---
title: "Decoherence Channels & Information Loss Interactive Lab | Sandbox Physics"
description: "Does losing phase also mean losing energy? No. Pure phase damping destroys coherence but leaves the populations, and so the energy, unchanged."
canonical_url: "https://sandboxphysics.com/labs/decoherence-channels/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/decoherence-channels/"
last_modified: "2026-10-28"
---

Q048 · How an environment changes a qubit

# Decoherence Channels & Information Loss

**Does losing phase also mean losing energy?** No. Pure phase damping destroys coherence but leaves the populations, and so the energy, unchanged. Relaxation into a cold bath does give energy away and ends in the ground state. Measuring along all three axes tells the two apart.

Watch the level populations and the phase alignment as two separate things. Predict what phase damping changes, then compare it with relaxation into a cold bath. Check the final state with three independent sets of simulated counts, and move on to state reconstruction and decay fits when you are ready.

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

The channels are Markov processes acting on a two-level system, with ideal preparation and readout. The north pole of the Bloch sphere is the ground state. The thermal bath sets a two-level Gibbs population. State reconstruction uses radial projection, not maximum likelihood. The propagated Wilson bounds are approximate and leave out preparation, detector and model errors. Phase damping can leave the populations unchanged, and relaxation at zero temperature can restore purity.

Explore the evidence · counts, fits and raw data

Simulated acquisition

## Use the records to identify the noise.

Predict which components change. Acquire three bases for the current state, then a time scan. Colored points and 95% Wilson bars come from separate preparation ensembles; dashed curves are model references.

No acquired record yet.

### Inference from acquired counts

$\text{—}$

### Current-state reconstruction

$\widehat\rho=\text{—}$

$\text{—}$

Current counts and 95% intervals

| Basis | Positive / total | 95% Wilson interval |
| --- | --- | --- |

Model density matrix · not reconstructed data

$\rho=\frac{I+\boldsymbol r\cdot\boldsymbol\sigma}{2}$

Latest raw events · full record in CSV

| Event / run | Protocol / basis | Duration (ms) | Outcome |
| --- | --- | --- | --- |

Scientific basis: [IBM Quantum · channels](https://quantum.cloud.ibm.com/learning/en/courses/tools-for-quantum-advantage/noise-and-errors) · [IBM Quantum · noise models](https://quantum.cloud.ibm.com/docs/en/guides/build-noise-models)

Physics tutorial

## Reconstruct information after a channel

**Background** A density matrix records both population and coherence. Different environments change them in different ways.

**Why it matters** Measuring a single population cannot tell you how pure the state is. Three separately prepared ensembles give the complementary information needed to reconstruct one qubit.

Start with the essentials

- **Focus question**: Can a noisy process make an initially pure state mixed, then pure again?
- **One-sentence intuition**: Relaxation into a cold bath ends in the pure ground state. Pure phase damping leaves the populations alone, and depolarization drives the state toward the maximally mixed state.

### Core mathematical model

#### Thermal relaxation with pure dephasing

$$
r_z(t)=r_{z,\mathrm{eq}}+[r_z(0)-r_{z,\mathrm{eq}}]e^{-\Gamma_1t},\quad r_{x,y}(t)=r_{x,y}(0)e^{-(\Gamma_1/2+\Gamma_\varphi)t}
$$

The north pole is the ground state. Rates are non-negative and measured in inverse milliseconds. The transverse decay rate includes half of the longitudinal rate.

#### Two-level Gibbs bath

$$
q=\frac{1}{1+e^{hf_{01}/(k_BT_b)}},\quad r_{z,\mathrm{eq}}=1-2q
$$

The bath fraction comes from the displayed gap in GHz and temperature in kelvin. At zero temperature the excited fraction is zero. This is an effective bath, not a specific device.

#### Reconstruction from counts

$$
\widetilde r_j=2\frac{n_{j,+}}{N_j}-1,\quad \widehat{\boldsymbol r}=\frac{\widetilde{\boldsymbol r}}{\max(1,|\widetilde{\boldsymbol r}|)},\quad \widehat\rho=\frac{I+\widehat{\boldsymbol r}\cdot\boldsymbol\sigma}{2}
$$

Each basis uses its own separately prepared ensemble. Radial Euclidean projection pulls the estimate back inside the Bloch ball so that the state is physical. It is not maximum likelihood, and with finite samples it can introduce bias.

#### Purity and entropy

$$
\mathcal P=\frac{1+|\boldsymbol r|^2}{2},\quad S=-\sum_{\pm}\lambda_\pm\log_2\lambda_\pm,\quad\lambda_\pm=\frac{1\pm|\boldsymbol r|}{2}
$$

Approximate joint Wilson bounds on the components are propagated into conservative ranges for purity and entropy. These ranges leave out systematic errors in preparation and measurement.

### Common difficulties

#### Noise does not always lower purity

**Typical misconception** Every channel always lowers the purity.

**Better mental model** Amplitude damping is non-unital, so it can leave the qubit in the pure ground state. Depolarization and pure dephasing are different channels.

#### One qubit is not measured three times

**Typical misconception** The three records are three measurements made one after another on the same qubit.

**Better mental model** Every recorded result comes from a fresh preparation. Averages over three separate ensembles estimate complementary components of the state.

#### A physical estimate does not certify the device

**Typical misconception** Once the projected estimate is physical, the detector and the channel must be right.

**Better mental model** Projection is only a statistical constraint. The model assumes ideal preparation and readout, and real device calibration and process tomography lie outside this experiment.

### Run the experiment

1. 01

   #### Measure in all three bases

   Choose Thermal relaxation and acquire all three bases. Open the reconstructed density matrix and the count table.

   **What to observe:** The green reconstructed state comes only from the counts. The purple state and the dashed curves are separate model references.

2. 02

   #### Follow the energy into a cold bath

   Choose Cold excited state and acquire a time scan. Move the exposure from zero, through the middle of the range, to four milliseconds.

   **What to observe:** The longitudinal population changes, and the purity first falls, then recovers. When the input has no transverse coherence, the fit flags its result as only weakly identified.

3. 03

   #### Lose phase without energy

   Choose Phase loss only and acquire a time scan.

   **What to observe:** The longitudinal probability stays fixed while the transverse probabilities approach one half. The entropy rises even though the populations do not relax.

4. 04

   #### Test the reconstruction

   Choose No noise, reduce the number of shots and acquire three bases, then increase the shots. Also try an unpolarized input.

   **What to observe:** Sampling noise can put the raw Bloch vector outside the ball. Projection makes the state positive again, but the uncertainty stays visible. An unpolarized input cannot reveal the depolarization rate.

Physical conclusion

Measure in all three bases to tell a change in population from a loss of coherence. Report every inferred state together with its reconstruction rule and its uncertainty.

## Related experiments and articles

Quantum evidence · Reading path

### Clocks, traps and single-quantum control

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

1. [Article **How to measure one quantum system and keep it available**](https://sandboxphysics.com/stories/quantum-evidence/single-quantum-measurement-backaction/)
2. [Lab **Cavity Quantum Excitation Exchange** Watch an atom and a cavity trade one excitation](https://sandboxphysics.com/labs/cavity-quantum-exchange/)
3. [Lab **Fluorescence & Quantum Jumps** See quantum jumps in one atom’s fluorescence](https://sandboxphysics.com/labs/fluorescence-quantum-jumps/)
4. [Lab **Trapped-Ion Sideband Spectroscopy** Probe a trapped ion’s motion through its sidebands](https://sandboxphysics.com/labs/trapped-ion-sideband-spectroscopy/)
5. [Article **A cavity cat loses coherence before it loses its energy**](https://sandboxphysics.com/stories/quantum-evidence/cavity-cat-coherence-energy-decay/)
6. [Lab **Kerr Cats & Wigner Interference** Compare photon loss, branch interference and parity measurements](https://sandboxphysics.com/labs/kerr-cat-interference/)
7. [Lab **Quantum State & Process Tomography** Compare with state reconstruction, a separate task](https://sandboxphysics.com/labs/quantum-state-process-tomography/)
8. [Article **Counting stored photons one atom at a time**](https://sandboxphysics.com/stories/quantum-evidence/qnd-photon-counting-atomic-records/)
9. [Lab **Cavity Photon Counting & Feedback** Accumulate probe-atom outcomes and infer cavity photon number](https://sandboxphysics.com/labs/cavity-photon-qnd-feedback/)
10. [Lab **Ramsey Frequency Measurement** See how a phase becomes a population readout](https://sandboxphysics.com/labs/ramsey-frequency/)
11. [Article **Keeping a chosen number of photons in a cavity**](https://sandboxphysics.com/stories/quantum-evidence/quantum-feedback-photon-number-verification/)
12. [Lab **Quantum Error Correction** Find errors while leaving an encoded message unread](https://sandboxphysics.com/labs/quantum-error-correction/)

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)