Quantum network telescopes

Chapter opening

Quantum network telescopes address a specific engineering bottleneck in long-baseline optical interferometry: the single-photon coherent state carried by weak starlight is hard to deliver to one beam combiner across kilometer to hundred-kilometer baselines with low loss and low phase noise. The quantum approach changes what has to travel far. Instead of transporting unknown starlight, it distributes entangled resources that can be prepared in advance, verified, discarded, and tried again. After starlight arrives, it interacts only locally with quantum memories or auxiliary photons, and the measurement results are combined with classical communication. The quantum repeater telescope of Gottesman–Jennewein–Croke, the memory-assisted optical quantum network of Khabiboulline–Borregaard–De Greve–Lukin, and the nonlocal optical interferometry experiment of Stas et al. have moved the idea from resource estimates toward experimental prototypes [Gottesman et al., 2012, Khabiboulline et al., 2019, Marchese and Kok, 2023, Padilla et al., 2026, Stas et al., 2026, Zhang and Jennewein, 2025].

Why traditional optical beam combination stalls at baseline

A two-telescope amplitude interferometer measures complex visibility; its Fourier relation to sky brightness was given in Eq. (92) of Chapter Spatial coherence and intensity interferometry. Quantum network schemes focus on extremely weak starlight: the mean photon number per coherence-time window is \(\epsilon\ll1\). Most windows are empty, and a small fraction contain one astronomical photon. If path information is not destroyed before detection, that photon is not classically labeled as “belonging to the left telescope” or “belonging to the right telescope.” It is a superposition of the two receiving paths. For a single point source, the one-photon state across two apertures is

(327)\[|\psi_\star\rangle = \frac{|1\rangle_L|0\rangle_R + e^{i\phi} |0\rangle_L|1\rangle_R}{\sqrt2}, \qquad \phi = \frac{2\pi{\bf B}\cdot\boldsymbol\theta}{\lambda}.\]

Here \(|1\rangle_L|0\rangle_R\) means that the left spatial mode contains one photon and the right mode is empty in that time window; \(|0\rangle_L|1\rangle_R\) means the opposite. \(\phi\) is the geometric phase, \({\bf B}\) is projected baseline, \(\boldsymbol\theta\) is the point-source angular offset from the phase center, and \(\lambda\) is wavelength. An extended source is an incoherent mixture of many point-source phases. After mixing, the surviving quantity is the complex visibility \(V\), and the one-photon density matrix is

(328)\[\begin{split}\rho_1 = \frac{1}{2} \begin{pmatrix} 1 & V\\ V^* & 1 \end{pmatrix}_{\{|10\rangle,|01\rangle\}} .\end{split}\]

Conventional amplitude interferometry has to bring the two spatial modes to the same beam splitter. If one path travels through a lossy link of length \(L\), the single-photon transmission is commonly written

(329)\[\eta_{\rm ch}(L) = 10^{-\alpha_{\rm dB}L/10}.\]

\(\alpha_{\rm dB}\) is in \({\rm dB\,km^{-1}}\). Visible light in ordinary fiber can suffer \(20\)–30 \({\rm dB\,km^{-1}}\), so after \(1\,{\rm km}\) the transmission is already below \(10^{-2}\)–\(10^{-3}\). Telecom fiber at 1550 nm can reach \(\sim0.2\,{\rm dB\,km^{-1}}\), but stellar frequency conversion, coupling, phase stabilization, and background noise multiply the ideal transmission by additional efficiency factors. Clear-air free-space links can be estimated at \(\sim0.5\,{\rm dB\,km^{-1}}\), but atmospheric turbulence and pointing errors are not a simple exponential loss [Gottesman et al., 2012, Khabiboulline et al., 2019, Rajagopal et al., 2024].

Figure 98 The appeal and difficulty of long baselines come from the same scale. The left panel shows transmission for several links if the astronomical photon is transported directly. Visible fiber is already severely lossy at kilometer scales, and telecom fiber becomes expensive at hundred-kilometer scales. The right panel shows the angular-resolution scale λ/B: 600 nm light reaches hundreds of \(\mu{\rm as}\) on a 1 km baseline and \(\mu{\rm as}\) scales on a 100 km baseline.

The basic angular-resolution scale is

(330)\[\theta_{\rm res} \sim \frac{\lambda}{B} = 124\,\mu{\rm as} \left(\frac{\lambda}{600\,{\rm nm}}\right) \left(\frac{1\,{\rm km}}{B}\right).\]

For \(B=10\,{\rm km}\), this is \(12\,\mu{\rm as}\). For \(B=100\,{\rm km}\), it is \(1.2\,\mu{\rm as}\). The attraction of quantum network telescopes lies at this scale. They do not necessarily improve the single-aperture sensitivity, but they may extend optical and near-infrared interferometry from hundreds of meters to kilometers, tens of kilometers, or more. HBT intensity interferometry already avoids optical phase transport, but it mainly measures \(|V|^2\), with different sensitivity and phase-recovery routes. The quantum-network route aims to keep first-order coherence phase information without transporting unknown starlight over long distances [Crawford et al., 2023, Hanbury Brown, 1956, Kellerer, 2014, Kurek et al., 2016, Rajagopal et al., 2024].

How preshared entanglement replaces transporting starlight

The Gottesman–Jennewein–Croke scheme uses a known path-entangled laboratory photon,

(331)\[|\Phi_\delta\rangle = \frac{|1\rangle_L|0\rangle_R + e^{i\delta} |0\rangle_L|1\rangle_R}{\sqrt2}\]

to interfere locally with the unknown astronomical photon. The entangled state can be distributed by a quantum network ahead of time; if distribution fails, the network simply tries again and no starlight is lost. Once starlight arrives, each site sends the stellar mode and the laboratory mode into a local beam splitter and keeps only events in which both sides detect one photon. The correlated and anticorrelated click probabilities contain

(332)\[P_{\pm}(\delta) = \frac{1}{2} \left[ 1 \pm {\rm Re} \left( V e^{-i\delta} \right) \right].\]

Scanning or changing \(\delta\) estimates the real and imaginary parts of \(V\). The local beam splitters and coincidence detection act as a Bell-state projection: which-path information between the stellar mode and the laboratory entangled mode is erased, leaving only the phase relation between paths. A Bell-state measurement projects two photons onto a maximally entangled two-mode basis. Linear optics can unambiguously identify only part of the click patterns, so about half of the useful stellar events enter the estimator. A complete Bell-state measurement or more complex quantum processing could in principle remove this 50% loss [Bennett et al., 1993, Gottesman et al., 2012, Wootters and Zurek, 1982].

The first constraint is resource rate. If the observing bandwidth is \(\Delta\nu\), the coherence time is about \(1/\Delta\nu\). A direct GJC route needs a matching entangled photon in every coherence-time window that could contain starlight. \(\Delta\nu=10\,{\rm GHz}\) means \(10^{10}\) windows per second. Rajagopal et al.’s astronomical roadmap points out that present high-quality entangled-photon sources are far from that rate. GJC is better viewed as a short-baseline on-sky proof of principle than as a near-term replacement for existing optical interferometric arrays [Gottesman et al., 2012, Rajagopal et al., 2024].

The Khabiboulline–Borregaard–De Greve–Lukin scheme uses the fact that the source is weak: within a long measurement window, the mean number of relevant stellar photons is \(\epsilon\ll1\). Split the window into \(M\sim1/\epsilon\) time bins, and only one time bin is likely to contain a photon. A unary code would require \(M\) Bell pairs. A binary code stores the arrival time using only

(333)\[n_{\rm mem} = \left\lceil \log_2(M+1) \right\rceil \simeq \left\lceil \log_2(1/\epsilon) \right\rceil\]

memory qubits, with each qubit pair using one Bell pair for a nonlocal parity check. If \(M=10^6\), about 20 qubits encode the arrival time, whereas a unary code would require one million entangled pairs. Representative numbers in the paper are: for \(\Delta f=1\,{\rm MHz}\) and a 1 s measurement window, \(N=10^6\) time bins give \(\log_2N\simeq20\); in one astronomical example, a 10th-magnitude star, \(10\,{\rm m^2}\) collecting area, and \(10\,{\rm GHz}\) detection bandwidth lead to a resource target of about \(20\)–30 qubits and a \(\sim200\,{\rm kHz}\) entanglement supply rate. The supplementary analysis of Stas et al. also uses 20 SiV nodes, a 1 kHz zero- distance entanglement rate, and a 1 s window to illustrate this logarithmic scaling path [Czupryniak et al., 2022, Khabiboulline et al., 2019, Rajagopal et al., 2024, Stas et al., 2026].

Figure 99 Weak starlight makes time-bin encoding useful. The left panel compares Bell-pair demand for unary and binary codes. When the mean photon number per bin ϵ is small, M ∼ 1/ϵ bins can be labeled by log₂(M + 1) memory qubits. The right panel shows that a 1 s measurement window with 1 MHz bandwidth has about 10⁶ bins, or about 20 qubits.

Quantum repeaters are the underlying communication technology for these schemes. Direct transmission of an unknown quantum state is limited by loss and the no-cloning theorem. A repeater divides the full distance into segments, builds entanglement over short links, and connects the links by entanglement swapping. An ideal repeater can replace exponential loss with milder resource scaling, but real systems still face Bell-state measurement success probability, memory lifetime, dark counts, gate fidelity, and frequency conversion. The DLCZ atomic-ensemble protocol, quantum-internet roadmaps, and quantum-memory reviews all place memory at the center of the resource budget because memory synchronizes probabilistic success events [Briegel et al., 1998, Duan et al., 2001, Kimble, 2008, Sangouard et al., 2011, Ursin et al., 2006, Van Meter, 2012].

Resource rates, storage time, and fidelity

The first resource constraint is entanglement supply. If the accepted starlight event rate is \(R_\star\) and each event consumes on average \(n_{\rm pair}\) Bell pairs, then

(334)\[R_{\rm ent} \gtrsim \frac{n_{\rm pair}R_\star}{p_{\rm ready}},\]

where \(p_{\rm ready}\) is the probability that usable Bell pairs are ready when starlight arrives. \(R_\star\) is not the telescope’s total photon rate. It is the rate of events that enter the target spatial mode, frequency channel, polarization channel, and time window and then pass quality cuts. For bright broadband sources, \(R_\star\) can be very high and GJC-type schemes are overwhelmed by resource rate. For narrowband weak sources, \(R_\star\) is small enough that memory-assisted schemes can trade lower \(R_{\rm ent}\) for a long baseline.

The second resource constraint is storage time. At minimum, the quantum state or measurement record has to survive until classical communication and nonlocal checks finish:

(335)\[T_{\rm mem} \gtrsim \max\!\left[ \frac{B}{c}, T_{\rm ent}, T_{\rm proc}, T_{\rm win} \right].\]

\(B/c=3.3\,\mu{\rm s}\,(B/{\rm km})\). A \(100\,{\rm km}\) baseline requires only \(0.33\,{\rm ms}\) of light-travel time, but a Khabiboulline-type binary time-bin scheme may need a measurement window \(T_{\rm win}\sim1\,{\rm s}\) for narrowband weak light, which is far stricter. Quantum-memory papers usually describe hardware by fidelity, efficiency, storage time, bandwidth, multimode capacity, and wavelength. Conditional fidelity for single-photon storage is the mode overlap between the retrieved and written wavepacket, and efficiency is the probability of successful photon retrieval. For unknown-state teleportation or nonlocal interference, the product of these quantities, together with phase noise and mode matching, enters the final visibility [Heshami et al., 2016, Lvovsky et al., 2009, Simon et al., 2010].

Figure 100 Entanglement rate and storage time provide the first resource closure conditions. The left panel converts accepted starlight rate R_⋆ into the required Bell-pair rate; the more entangled pairs consumed per event, the higher the demand line. The right panel converts baseline into B/c. For kilometer baselines, light-travel time is microseconds to milliseconds, but narrowband memory schemes are often set by the measurement window and entanglement-generation time.

Resource budgets often multiply the main loss factors into an effective fidelity scale,

(336)\[F_{\rm eff} \simeq F_{\rm Bell} \eta_{\rm write} \eta_{\rm read} \eta_{\rm conv} \exp(-T/T_2) (1-p_{\rm dark}) M_{\rm mode}.\]

\(F_{\rm Bell}\) is the fidelity of the preshared Bell pair; \(\eta_{\rm write}\) and \(\eta_{\rm read}\) are write and read efficiencies; \(\eta_{\rm conv}\) is frequency-conversion efficiency; \(T_2\) is coherence time; \(p_{\rm dark}\) is the effective dark-trigger probability; and \(M_{\rm mode}\le1\) describes frequency, time, polarization, and spatial-mode matching. This is not a complete quantum-channel model, but it quickly exposes bottlenecks. For example, \(T/T_2=1\) alone gives a coherence factor \(e^{-1}\simeq0.37\). If \(F_{\rm Bell}=0.8\), read and write are both \(0.7\), and conversion is \(0.8\), the product is already \(\sim0.3\) before including dark counts or mode mismatch.

Figure 101 Effective resource quality is set jointly by the link and the memory. The left panel shows channel factors for several dB/km losses. The right panel shows storage time relative to T₂. A long-baseline scheme can have attractive angular resolution only if Bell-pair fidelity, read/write efficiency, frequency conversion, and storage coherence close at the same time.

Frequency conversion is an additional difficulty in the astronomical version. Many quantum-memory materials couple strongly at frequencies that are not the target astronomical band, while long-distance fiber favors the telecom band. Quantum frequency conversion must reduce noise while preserving single-photon coherence and polarization or time-bin encoding. If the goal is to interfere with starlight, the converted spectral width, central frequency, time wavepacket, and polarization have to match the stellar mode. A 1% mode mismatch does not only lose 1% of the photons; it directly lowers interference visibility [Heshami et al., 2016, Kumar, 1990, Rajagopal et al., 2024, Simon et al., 2010].

Continuous variables, single-photon assistance, and resolution limits

Here “continuous variable” means the two quadratures of the optical field, not a discrete left/right-path qubit. Continuous-variable teleportation uses a preshared two-mode squeezed vacuum and local measurements to transfer quadrature information from one mode to a remote mode. If the resource state is

(337)\[|\psi_{\rm TMSV}\rangle = \sqrt{1-\lambda^2} \sum_{n=0}^{\infty} \lambda^n |n\rangle_A|n\rangle_B, \qquad \bar N = 2\sinh^2 r,\]

\(r\) is the squeezing parameter and \(\bar N\) is the total mean photon number in the two modes. Only the ideal limit \(r\to\infty\) teleports an arbitrary continuous-variable state without noise. Finite \(r\) adds effective Gaussian noise, usually decreasing as \(e^{-2r}\). Gottesman et al. already noted that CV teleportation can avoid the 50% limitation of single-qubit Bell measurement, but continuous-variable repeaters and high-fidelity long-distance squeezed resources are harder. Recent optimality analyses also caution that resource comparisons must account for photon-number superselection, locality, and finite entanglement budgets; squeezing is only one entry in the resource ledger [Braunstein and Kimble, 1998, Gottesman et al., 2012, Zhang and Jennewein, 2025].

Another nearer-term route avoids long-lived quantum memories and uses locally or ground-generated single photons to assist stellar interference. In the Marchese–Kok scheme, the astronomical photon is measured as early as possible at the receiving site, while the auxiliary single photon is transmitted across the baseline. Loss mainly affects the “retryable” ground photon. For small- angle astrometry, phase and angle are related by

(338)\[\phi = \frac{2\pi B\theta}{\lambda}, \qquad \sigma_\theta \ge \frac{\lambda}{2\pi B} \frac{1}{\sqrt{N_{\rm ev}\mathcal F_\phi}},\]

where \(N_{\rm ev}\) is the effective number of events and \(\mathcal F_\phi\) is the single-event phase Fisher information. In a model with \(\lambda=628\,{\rm nm}\) and fiber attenuation length \(L_0=10\,{\rm km}\), Marchese and Kok obtained astrometric scales of order tens of \(\mu{\rm as}\). Modak and Kok further showed that the stellar-mode occupation \(\epsilon\ll1\) and indistinguishability between auxiliary photons and starlight strongly affect the gain. If \(\epsilon\) drops from 1 to \(0.01\), the advantage of adding auxiliary photons weakens quickly. If indistinguishability is only \(96\%\), a three-photon scheme may still help, but higher photon number does not necessarily keep improving performance [Marchese and Kok, 2023, Modak and Kok, 2025].

The distributed entanglement imaging work of Padilla, Sajjad, Saif, and Guha pushes the question into more general multimode imaging limits. Each receiving station first performs local spatial-mode sorting, and preshared Bell pairs are used to simulate a nonlocal beam splitter or more general interferometric network. Baseline is only one resource. Spatial-mode information within each aperture, source-structure priors, array geometry, and measurement-basis choice all change the Fisher information. For binary-star separation, aiming only at the Rayleigh-scale \(\lambda/B\) can miss the small-separation advantage from local mode sorting. Aiming only at local superresolution loses the phase lever arm supplied by the long baseline [Padilla et al., 2026, Zhang and Jennewein, 2025].

Experimental prototypes and error budgets

The 2026 experiment by Stas et al. moved “nonlocal phase measurement” from a roadmap into the laboratory. They used two SiV diamond nanocavity nodes, an electron spin, and a \({}^{29}{\rm Si}\) nuclear-spin memory. A remote Bell pair was generated first; a weak signal photon then interacted locally with the nodes, and photon erasure plus nonlocal nondestructive heralding filtered out vacuum events. The experiment achieved an electron Bell-state fidelity \(F=0.83(3)\). At an entanglement rate of \(13\,{\rm Hz}\), \(F\ge0.5\); at \(1.9\,{\rm Hz}\), \(F=0.79(3)\). In the full nonlocal phase measurement, the heralded visibility increased from the unheralded \(0.031(18)\) to \(0.090(26)\). With a \(1.55\,{\rm km}\) fiber baseline, the nuclear parity oscillation visibility was \(0.11(4)\), and the Bell-pair fidelity remained above the verifiable entanglement threshold at about \(F=0.63(3)\) [Stas et al., 2026].

The phase error in such an experiment is set jointly by the number of effective trials, heralding success probability, and measured phase-oscillation visibility. In Fisher-information form,

(339)\[\mathcal I_\phi \simeq N_{\rm tr}\, p_{\rm succ}\, V_{\rm meas}^2, \qquad {\rm Var}(\hat\phi)\ge \mathcal I_\phi^{-1}.\]

\(N_{\rm tr}\) is the number of protocol trials, \(p_{\rm succ}\) is the successful-herald probability, and \(V_{\rm meas}\) is the phase-oscillation visibility. In the implementation of Stas et al.,

(340)\[p_{\rm succ} = \eta_{\rm erasure}\eta_{\rm herald} P(n_{\rm photon}\ge1),\]

while multiphoton events, mis-heralding, and Bell-state infidelity reduce \(V_{\rm meas}\). This explains why a high heralding rate is not automatically good. If the rate is increased by raising the mean photon number but multiphoton contamination lowers visibility, \(\mathcal I_\phi\) can decrease rather than increase. The phase error is then converted to angular error with Eq. (338). A longer baseline turns the same \(\sigma_\phi\) into a smaller \(\sigma_\theta\), but it also increases entanglement-distribution overhead, phase-locking difficulty, and latency.

Figure 102 The statistical gain of a nonlocal phase measurement depends on both success probability and visibility. The left panel shows the single-trial Fisher-information scale \(p_{\rm succ}V^2\); reducing visibility by a factor of three reduces information by a factor of nine. The right panel converts trial number into phase error, showing that high repetition rate, low mis-heralding, and high Bell fidelity must hold at the same time.

The two-photon precision astrometry experiment of Crawford et al. offers another near-term step. Using two quasi-thermal light sources and time-tagging detectors in a benchtop analogue, they observed photon-pair coincidences that varied with phase. This is not a complete quantum network telescope, but it is a useful pre-on-sky validation platform: time tagging, polarization matching, coherence time, HBT-peak fitting, phase stability, and data selection are all relevant to real weak astronomical light [Crawford et al., 2023].

Putting the resources on one plot, current experiments are roughly in the \(R_{\rm ent}\sim1\)–10 \({\rm Hz}\), short-baseline, low-effective-visibility region. Astronomically useful memory-assisted narrowband schemes may require \(R_{\rm ent}\sim{\rm kHz}\) to \(100\,{\rm kHz}\), \(T_{\rm mem}\sim{\rm ms}\) to seconds, tens of memory qubits, and high mode matching. Broadband imaging is harder. The resource constraints have to close together: insufficient \(R_{\rm ent}\) wastes stellar events; insufficient \(T_{\rm mem}\) makes the parity check miss the window; insufficient \(F_{\rm eff}\) erases visibility; and a bad estimate of \(R_\star\) can make the whole scheme infeasible before the first observing night.

Figure 103 The resource space for quantum network telescopes is set by entanglement rate and storage time. White lines mark the B/c time for 1 km, 100 km, and 10⁴ km baselines. Points indicate the scale of current Hz-rate experiments and longer-term kHz–s targets. Color is only a resource- product scale; full feasibility also multiplies fidelity, mode matching, and astronomical photon rate.

Complementarity with intensity interferometry

Quantum network telescopes are a long-term complementary route. In the near term they have to develop alongside ELT, VLTI, CHARA, CTAO, and intensity interferometry arrays. Immediate targets are intensity interferometry and two-photon correlations: the hardware is close to existing large-area light collectors, SNSPD/SPAD time tagging, narrowband filtering, and offline correlation, and the science cases concentrate on bright-star angular diameters, binaries, and line-emitting regions. The next step adds local mode sorting, two-photon astrometry, and GJC-type short-baseline on-sky demonstrations to show that stellar modes can interfere stably with laboratory entangled resources. Memory-assisted nonlocal first-order coherence measurement needs quantum memories, frequency conversion, entanglement distribution, Bell fidelity, and astronomical synchronization to mature together, so it belongs to a farther technical horizon [Crawford et al., 2023, Hanbury Brown, 1956, Rajagopal et al., 2024, Stas et al., 2026].

Observation planning can start from a simple closure condition,

(341)\[N_{\rm useful} = R_\star T_{\rm obs} p_{\rm ready} p_{\rm succ} V_{\rm meas}^2 \gtrsim N_{\rm req}(\sigma_\theta,{\bf B},\lambda).\]

\(T_{\rm obs}\) is total observing time, and \(N_{\rm req}\) is set by the target angular precision, array geometry, and number of model parameters. This equation puts astronomy and quantum engineering on the same ledger. Bright sources, narrow bands, known arrival times, or periodic signals reduce resource pressure. Faint broadband continuum sources amplify every difficulty. The same ledger also applies to more general observing designs, with the observable changed from nonlocal phase to \(|V|^2\), \(g^{(2)}\), polarization angle, or time delay.

The most valuable present product of quantum network telescope work is this feasibility ledger, not a mature instrument design. The next part returns to observing design: scientific parameters must first be translated into event rates, channels, baselines, backgrounds, and covariances before one can choose among intensity interferometry, polarization event tables, transient triggers, or future nonlocal phase measurements.