648 Hilbert-space dimensionality in a biphoton frequency comb: entanglement of formation and Schmidt mode decomposition

Abstract Qudit entanglement is an indispensable resource for quantum information processing since increasing dimensionality provides a pathway to higher capacity and increased noise resilience in communications, cluster-state computations. In continuous-variable time–frequency entanglement, encoding multiple qubits per photon only limited by the frequency correlation bandwidth detection timing jitter. Here, we focus on discrete-variable biphoton comb (BFC), generating filtering signal idler outputs with fiber Fabry–Pérot cavity 45.32 GHz free-spectral range (FSR) 1.56 full-width-at-half-maximum (FWHM) from continuous-wave (cw)-pumped type-II spontaneous parametric downconverter (SPDC). We generate BFC whose time-binned/frequency-binned Hilbert space at least 324, based assumption of pure state. Such BFC’s doubles up 648, after combining its post-selected polarization indicating potential 6.28 bits/photon classical-information capacity. The exhibits recurring Hong–Ou–Mandel (HOM) dips over 61 time bins maximum visibility 98.4% without correction accidental coincidences. measurement, it violates Clauser–Horne–Shimony–Holt (CHSH) inequality 18.5 standard deviations S -parameter 2.771. It has Franson interference recurrences 16 96.1% From zeroth- third-order interference, infer formation ( E ) 1.89 ± 0.03 ebits—where 2 ebits maximal 4 × dimensional biphoton—as lower bound time-bin high-dimensional entanglement. To further characterize BFCs obtain Schmidt mode decompositions generated using cavities 45.32, 15.15, 5.03 FSRs. These confirm scaling Fourier-transform duality. Moreover, present theory conjugate interferometry—because characterized state’s joint-temporal intensity (JTI)—which can help distinguish between pure-state mixed state entangled pairs, although experimental implementation challenging not yet available. summary, our serves as platform key distribution (QKD).