Passive Photon-Sorting Circuit

• Passive photon-sorting circuits are optical devices that separate photons by quantum properties like number, spin, and wavelength without active modulation.
• They employ both fixed linear elements and intrinsic nonlinear scattering to map photon-number sectors into orthogonal modes with high fidelity.
• These circuits underpin advanced applications such as Bell measurements and quantum gates, with progress focused on optimizing emitter-waveguide integration.

Searching arXiv for recent and related work on passive photon sorting, photon-number routing, and passive optical sorting mechanisms. A passive photon-sorting circuit is an optical, nanophotonic, or waveguide-QED device that routes, separates, or infers photons according to a quantum number without active modulation during the sorting process. In the literature, the sorted degree of freedom includes photon number, spin or helicity, orbital angular momentum, temporal mode, and wavelength. “Passive” is used in a technical rather than purely linear-optical sense: some implementations use only fixed linear components and static dielectric structuring, whereas others use intrinsic emitter-induced or material nonlinearities while still avoiding measurement-based feedforward, dynamically switched control, or external time-dependent modulation during the optical interaction (Ralph et al., 2015, Yang et al., 2022, Nielsen et al., 23 Apr 2026).

1. Definition and taxonomic scope

The term denotes a family of circuits rather than a single architecture. In one class, a passive sorter is a router: the one-photon and two-photon sectors, or different internal photonic states, are directed into different output modes. In another class, the circuit is passive in hardware but detection-oriented in function, as in loop-based multiplexing where photons are “sorted across time bins.” A further class consists of wavelength-selective or angular-momentum-selective passive nanostructures that direct different spectral or modal components to different ports (Sullivan et al., 2023, Wang et al., 2016, Kaptanoglu et al., 2019).

A recurring distinction in the literature is between routing and inference. The passive two-level-scatterer proposals and waveguide-emitter experiments do not merely estimate photon number; they map Fock sectors into orthogonal optical modes. By contrast, the storage-loop detector uses a single-photon detector, a storage loop, and a tunable outcoupler to infer the initial photon number from a click record, with the passive case defined by a fixed outcoupling choice, $\epsilon_k=\epsilon$ for all $k$ (Ralph et al., 2015, Sullivan et al., 2023).

Sorted quantity	Passive mechanism	Representative result
Photon number / Fock sector	Two-level emitters, quantum dots, interferometric scattering	$62\%\pm2\%$ overall sorting success (Nielsen et al., 23 Apr 2026)
Temporal mode by photon number	Two chirally coupled two-level emitters	Fidelity $\gtrsim 0.9997$ (Yang et al., 2022)
Spin / helicity	Bragg-modulated cylindrical waveguide with effective SOI	Spin-dependent directional blocking (Li et al., 2018)
Orbital angular momentum	Symmetric multiport beam splitters and Dove prisms	Scalable nondestructive sorting (Wang et al., 2016)
Wavelength	Slit-groove arrays or dichroic concentrators	Crosstalk below $1.0\%$ (Villate-Guío et al., 2014); Cherenkov purity better than $90\%$ (Kaptanoglu et al., 2019)

This breadth has an important conceptual consequence. A passive photon-sorting circuit is not restricted to a beam-splitting device in the narrow sense. It may instead be a nonlinear scattering primitive, a nondestructive mode demultiplexer, a wavelength-selective concentrator, or a time-multiplexed detector architecture.

2. Photon-number sorting through passive nonlinear scattering

The modern photon-number-sorting literature is anchored by passive two-level nonlinearities. In "Photon Sorting, Efficient Bell Measurements and a Deterministic CZ Gate using a Passive Two-level Nonlinearity" (Ralph et al., 2015), a single two-level scatterer embedded in a unidirectional waveguide or cavity-like structure transforms single-photon and two-photon components differently. For a single photon, the transmission amplitude is

$$t_k = \frac{ck - \omega_0 + i(\gamma-\Gamma)/2}{ck - \omega_0 + i(\gamma+\Gamma)/2},$$

whereas the two-photon sector acquires a genuinely interacting scattering contribution. The key sorting regime is obtained at $\eta=0.5$, for which

$$\alpha |1_f \rangle + \xi |2_f \rangle \to \alpha |1_{f'} \rangle + \xi |\bar 2_{f'} \rangle.$$

Here the one-photon sector and two-photon sector are mapped to orthogonal modes. The paper is explicit that the sorter does not simply detect photon number; it converts photon-number information into orthogonal optical modes, after which active Gaussian frequency conversion and passive filtering can separate them deterministically (Ralph et al., 2015).

Waveguide-QED theory subsequently showed that passive sorting can approach determinism. In "Deterministic Photon Sorting in Waveguide QED Systems" (Yang et al., 2022), a pair of two-level emitters chirally coupled to a waveguide scatter the single-photon and two-photon parts of an input pulse into orthogonal temporal modes with fidelity $\gtrsim 0.9997$. The first emitter generates a multimode two-photon field; the second emitter recombines the field amplitudes, and the net two-photon scattering induces a self-time reversal of the pulse mode. The sorting error is defined as

$k$0

with sorting fidelity $k$1. The same framework supports a deterministic nonlinear-sign gate with fidelity $k$2 (Yang et al., 2022).

The first on-chip solid-state realization of this logic is "Photon Sorting with a Quantum Emitter" (Nielsen et al., 23 Apr 2026). There the sorter is a nonlinear Mach-Zehnder interferometer comprising two balanced beam splitters, a nonlinear element in the arms, and a phase shift that depends on photon number. In the ideal Kerr-like picture the nonlinear element implements

$k$3

so that for $k$4 a one-photon state acquires no nonlinear phase while a two-photon state acquires a $k$5 phase shift. The experiment replaces a true Kerr medium by few-photon scattering from a solid-state quantum emitter, specifically a quantum dot embedded in a nanobeam waveguide, with a single-sided waveguide terminated by a photonic crystal mirror and embedded on-chip into a linear optical circuit (Nielsen et al., 23 Apr 2026).

The measured performance establishes passive photon-number-dependent routing beyond the linear-optical benchmark. At resonance, the one-photon sorting probability was $k$6, the two-photon sorting probability was $k$7, and the average success probability

$k$8

was $k$9. The paper further estimates a Bell-state-measurement scheme with post-selected success probability approximately $62\%\pm2\%$0 without ancillary photons, above the linear-optical limit of $62\%\pm2\%$1, and states that the architecture can be readily improved to $62\%\pm2\%$2 with design optimisations (Nielsen et al., 23 Apr 2026).

3. Passive sorting by spin, orbital angular momentum, and wavelength

Not all passive photon-sorting circuits rely on few-photon nonlinearity. In "The Design for a Nanoscale Single-Photon Spin Splitter" (Li et al., 2018), the mechanism is entirely photonic: a Bragg-modulated cylindrical waveguide combines transverse confinement, which produces an effective spin-orbit interaction of light, with a longitudinal Bragg grating, which creates photonic stopbands. The guided-mode equation contains an SOI correction,

$62\%\pm2\%$3

and the SOI shifts the propagation constant differently for the two helicities. The resulting Bragg band gap becomes spin dependent, so that spin-up photons are blocked in one direction and spin-down photons in the opposite direction (Li et al., 2018). The effect is small but explicit in the example analyzed: the SOI correction is about $62\%\pm2\%$4 of the original $62\%\pm2\%$5 away from cutoff, and the band-gap shift is about

$62\%\pm2\%$6

A second linear-optical lineage sorts orbital angular momentum. "Scalable orbital-angular-momentum sorting without destroying photon states" (Wang et al., 2016) uses symmetric multiport beam splitters and Dove prisms in a cascading structure. A rotated Dove prism induces the OAM-dependent phase

$62\%\pm2\%$7

and with path phases chosen as $62\%\pm2\%$8, interference at the second multiport sends each OAM value to a unique output port. The sorter is nondestructive because the photon is not absorbed or measured during sorting, and it preserves both OAM and spin angular momentum by using an improved Dove-prism module with a half-wave plate. The proposed PCS, PMCS, and TDCS architectures reduce hardware overhead substantially; for $62\%\pm2\%$9, the paper states that a direct sorter would need $\gtrsim 0.9997$0 beam splitters, while PCS, PMCS, and TDCS require only $\gtrsim 0.9997$1, $\gtrsim 0.9997$2, and $\gtrsim 0.9997$3, respectively (Wang et al., 2016).

Wavelength-sorting devices form another passive branch. "Mechanisms for photon sorting based on slit-groove arrays" (Villate-Guío et al., 2014) analyzes a Double-Pixel nanostructure in a thin gold film, with pixel 1 optimized for $\gtrsim 0.9997$4 and pixel 2 for $\gtrsim 0.9997$5. Each pixel uses a central subwavelength slit surrounded by grooves that scatter incoming light into surface plasmon polaritons and funnel energy into the slit. In the non-overlapping Double-Pixel, the transmission peaks are well resolved, the full width at half maximum is about $\gtrsim 0.9997$6 nm, and the crosstalk is below $\gtrsim 0.9997$7 (Villate-Guío et al., 2014). The paper identifies three regimes—non-overlapping pixels, overlapping grooves, and groove-overlap with the neighbor slit—showing that photon sorting depends strongly on the effective area shared by overlapping pixels.

A macroscopic wavelength-sorting embodiment is the "dichroicon" of "Spectral Photon Sorting For Large-Scale Cherenkov and Scintillation Detectors" (Kaptanoglu et al., 2019). This Winston-style concentrator uses dichroic reflectors to send long-wavelength light to the aperture PMT and short-wavelength light through the barrel to a separate detector. The benchtop measurements show that Cherenkov light can be identified with better than $\gtrsim 0.9997$8 purity while maintaining a high collection efficiency for the scintillation light (Kaptanoglu et al., 2019). In this case, the circuit sorts photons by wavelength at the surface level, not after detection, and the optical function is achieved with very low absorption because the dichroic filters redirect rather than remove photons.

4. Detection-oriented and correlation-engineered passive sorting

A passive photon-sorting circuit need not output distinct spatial ports. In "Photon Number Resolving Detection with a Single-Photon Detector and Adaptive Storage Loop" (Sullivan et al., 2023), the passive configuration is a loop-based photon-number-resolving detector consisting of a single click detector, a storage loop, and a tunable outcoupler fixed in advance. An input pulse with $\gtrsim 0.9997$9 photons is coupled into a fiber storage loop with storage efficiency $1.0\%$0; on each round trip, a fraction $1.0\%$1 of the remaining photons is sent to a single-photon detector with efficiency $1.0\%$2 and dark count probability $1.0\%$3; and in the passive case $1.0\%$4 for all $1.0\%$5. The detector reports only binary outcomes, $1.0\%$6, so the photons are not resolved simultaneously but are sorted across time bins. This architecture is distinct from other multiplexing schemes because the photons are stored and released in a controlled way while detection clicks are recorded (Sullivan et al., 2023).

The same paper makes clear where passivity ends. If $1.0\%$7 is updated from the posterior distribution $1.0\%$8, the setup becomes adaptive rather than passive. The adaptive scheme can extend the dynamic range by up to an order of magnitude relative to the best passive fixed-$1.0\%$9 choice, but that improvement is not a property of the passive circuit itself (Sullivan et al., 2023). This distinction matters because the phrase “passive photon-sorting circuit” is sometimes used loosely for systems whose core hardware is passive but whose best performance depends on real-time feedback.

Earlier semiconductor experiments showed a different detection-side meaning of sorting. "A semiconductor photon-sorter" (Bennett et al., 2016) demonstrated that a single quantum dot weakly coupled to a cavity can modify the counting statistics of a Poissonian beam, sorting the photons in number. The passive single-photon nonlinearity is created by coherent interference between the cavity-reflected field and the resonantly Rayleigh scattered field of the dot, together with conditional emitter dynamics after a photon detection event. The output autocorrelation reached $90\%$0 without polarization filtering; at detunings $90\%$1 and $90\%$2 the paper reports $90\%$3 and $90\%$4, respectively; and the transition could enhance the reflected signal by $90\%$5 at negative detuning and suppress it by $90\%$6 at positive detuning, for a total modulation of $90\%$7 (Bennett et al., 2016). The same device also used a single-hole spin to sort polarization-correlated photons from an uncorrelated stream.

Material nonlinearity provides a further passive route. "Quantum correlated photons via a passive nonlinear microcavity" (Zhao et al., 2023) used a waveguide-coupled $90\%$8 nonlinear microcavity in an InGaP photonic integrated circuit to create non-classical correlations, including photon anti-bunching, through interference between uncorrelated light and a two-photon bound state. The interaction Hamiltonian is

$90\%$9

and the correlation function is written as

$$t_k = \frac{ck - \omega_0 + i(\gamma-\Gamma)/2}{ck - \omega_0 + i(\gamma+\Gamma)/2},$$0

From second-harmonic generation the paper extracts $$t_k = \frac{ck - \omega_0 + i(\gamma-\Gamma)/2}{ck - \omega_0 + i(\gamma+\Gamma)/2},$$1; it reports violations of the relevant classical inequalities at $$t_k = \frac{ck - \omega_0 + i(\gamma-\Gamma)/2}{ck - \omega_0 + i(\gamma+\Gamma)/2},$$2 and $$t_k = \frac{ck - \omega_0 + i(\gamma-\Gamma)/2}{ck - \omega_0 + i(\gamma+\Gamma)/2},$$3 for two representative datasets; and in a bound-state-dominated regime it observes $$t_k = \frac{ck - \omega_0 + i(\gamma-\Gamma)/2}{ck - \omega_0 + i(\gamma+\Gamma)/2},$$4 with an estimated transmitted two-photon bound-state amplitude of $$t_k = \frac{ck - \omega_0 + i(\gamma-\Gamma)/2}{ck - \omega_0 + i(\gamma+\Gamma)/2},$$5 (Zhao et al., 2023). This is more accurately a passive photon-correlating element than a literal spatial sorter, but it belongs to the same family of passive circuits that exploit fixed nonlinear scattering to reshape photon-number sectors.

5. Roles in Bell measurements, photonic gates, and networked protocols

One of the principal motivations for passive photon sorting is the Bell-state measurement. In the 2026 quantum-dot interferometer, the measured sorting performance implies a Bell-state-measurement scheme with post-selected success probability approximately $$t_k = \frac{ck - \omega_0 + i(\gamma-\Gamma)/2}{ck - \omega_0 + i(\gamma+\Gamma)/2},$$6 without ancillary photons, exceeding the linear-optical limit of $$t_k = \frac{ck - \omega_0 + i(\gamma-\Gamma)/2}{ck - \omega_0 + i(\gamma+\Gamma)/2},$$7 (Nielsen et al., 23 Apr 2026). The mechanism is explicit: the $$t_k = \frac{ck - \omega_0 + i(\gamma-\Gamma)/2}{ck - \omega_0 + i(\gamma+\Gamma)/2},$$8 states contain at most one photon per path and are measured directly, whereas the $$t_k = \frac{ck - \omega_0 + i(\gamma-\Gamma)/2}{ck - \omega_0 + i(\gamma+\Gamma)/2},$$9 states bunch and require sorting to become unambiguous. The paper identifies boosted Bell measurements, fusion-based quantum computing, entanglement swapping, quantum repeater performance, loss tolerance in fusion-based schemes, and secret-key rates in repeater networks as practical implications (Nielsen et al., 23 Apr 2026).

The 2015 passive-two-level-scatterer proposal connects sorting even more directly to gate synthesis. After the passive nonlinear stage maps one- and two-photon sectors into orthogonal modes, the circuit uses sum-frequency generation and passive dichroic routing to realize efficient Bell measurements and a deterministic nonlinear-sign gate; with gradient echo memory and a second two-level scatterer, this becomes the core of a deterministic CZ-gate construction (Ralph et al., 2015). The important nuance is that the nonlinearity itself is passive, while perfect mode separation in that architecture relies on active Gaussian operations.

The waveguide-QED work of 2022 shows that the sorting primitive itself can already be close to ideal before being embedded into larger circuits. The reported photon-sorting fidelity $\eta=0.5$0 and nonlinear-sign gate fidelity $\eta=0.5$1 indicate that, in the chiral two-emitter model, the main challenge is not the logical principle but the realization of sufficiently ideal scattering conditions (Yang et al., 2022).

Related work also marks the boundary of the term. "Passive photonic CZ gate with two-level emitters in chiral multi-mode waveguide QED" (Levy-Yeyati et al., 2024) is best viewed as a passive nonlinear photonic logic element or conditional router rather than a literal photon sorter. Its operation depends on a conditional nonlinear $\eta=0.5$2-phase shift between polariton eigenstates in a two-mode chiral waveguide, with fidelity arbitrarily close to $\eta=0.5$3 in the limit of large number of emitters and coupling efficiency (Levy-Yeyati et al., 2024). A plausible implication is that photon sorting and conditional phase processing should be treated as adjacent, but not identical, categories within passive photonic quantum circuitry.

6. Technical limits, common misconceptions, and current directions

A common misconception is that “passive” means “purely linear.” The literature does not support that equivalence. The quantum-dot interferometer, the two-level-scatterer proposals, the chirally coupled emitter pair, the semiconductor microcavity device, and the $\eta=0.5$4 InGaP circuit are all passive in the operational sense that they use no active switching, control pulses, measurement feedback, or external clocked modulation during the sorting operation, yet they rely on intrinsic nonlinearity at the level of photon scattering (Yang et al., 2022, Nielsen et al., 23 Apr 2026, Zhao et al., 2023).

A second misconception is that a photon sorter must be a detector. Several papers state the opposite explicitly or by construction. The passive two-level-scatterer protocols and the deterministic waveguide-QED scheme map Fock sectors into different optical modes rather than directly measuring them (Ralph et al., 2015, Yang et al., 2022). By contrast, the storage-loop architecture infers $\eta=0.5$5 from a click record and is therefore a photon-number-resolving detector whose passive implementation sorts photons across time bins rather than across ports (Sullivan et al., 2023).

Current technical limits depend on platform. For the on-chip quantum-dot sorter, the principal limitations are finite waveguide coupling $\eta=0.5$6, pure dephasing, spectral diffusion, and inelastic scattering that distorts the photon wavepacket; these are identified as the reasons the two-photon sorting is only about $\eta=0.5$7 unfiltered and why the Bell-state-measurement success does not yet approach the ideal noiseless limit of $\eta=0.5$8 for that architecture (Nielsen et al., 23 Apr 2026). In the spin-splitting waveguide, the SOI-induced shifts are intrinsically small (Li et al., 2018). In the storage-loop detector, performance degrades strongly for lower $\eta=0.5$9, especially around $$\alpha |1_f \rangle + \xi |2_f \rangle \to \alpha |1_{f'} \rangle + \xi |\bar 2_{f'} \rangle.$$0, because loop loss becomes the dominant bottleneck (Sullivan et al., 2023). In the dichroicon, off-axis behavior and angle-dependent filter response constrain collection and purity (Kaptanoglu et al., 2019).

The most concrete near-term direction is emitter-waveguide improvement. For the 2026 sorter, the paper argues that improving $$\alpha |1_f \rangle + \xi |2_f \rangle \to \alpha |1_{f'} \rangle + \xi |\bar 2_{f'} \rangle.$$1 toward near-unity using a photonic crystal waveguide can raise the two-photon sorting probability to about $$\alpha |1_f \rangle + \xi |2_f \rangle \to \alpha |1_{f'} \rangle + \xi |\bar 2_{f'} \rangle.$$2 for the measured noise parameters; a state-of-the-art coupling of $$\alpha |1_f \rangle + \xi |2_f \rangle \to \alpha |1_{f'} \rangle + \xi |\bar 2_{f'} \rangle.$$3 would push the normalized Bell-state-measurement success probability above $$\alpha |1_f \rangle + \xi |2_f \rangle \to \alpha |1_{f'} \rangle + \xi |\bar 2_{f'} \rangle.$$4; and with further design optimization the architecture can exceed $$\alpha |1_f \rangle + \xi |2_f \rangle \to \alpha |1_{f'} \rangle + \xi |\bar 2_{f'} \rangle.$$5 (Nielsen et al., 23 Apr 2026). Parallel scaling strategies appear elsewhere: large even emitter arrays in chiral multi-mode waveguide QED improve gate fidelity substantially (Levy-Yeyati et al., 2024), and cascading OAM structures reduce the number of beam splitters needed for high-dimensional sorting (Wang et al., 2016). Taken together, these results suggest that passive photon-sorting circuits are evolving from isolated proof-of-principle devices into a broader class of integrated photonic primitives for quantum measurement, nonlinear routing, and photonic information processing.