An Open Dossier · 001 · v1.0.1 (living) · June 2026

Temporal-Imaging-Enhanced Dispersive-Optics Quantum Key Distribution

Energy–time entangled photon pairs carry 16–20 bits of potential key per coincidence; demonstrated systems extract 3–7, limited by detector timing jitter. This work proposes placing single-photon time lenses inside the receivers of a dispersive-optics QKD link, magnifying arrival-time structure before detection so the effective resolution beats the jitter by the magnification M — projecting 13–15 bits per coincidence and key rates of order 108 b/s from demonstrated components (rate figure amended hours after launch: architecture-dependent, issue #1), with a nonlocal variant in which the fiber's own dispersion completes an imaging system that exists only in coincidences. Every number below is recomputable in your browser. Don't trust this paper — run it.

01 · Table 1, alive

How many bits can one photon pair carry?

This is the paper's central equation with handles on it. Pick a detector, a lens, and a guard factor; the photon information efficiency recomputes live from Eqs. (2)–(6) of the manuscript. The presets reproduce every row of Table 1.

13.1bits per coincidence (PIE)
effective width σobs
1.86 ps
projected key rate*
3.1×10⁷ b/s
vs. no lens (M=1)
+4.5 bits
presets: 2007 SPCM · Zhong 2015 · demonstrated lens (Joshi '22) · 3 ps SNSPD + lens · projected EO lens   *8 ch × 10⁶ cps × κ=0.5 × 0.6·PIE, saturation-limited (Eq. 7) · rate projections architecture-dependent — see issue #1
02 · The claims, executable

Run the paper

Sixteen checks recompute every number in the manuscript from its stated assumptions — the same arithmetic as the repository's verify_numbers.py, which CI reruns on every commit. During this paper's own audit, this process caught Table 1 overstating its result by 1.5–2.5 bits; the paper was corrected, and the catch is published in the audit trail.

verification console · 16 checks · model: Eqs. (2)–(7)
IDLEAwaiting run.
03 · Learn as you read

The five ideas this paper stands on

Schmidt number — the alphabet's size
A cw-pumped down-conversion pair is correlated to ~100 femtoseconds but coherent over ~a microsecond. The ratio K = Tcohc counts the independent "letters" the pair can encode — 10⁵–10⁶ of them, i.e. 16–20 bits per detected pair. The whole game is reading letters as small as the correlation time.
The time lens — a magnifier for moments
Dispersion is to time what diffraction is to space, so a quadratic phase in time acts exactly like a lens. Dispersion → lens → dispersion magnifies a waveform's time axis by M. Put one before your detector and a 30 ps-blurry detector resolves 30/M ps features. Demonstrated on single photons at M = 158 (Joshi et al., Optica 2022).
Nonlocal dispersion cancellation — the strange one
The pair's frequencies are anticorrelated, so dispersion applied to one photon and opposite dispersion applied to its distant partner cancel — but only in the coincidences (Franson 1992). Each photon alone is a nanosecond blur; together they are sharp. The paper conscripts this twice: as the security check, and to let the fiber itself act as a lens element.
Why not Franson interferometers?
The classic security check postselects on interferometer paths, and that postselection is a provable loophole — attacked with purely classical light (Jogenfors et al., Sci. Adv. 2015). The dispersive check involves no path postselection: two measured variances bound the eavesdropper's information through an entropic uncertainty relation.
PIE — why bits-per-photon beats raw speed
Record QKD systems extract ≲1 bit per detected photon and win by clocking fast. Wherever detected photons are the scarce resource — long-haul fiber, satellites, saturated detectors, multiplexed networks — photon information efficiency sets the rate. Moving PIE from ~7 to ~13–15 bits is the claim of this work.

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