two outer qubits share a Bell state. Each one alone stays fully mixed, and without the message the outer pair as a whole is fully mixed too.

Physical conclusion

Entanglement, two classical bits and a local correction work together. Teleportation uses up the input; entanglement swapping transfers correlations.

## Related experiments and articles

Quantum evidence · Reading path

### Bell tests and photon information

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **A readiness signal makes the Bell trial countable**](https://sandboxphysics.com/stories/quantum-evidence/event-ready-bell-trials-finite-statistics/)
2. [Lab **Bell Correlations & CHSH** See when the herald arrives and check every accepted outcome window](https://sandboxphysics.com/labs/bell-chsh/)
3. [Article **How the 1997 photon experiment transferred a quantum state**](https://sandboxphysics.com/stories/quantum-evidence/quantum-teleportation-conditional-records/)
4. [Lab **Quantum State & Process Tomography** Compare reconstruction of an output state](https://sandboxphysics.com/labs/quantum-state-process-tomography/)
5. [Article **A joint measurement entangles two photons that never met**](https://sandboxphysics.com/stories/quantum-evidence/entanglement-swapping-fourfold-records/)
6. [Article **The later measurement sorts earlier photon detections**](https://sandboxphysics.com/stories/quantum-evidence/delayed-choice-swapping-sorted-records/)
7. [Lab **Which Path & Quantum Eraser** Sort the same detections into complementary groups](https://sandboxphysics.com/labs/quantum-eraser/)
8. [Article **Dense coding sends three distinguishable messages with one photon**](https://sandboxphysics.com/stories/quantum-evidence/dense-coding-three-messages-resources/)
9. [Lab **Quantum State & Born Measurement** Rotate a single qubit](https://sandboxphysics.com/labs/qubit-state/)
10. [Lab **Hong–Ou–Mandel Two-Photon Interference** See the two-photon interference the analyzer uses](https://sandboxphysics.com/labs/hong-ou-mandel/)

Quantum & fields · Starter path

## Start from a single measurement

Predict an outcome, then count what the measurements actually give. The path starts with one qubit and moves on to wave packets, bound states and two-photon interference.

[Start here → **Quantum State & Born Measurement** Predict a probability, turn the analyzer, then compare your prediction with the measured frequency over many shots. Observe · 15 min](https://sandboxphysics.com/labs/qubit-state/)

1. [1 Quantum State & Born Measurement](https://sandboxphysics.com/labs/qubit-state/)
2. [2 Stern–Gerlach Sequence](https://sandboxphysics.com/labs/stern-gerlach-sequence/)
3. [3 Wave Packet & Uncertainty](https://sandboxphysics.com/labs/wave-packet-uncertainty/)
4. [4 Quantum Harmonic Oscillator](https://sandboxphysics.com/labs/quantum-harmonic-oscillator/)
5. [5 Which Path & Quantum Eraser](https://sandboxphysics.com/labs/quantum-eraser/)
6. [6 Hong–Ou–Mandel Two-Photon Interference](https://sandboxphysics.com/labs/hong-ou-mandel/)

[View the full path →](https://sandboxphysics.com/topics/quantum/#starter-path)