QKD receiver characterization (Polarization)

QKD receivers are subject to imperfections which, if not adequately considered in security proofs, may compromise the security of generated secret keys. This project considers receivers that measure polarization in the Pauli $Z$ and Pauli $X$ bases (a passive-basis-choice "BB84 measurement"). Such a receiver consists of a polarization analysis module (PAM) followed by single-photon detectors. A simple schematic is given below.

                    ┌── PBS ── H ── det H     (Z / rectilinear arm)
                    │       └── V ── det V
channel ── PC ── BS ┤
                    │       ┌── + ── det +    (X / diagonal arm)
                    └── HWP ┤
                     ~22.5° └── − ── det −

Light from the quantum channel (single-mode fibre, optionally after a polarization controller PC) is split by a non-polarizing beam splitter (BS) into a rectilinear ($H/V$) arm and a diagonal ($+/-$) arm. An HWP near $22.5^{\circ }$ rotates the $X$-arm basis before its PBS. The four ports are monitored by detectors labelled $H,V,+,-$.

Imperfections such as arm-dependent loss, biased beam-splitting ratios, or a low PBS extinction ratio may leak (partial) key information to an adversary or enable active attacks that bias detectors. As part of my work/PhD, I have been working on (theoretical) methods to integrate PAM characterization data into a QKD security proof. This project aims to build calibrated polarization preparation and characterize first a self-assembled PAM and subsequently the PAM of a real QKD receiver.

Project plan

The project proceeds along the following steps:

1. Assemble a free-space polarization-state generator (PSG: QWP + HWP after a fixed linear polarizer) able to span the full Bloch / Poincaré sphere.
2. Assemble an analyzer to calibrate the QWP and HWP.
3. Validate preparation of $H,V,D,A,R,L$-polarized states and rigorously derive an uncertainty budget for the physically prepared states.
4. Connect the calibrated PSG to
   • (4.1) a self-assembled PAM, and
   • (4.2) the PAM of a commercial QKD system.

   Use a self-assembled fibre polarization controller, or the QKD receiver's own polarization controller, to rotate the reference frame (basis of the calibrated PSG) into the receiver frame (basis of the QKD receiver).

5. Measure the input–output power ratio for all four PAM output ports, and from this derive an instrument matrix for the QKD receiver — or rather, an uncertainty region of instrument matrices, due to non-zero preparation and measurement uncertainty.
6. (Outside this course.) Calculate a conservative secure key rate for a worst-case PAM inside that uncertainty region. Maybe: Do measurements in attenuated form, click counts of QKD receiver's APDs instead of power meter.

Required equipment (expected)

Item	Use	Notes / qty
Laser source at 1550 nm	For preparation and power-ratio measurements	Isolator needed?
Variable optical attenuator (VOA)	Power control without changing laser drive	Range covering both powermeter / polarimeter operation (+ maybe APDs)
High-extinction linear polarizer $P_0$ (Glan-type?)	Defines generator $H$ axis, fixed (not rotatable)	1
QWP and HWP	PSG: span the Poincaré sphere	1 each for the generator (maybe one extra QWP if a validation analyzer is built instead of just using polarimeter)
Automated rotation mounts / stages	Calibrated plate angles	≥2 (QWP, HWP); extra for analyzer plates
Analyzer PBS + two power meters	Calibrate QWP/HWP (parallel and crossed ports, must be able to rotate PBS)	Dual-channel preferred
Monitor pick-off (/Beamsplitter) + photodiode	Normalize source drift during scans	1
Polarimeter	Independent validation of prepared $H,V,D,A,R,L$
Fibre coupler, SMF patch leads	Launch into fibre-coupled PAM / QKD Rx
Fibre polarization controller	Align generator frame to receiver frame	Freeze settings during calibrated acquisitions; may be possible to instead use the QKD Rx controller
Four-port power detection	PAM input–output ratios on $H,V,+,-$
Self-assembled PAM	First characterization target (step 4.1)	(done / provided by colleague)
Commercial QKD receiver (PAM)	Second characterization target (step 4.2)	Already available, access to four PAM output ports
Breadboard / cage rods, mounts, irises	Alignment
Temperature logger	Waveplate / lab drift	(optional for uncertainty budget)