FR10-B · Choose the whole pulse

Quantum Pulse Gate

Can choosing how to detect one photon purify its partner? A detector that accepts one coherent pulse mode prepares its partner in a pure conditional state, provided the pair was pure. A frequency filter followed by unresolved detection can leave a mixture because several distinguishable modes still trigger the same click.

Shape the mode accepted by a herald detector and watch the partner photon change. Compare coherent selection with an intensity filter, then test a reconstructed state with a measurement kept aside.

Herald probability · model $0.500$

Conditional purity · model $1.00$

Purity · saved counts $1.00$

Held-out probability · prediction $0.505$

Prepare a mode, then test it

Which click prepares which pulse?

Drag the gold gate pulse to select a mode; acquire again to save new data.

Herald selectionPair phase

\theta

\pi

Gate mixing

\alpha

45^\circ

Gate relative phase

\phi

0.333\pi

The default synthetic record is ready.

Conversion kernel and sampling

Second Schmidt coefficient

\kappa_1

0

Samples per projection

N

2400

The second Schmidt coefficient adds an unresolved converted mode. Its value is illustrative; coupling follows the published mode-conversion law.

Model and reading

A low-gain, pure photon pair occupies two orthonormal frequency bins. The gate uses a two-channel Schmidt conversion kernel; its optional leakage coefficient is illustrative. The model omits multipair emission, detector loss, dark counts and material propagation. Saved counts are synthetic binomial samples. Wave animation and distances are schematic.

Signal ribbon brightness follows bin populations; ripple depth follows inter-bin coherence. These are mode symbols, not a single-photon electric field. Arrow keys on the focused scene change phase and mixing.

The analyzer measures each Pauli direction on a separate conditional ensemble. The held-out direction is fixed before acquisition. Noise bars use a first-order sampling approximation; positivity projection can affect their coverage near pure states.

Eckstein et al. · 2011 · Bhattacharjee et al. · 2026 preprint

Model assumptions

Synthetic acquisition · saved independently of controls

Can the saved counts predict another measurement?

Default record · 2400 samples per projection

p_{\rm held}=\frac{1+\boldsymbol n\cdot\widehat{\boldsymbol r}}2

p_{\rm pred}=0.505,\quad p_{\rm obs}=0.489

How the reconstruction uses the record

Each axis gives its positive-click fraction. Twice that fraction minus one estimates a Bloch-vector component. If sampling puts the vector outside the unit ball, radial projection restores a physical density matrix. The held-out counts do not enter this estimate.

\widehat{\boldsymbol r}=(0,0,1)

Start with the essentials

Focus question: Can choosing how to detect one photon purify its partner?
One-sentence intuition: A rank-one idler measurement leaves a pure signal state when the original pair is pure; the probability of that outcome is a separate question.

Core mathematical model

Coherent heralding

q=\begin{pmatrix}\cos\alpha\\e^{i\phi}\sin\alpha\end{pmatrix},\quad v=Fq^*,\quad p=v^\dagger v,\quad\rho_s=\frac{vv^\dagger}{p}

The two components refer to orthonormal frequency bins. The idler detector accepts the mode q. Amplitudes add before the probability is calculated; a nonzero outcome leaves one normalized signal vector.

Unresolved intensity filtering

\widetilde\rho_s=F\begin{pmatrix}\cos^2\alpha&0\\0&\sin^2\alpha\end{pmatrix}F^\dagger,\quad\rho_s=\frac{\widetilde\rho_s}{\operatorname{Tr}\widetilde\rho_s}

Each transmitted idler frequency contributes a conditional signal state. The detector pools their probabilities. At the opposite pair phase and equal transmission, the result is maximally mixed.

A second converted mode

T=\begin{pmatrix}\sqrt{\eta_0}q^\dagger\\\sqrt{\eta_1}q_\perp^\dagger\end{pmatrix},\quad\eta_k=\sin^2(g\kappa_k),\quad g=\frac\pi2

The two output modes are unresolved by the herald detector. A second nonzero Schmidt coefficient adds another conditional state. This finite kernel follows the mode-coupling law of Eckstein, Brecht and Silberhorn; the leakage value here is illustrative.

Common difficulties

Purity and success answer different questions

Typical misconceptionA pure conditional state means every generated pair is accepted.

Better mental modelPurity describes accepted events. The herald probability counts how often those events occur. A setting can prepare a pure state very rarely.

Run the experiment

01
Compare two kinds of selection
Predict the purity, then compare Select a pure pulse with Pass both colors.
What to observe: The coherent herald gives a pure state. With the same bin transmission weights, unresolved intensity filtering gives purity one half.
02
Change the phase of the gate
Drag the gold pump dial. Its angle changes Gate relative phase; its radius changes Gate mixing.
What to observe: The prepared signal mode rotates. A coherent selection can change its phase without losing purity.
03
Make a prediction from saved counts
Choose Acquire projections. Change the gate, then compare the saved reconstruction with the live model before acquiring again.
What to observe: The saved data stay fixed when controls move. Three projection settings reconstruct the state; the fourth setting checks a prediction and never enters the fit.

Quantum Pulse Gate

Can the saved counts predict another measurement?