Photon-to-Magnon Quantum Teleportation

• Photon-to-magnon quantum teleportation is a protocol that transfers photonic quantum states to collective excitations in matter using Bell measurements and active feed-forward.
• The approach spans different platforms, including telecom-to-AFC teleportation in rare-earth crystals and both discrete- and continuous-variable schemes in YIG spheres.
• Experiments demonstrate long-distance operation and temporal multiplexing, while proposals focus on enhancing fidelity with optimized resources and non-Gaussian distillation.

Searching arXiv for the specified teleportation and optomagnonic papers to ground the article in the cited literature. First, retrieving the 2022 experimental telecom-photon to solid-state collective-excitation teleportation paper. Now retrieving the 2023 discrete-variable optomagnonic teleportation proposal. Finally, retrieving the 2025 continuous-variable optomagnonic teleportation paper with non-Gaussian distillation. Photon-to-magnon quantum teleportation denotes a class of protocols in which an optical quantum state is transferred, by Bell-measurement conditioning and feed-forward, to a collective excitation in matter. In the present literature, the expression spans physically distinct targets: a delocalized collective excitation in a rare-earth–doped solid-state ensemble, dual-rail magnons in macroscopic yttrium-iron-garnet (YIG) spheres, and the uniform Kittel magnon mode in a cavity optomagnonic platform. The experimentally realized benchmark is long-distance teleportation from a telecom photon to a solid-state collective excitation stored in a praseodymium-doped crystal, whereas the YIG-based schemes remain proposals in discrete-variable and continuous-variable settings (Lago-Rivera et al., 2022, Fan et al., 2023, Lu et al., 16 Jul 2025).

1. Scope of the term and physical realizations

The topic is unified by the transfer of photonic quantum information to a many-body excitation, but the relevant “magnon” is not the same object in all implementations. In the solid-state ensemble experiment, the target is a single collective excitation delocalized over $N$ ions in an atomic frequency comb (AFC) memory. This mode is magnon-like because it is a delocalized single excitation with a well-defined phase pattern, but it is stored as an optical excited-state coherence rather than as a ground-state spin-wave. By contrast, the YIG proposals concern genuine magnetostatic magnons in ferrimagnetic media at GHz frequencies (Lago-Rivera et al., 2022, Fan et al., 2023, Lu et al., 16 Jul 2025).

Regime	Target excitation	Status
Telecom-to-AFC teleportation	Collective optical excitation in a Pr$^{3+}$-doped crystal	Demonstrated over 1 km with active feed-forward and multiplexing
Discrete-variable optomagnonic teleportation	Dual-rail magnons in two YIG spheres	Proposed
Continuous-variable optomagnonic teleportation	Kittel magnon mode in a YIG sphere inside a microwave cavity	Proposed with non-Gaussian distillation

This distinction is central to terminology. A true spin-wave in an ensemble memory has the form

$$|W_{\rm spin}\rangle = \frac{1}{\sqrt{N}} \sum_j e^{i (k_s-k_c)\cdot r_j}\, |g\ldots s_j\ldots g\rangle,$$

whereas the AFC optical excitation is

$$|W_{\rm opt}\rangle = \frac{1}{\sqrt{N}} \sum_{j=1}^{N} e^{i k\cdot r_j} |g_1\ldots e_j\ldots g_N\rangle.$$

Microwave magnons in YIG instead correspond to collective precessional modes of a macroscopically magnetized solid. Much of the literature’s ambiguity arises from collapsing these distinct collective excitations under the same label.

2. Teleportation structure, encodings, and Bell measurements

All photon-to-magnon teleportation schemes considered here are organized around the standard teleportation identity

$$(|\psi\rangle_A \otimes |\Phi^+\rangle_{BC}) \to {\rm BSM}_{AB} \Rightarrow \rho_C = \sigma_i |\psi\rangle\langle\psi| \sigma_i,$$

with Bell states

$$|\Phi^\pm\rangle = \frac{|00\rangle \pm |11\rangle}{\sqrt{2}}, \qquad |\Psi^\pm\rangle = \frac{|01\rangle \pm |10\rangle}{\sqrt{2}}.$$

What changes across platforms is the logical encoding of $|0\rangle,|1\rangle$, the entanglement resource, and the experimentally accessible Bell subspace (Lago-Rivera et al., 2022, Fan et al., 2023, Lu et al., 16 Jul 2025).

In the telecom-to-solid-state experiment, the input is a time-bin qubit

$$|\psi\rangle_{IQ} = \alpha|e\rangle + e^{i\phi}\beta|l\rangle,$$

and the entanglement resource is an energy-time entangled photon pair,

$$|\Phi^+\rangle_{s,i} = \frac{|e_s e_i\rangle + |l_s l_i\rangle}{\sqrt{2}}.$$

A linear-optics time-bin Bell-state measurement projects onto the $|\Psi^\pm\rangle$ subspace by detecting two consecutive clicks either at the same output, corresponding to $^{3+}$0, or at alternate outputs, corresponding to $^{3+}$1.

In the discrete-variable optomagnonic proposal, the unknown state is a polarization qubit,

$^{3+}$2

and teleportation maps it onto a dual-rail magnonic encoding distributed across two YIG spheres,

$^{3+}$3

The optomagnonic entangled resource is

$^{3+}$4

and the polarization Bell measurement resolves $^{3+}$5 using half-wave plates, polarizing beam splitters, and coincidence patterns.

In the continuous-variable optomagnonic proposal, the resource is a two-mode squeezed vacuum shared between a TE Stokes optical mode and a magnon mode,

$^{3+}$6

generated by pulsed Stokes Brillouin light scattering. The Bell measurement is a Braunstein–Kimble optical homodyne measurement, and the correction is a microwave-driven phase-space displacement of the magnon.

3. Telecom-photon teleportation to a solid-state collective excitation

The first long-distance implementation transfers a telecom photonic qubit to a matter qubit stored as a collective excitation in a Pr$^{3+}$7-doped crystal operated with the AFC protocol (Lago-Rivera et al., 2022). Alice employs a narrowband, cavity-enhanced SPDC source with linewidth $^{3+}$8 MHz, producing a $^{3+}$9 nm signal photon and a $$|W_{\rm spin}\rangle = \frac{1}{\sqrt{N}} \sum_j e^{i (k_s-k_c)\cdot r_j}\, |g\ldots s_j\ldots g\rangle,$$0 nm telecom idler photon. The SPDC pump coherence time is $$|W_{\rm spin}\rangle = \frac{1}{\sqrt{N}} \sum_j e^{i (k_s-k_c)\cdot r_j}\, |g\ldots s_j\ldots g\rangle,$$1 and the pair coherence time is $$|W_{\rm spin}\rangle = \frac{1}{\sqrt{N}} \sum_j e^{i (k_s-k_c)\cdot r_j}\, |g\ldots s_j\ldots g\rangle,$$2 ns. The $$|W_{\rm spin}\rangle = \frac{1}{\sqrt{N}} \sum_j e^{i (k_s-k_c)\cdot r_j}\, |g\ldots s_j\ldots g\rangle,$$3 nm signal is stored in the AFC memory, while the $$|W_{\rm spin}\rangle = \frac{1}{\sqrt{N}} \sum_j e^{i (k_s-k_c)\cdot r_j}\, |g\ldots s_j\ldots g\rangle,$$4 nm idler propagates to Bob through optical fiber. Bob prepares the input telecom qubit with an optical parametric oscillator operating in difference-frequency generation, attenuated to the single-photon level with mean photons per qubit $$|W_{\rm spin}\rangle = \frac{1}{\sqrt{N}} \sum_j e^{i (k_s-k_c)\cdot r_j}\, |g\ldots s_j\ldots g\rangle,$$5, and shaped into early and late time bins separated by $$|W_{\rm spin}\rangle = \frac{1}{\sqrt{N}} \sum_j e^{i (k_s-k_c)\cdot r_j}\, |g\ldots s_j\ldots g\rangle,$$6 ns.

The Bell-state measurement interferes Bob’s input qubit with Alice’s idler on a beamsplitter. In the time-bin basis,

$$|W_{\rm spin}\rangle = \frac{1}{\sqrt{N}} \sum_j e^{i (k_s-k_c)\cdot r_j}\, |g\ldots s_j\ldots g\rangle,$$7

A $$|W_{\rm spin}\rangle = \frac{1}{\sqrt{N}} \sum_j e^{i (k_s-k_c)\cdot r_j}\, |g\ldots s_j\ldots g\rangle,$$8 outcome teleports $$|W_{\rm spin}\rangle = \frac{1}{\sqrt{N}} \sum_j e^{i (k_s-k_c)\cdot r_j}\, |g\ldots s_j\ldots g\rangle,$$9, whereas a $$|W_{\rm opt}\rangle = \frac{1}{\sqrt{N}} \sum_{j=1}^{N} e^{i k\cdot r_j} |g_1\ldots e_j\ldots g_N\rangle.$$0 outcome teleports $$|W_{\rm opt}\rangle = \frac{1}{\sqrt{N}} \sum_{j=1}^{N} e^{i k\cdot r_j} |g_1\ldots e_j\ldots g_N\rangle.$$1. The experiment completes the protocol by active feed-forward: conditioned on $$|W_{\rm opt}\rangle = \frac{1}{\sqrt{N}} \sum_{j=1}^{N} e^{i k\cdot r_j} |g_1\ldots e_j\ldots g_N\rangle.$$2, Alice applies a $$|W_{\rm opt}\rangle = \frac{1}{\sqrt{N}} \sum_{j=1}^{N} e^{i k\cdot r_j} |g_1\ldots e_j\ldots g_N\rangle.$$3 phase shift between the early and late time bins, implementing

$$|W_{\rm opt}\rangle = \frac{1}{\sqrt{N}} \sum_{j=1}^{N} e^{i k\cdot r_j} |g_1\ldots e_j\ldots g_N\rangle.$$4

This is realized by a high-speed phase shifter at $$|W_{\rm opt}\rangle = \frac{1}{\sqrt{N}} \sum_{j=1}^{N} e^{i k\cdot r_j} |g_1\ldots e_j\ldots g_N\rangle.$$5 nm driven by real-time logic. The remaining $$|W_{\rm opt}\rangle = \frac{1}{\sqrt{N}} \sum_{j=1}^{N} e^{i k\cdot r_j} |g_1\ldots e_j\ldots g_N\rangle.$$6 correction was not implemented, although the authors state that it can be effected with an unbalanced Mach–Zehnder interferometer.

Two configurations were characterized. In the short-distance case, Alice and Bob were separated by a few meters, with AFC storage time $$|W_{\rm opt}\rangle = \frac{1}{\sqrt{N}} \sum_{j=1}^{N} e^{i k\cdot r_j} |g_1\ldots e_j\ldots g_N\rangle.$$7 and storage-and-retrieval efficiency $$|W_{\rm opt}\rangle = \frac{1}{\sqrt{N}} \sum_{j=1}^{N} e^{i k\cdot r_j} |g_1\ldots e_j\ldots g_N\rangle.$$8. In the long-distance case, $$|W_{\rm opt}\rangle = \frac{1}{\sqrt{N}} \sum_{j=1}^{N} e^{i k\cdot r_j} |g_1\ldots e_j\ldots g_N\rangle.$$9 km of telecom fiber separated Alice and Bob; the idler propagation time was $$(|\psi\rangle_A \otimes |\Phi^+\rangle_{BC}) \to {\rm BSM}_{AB} \Rightarrow \rho_C = \sigma_i |\psi\rangle\langle\psi| \sigma_i,$$0, and an additional electronic delay of $$(|\psi\rangle_A \otimes |\Phi^+\rangle_{BC}) \to {\rm BSM}_{AB} \Rightarrow \rho_C = \sigma_i |\psi\rangle\langle\psi| \sigma_i,$$1 simulated two-way signaling, giving a $$(|\psi\rangle_A \otimes |\Phi^+\rangle_{BC}) \to {\rm BSM}_{AB} \Rightarrow \rho_C = \sigma_i |\psi\rangle\langle\psi| \sigma_i,$$2 feed-forward latency. The AFC storage time was $$(|\psi\rangle_A \otimes |\Phi^+\rangle_{BC}) \to {\rm BSM}_{AB} \Rightarrow \rho_C = \sigma_i |\psi\rangle\langle\psi| \sigma_i,$$3 with $$(|\psi\rangle_A \otimes |\Phi^+\rangle_{BC}) \to {\rm BSM}_{AB} \Rightarrow \rho_C = \sigma_i |\psi\rangle\langle\psi| \sigma_i,$$4, leaving $$(|\psi\rangle_A \otimes |\Phi^+\rangle_{BC}) \to {\rm BSM}_{AB} \Rightarrow \rho_C = \sigma_i |\psi\rangle\langle\psi| \sigma_i,$$5 in memory after the Bell result arrived and before re-emission.

The architecture is time-multiplexed. Bob sends qubits every $$(|\psi\rangle_A \otimes |\Phi^+\rangle_{BC}) \to {\rm BSM}_{AB} \Rightarrow \rho_C = \sigma_i |\psi\rangle\langle\psi| \sigma_i,$$6, corresponding to $$(|\psi\rangle_A \otimes |\Phi^+\rangle_{BC}) \to {\rm BSM}_{AB} \Rightarrow \rho_C = \sigma_i |\psi\rangle\langle\psi| \sigma_i,$$7 kHz in the baseline test, and the fixed AFC storage time allows multiple teleported modes to be stored simultaneously. For the $$(|\psi\rangle_A \otimes |\Phi^+\rangle_{BC}) \to {\rm BSM}_{AB} \Rightarrow \rho_C = \sigma_i |\psi\rangle\langle\psi| \sigma_i,$$8 km link, a single-mode memory would be limited by the two-way communication latency $$(|\psi\rangle_A \otimes |\Phi^+\rangle_{BC}) \to {\rm BSM}_{AB} \Rightarrow \rho_C = \sigma_i |\psi\rangle\langle\psi| \sigma_i,$$9, hence $$|\Phi^\pm\rangle = \frac{|00\rangle \pm |11\rangle}{\sqrt{2}}, \qquad |\Psi^\pm\rangle = \frac{|01\rangle \pm |10\rangle}{\sqrt{2}}.$$0 kHz. Temporal multimodality increased the attempt rate to $$|\Phi^\pm\rangle = \frac{|00\rangle \pm |11\rangle}{\sqrt{2}}, \qquad |\Psi^\pm\rangle = \frac{|01\rangle \pm |10\rangle}{\sqrt{2}}.$$1 kHz, approximately $$|\Phi^\pm\rangle = \frac{|00\rangle \pm |11\rangle}{\sqrt{2}}, \qquad |\Psi^\pm\rangle = \frac{|01\rangle \pm |10\rangle}{\sqrt{2}}.$$2 above the single-mode limit, with the general scaling

$$|\Phi^\pm\rangle = \frac{|00\rangle \pm |11\rangle}{\sqrt{2}}, \qquad |\Psi^\pm\rangle = \frac{|01\rangle \pm |10\rangle}{\sqrt{2}}.$$3

where $$|\Phi^\pm\rangle = \frac{|00\rangle \pm |11\rangle}{\sqrt{2}}, \qquad |\Psi^\pm\rangle = \frac{|01\rangle \pm |10\rangle}{\sqrt{2}}.$$4. The logic hardware limited the realized rate to $$|\Phi^\pm\rangle = \frac{|00\rangle \pm |11\rangle}{\sqrt{2}}, \qquad |\Psi^\pm\rangle = \frac{|01\rangle \pm |10\rangle}{\sqrt{2}}.$$5 kHz, while faster electronics would allow up to $$|\Phi^\pm\rangle = \frac{|00\rangle \pm |11\rangle}{\sqrt{2}}, \qquad |\Psi^\pm\rangle = \frac{|01\rangle \pm |10\rangle}{\sqrt{2}}.$$6 MHz.

Performance was quantified by state fidelities. For $$|\Phi^\pm\rangle = \frac{|00\rangle \pm |11\rangle}{\sqrt{2}}, \qquad |\Psi^\pm\rangle = \frac{|01\rangle \pm |10\rangle}{\sqrt{2}}.$$7, the equator fidelity was $$|\Phi^\pm\rangle = \frac{|00\rangle \pm |11\rangle}{\sqrt{2}}, \qquad |\Psi^\pm\rangle = \frac{|01\rangle \pm |10\rangle}{\sqrt{2}}.$$8, the poles fidelity was $$|\Phi^\pm\rangle = \frac{|00\rangle \pm |11\rangle}{\sqrt{2}}, \qquad |\Psi^\pm\rangle = \frac{|01\rangle \pm |10\rangle}{\sqrt{2}}.$$9, and the average fidelity over arbitrary qubits was

$|0\rangle,|1\rangle$0

For the $|0\rangle,|1\rangle$1 km case with $|0\rangle,|1\rangle$2, $|0\rangle,|1\rangle$3, $|0\rangle,|1\rangle$4, and $|0\rangle,|1\rangle$5. These values exceed both the $|0\rangle,|1\rangle$6 classical limit for single-photon qubits and the $|0\rangle,|1\rangle$7 bound that accounts for the Poissonian statistics of weak-coherent inputs and the net process efficiency. The “probability per BSM of heralding a photon after the QM” was measured to be $|0\rangle,|1\rangle$8. No full process matrix $|0\rangle,|1\rangle$9 was reported.

The dominant imperfections were non-ideal $$|\psi\rangle_{IQ} = \alpha|e\rangle + e^{i\phi}\beta|l\rangle,$$0 resource fidelity due to spectral and temporal mode mismatch and SPDC multipair emission, residual distinguishability in the Bell measurement that reduced Hong–Ou–Mandel interference visibility, vacuum and multi-photon components of the weak-coherent input, reduced $$|\psi\rangle_{IQ} = \alpha|e\rangle + e^{i\phi}\beta|l\rangle,$$1 for longer storage, phase noise between the early and late bins, and residual detector background.

4. Discrete-variable optomagnonic teleportation in YIG

The discrete-variable proposal formulates photon-to-magnon teleportation in cavity optomagnonics using two macroscopic YIG spheres placed in the arms of an optical interferometer (Fan et al., 2023). Each arm contains one magnon mode $$|\psi\rangle_{IQ} = \alpha|e\rangle + e^{i\phi}\beta|l\rangle,$$2 and two optical whispering-gallery modes $$|\psi\rangle_{IQ} = \alpha|e\rangle + e^{i\phi}\beta|l\rangle,$$3 and $$|\psi\rangle_{IQ} = \alpha|e\rangle + e^{i\phi}\beta|l\rangle,$$4 with orthogonal polarizations, governed by

$$|\psi\rangle_{IQ} = \alpha|e\rangle + e^{i\phi}\beta|l\rangle,$$5

Under triple resonance, $$|\psi\rangle_{IQ} = \alpha|e\rangle + e^{i\phi}\beta|l\rangle,$$6, magneto-optical Brillouin light scattering selects either a Stokes parametric process or an anti-Stokes beam-splitter process. Pumping the TE mode $$|\psi\rangle_{IQ} = \alpha|e\rangle + e^{i\phi}\beta|l\rangle,$$7 on resonance with $$|\psi\rangle_{IQ} = \alpha|e\rangle + e^{i\phi}\beta|l\rangle,$$8 gives

$$|\psi\rangle_{IQ} = \alpha|e\rangle + e^{i\phi}\beta|l\rangle,$$9

whereas pumping the TM mode $$|\Phi^+\rangle_{s,i} = \frac{|e_s e_i\rangle + |l_s l_i\rangle}{\sqrt{2}}.$$0 with $$|\Phi^+\rangle_{s,i} = \frac{|e_s e_i\rangle + |l_s l_i\rangle}{\sqrt{2}}.$$1 gives

$$|\Phi^+\rangle_{s,i} = \frac{|e_s e_i\rangle + |l_s l_i\rangle}{\sqrt{2}}.$$2

The teleportation sequence has three steps. First, a weak TE single-photon pulse is split by a $$|\Phi^+\rangle_{s,i} = \frac{|e_s e_i\rangle + |l_s l_i\rangle}{\sqrt{2}}.$$3 beamsplitter into the two interferometer arms, where Stokes scattering prepares an optomagnonic EPR state. After polarization processing, the resource is

$$|\Phi^+\rangle_{s,i} = \frac{|e_s e_i\rangle + |l_s l_i\rangle}{\sqrt{2}}.$$4

with $$|\Phi^+\rangle_{s,i} = \frac{|e_s e_i\rangle + |l_s l_i\rangle}{\sqrt{2}}.$$5 and $$|\Phi^+\rangle_{s,i} = \frac{|e_s e_i\rangle + |l_s l_i\rangle}{\sqrt{2}}.$$6 denoting one magnon in the lower or upper arm. Second, a polarization Bell-state measurement mixes the Stokes photon with the unknown input polarization qubit,

$$|\Phi^+\rangle_{s,i} = \frac{|e_s e_i\rangle + |l_s l_i\rangle}{\sqrt{2}}.$$7

Conditioned on $$|\Phi^+\rangle_{s,i} = \frac{|e_s e_i\rangle + |l_s l_i\rangle}{\sqrt{2}}.$$8, the magnon state becomes

$$|\Phi^+\rangle_{s,i} = \frac{|e_s e_i\rangle + |l_s l_i\rangle}{\sqrt{2}}.$$9

and conditioned on $|\Psi^\pm\rangle$0, it becomes

$|\Psi^\pm\rangle$1

which is corrected by a feed-forward phase shift. Third, a delayed anti-Stokes interaction reads the dual-rail magnonic qubit back into a TE anti-Stokes photon for verification.

The scheme is explicitly heralded and operates in the weak-coupling, short-pulse regime $|\Psi^\pm\rangle$2, where the Stokes resource is

$|\Psi^\pm\rangle$3

The Bell measurement resolves $|\Psi^\pm\rangle$4 and discards $|\Psi^\pm\rangle$5, so the success probability per trial scales as

$|\Psi^\pm\rangle$6

A distinctive feature of the proposal is the explicit treatment of residual thermal magnon occupation. If each magnon mode begins in a thermal state with mean occupation $|\Psi^\pm\rangle$7 and $|\Psi^\pm\rangle$8, the conditional teleportation fidelity is

$|\Psi^\pm\rangle$9

The protocol requires $^{3+}$00 to maintain $^{3+}$01, and the paper emphasizes cryogenic operation around $^{3+}$02 mK, short pulses, and suppression of optical absorption heating. The same framework extends to entanglement swapping in a dual-interferometer architecture with four YIG spheres. There the magnon Bell-state fidelity is

$^{3+}$03

and the swapping success probability scales as

$^{3+}$04

The proposal’s principal significance lies in its dual-rail macroscopic encoding: teleportation is not to a single localized magnon in one resonator but to the joint state of two magnonic oscillators distributed across the interferometer arms.

5. Continuous-variable optomagnonic teleportation and non-Gaussian distillation

The continuous-variable proposal considers a YIG sphere supporting two optical whispering-gallery modes $^{3+}$05 and $^{3+}$06, the uniform Kittel magnon mode $^{3+}$07, and an auxiliary microwave cavity mode $^{3+}$08 (Lu et al., 16 Jul 2025). A strong TM-polarized optical drive activates Stokes scattering into a TE-polarized WGM under the triple-resonance condition $^{3+}$09. After linearization in the pump rotating frame, the relevant interaction is the two-mode squeezing Hamiltonian

$^{3+}$10

The auxiliary microwave cavity mediates both heralded magnon subtraction and phase-space displacement through

$^{3+}$11

The protocol is pulsed, with $^{3+}$12 ns for entanglement generation, $^{3+}$13 ns for magnon subtraction, $^{3+}$14 ns for displacement, and $^{3+}$15, so magnon dissipation and thermal effects are suppressed during the sequence. Representative parameters are $^{3+}$16 MHz, $^{3+}$17 MHz, $^{3+}$18 MHz, and $^{3+}$19 MHz. Dilution temperatures in the tens of mK place the GHz magnon near vacuum occupation.

Adiabatic elimination of the optical mode in the weak-coupling regime $^{3+}$20 yields a pulsed Bogoliubov transformation and the two-mode squeezed vacuum

$^{3+}$21

with

$^{3+}$22

Its covariance matrix is

$^{3+}$23

and the logarithmic negativity is

$^{3+}$24

Because currently achievable optomagnonic couplings are relatively weak, the protocol introduces non-Gaussian distillation by single-magnon subtraction and single-photon subtraction. Magnon subtraction is implemented with a short, weak, resonant microwave pulse. Conditioned on a single-microwave-photon detection, the squeezing parameter is modified according to

$^{3+}$25

and the magnon-subtraction success probability is approximately $^{3+}$26. A subsequent low-reflectivity beamsplitter and single-photon detector herald photon subtraction on the TE Stokes mode. The distilled EPR resource is

$^{3+}$27

Its entanglement exceeds that of the Gaussian TMSV across the full range analyzed, with logarithmic negativity

$^{3+}$28

Teleportation follows the Braunstein–Kimble prescription. The unknown optical input pulse is mixed with the distilled Stokes mode on a $^{3+}$29 beamsplitter, orthogonal quadratures are measured by homodyne detection, and the results are sent to Bob. The required magnon displacement is

$^{3+}$30

implemented by a coherent resonant microwave pulse. In the weak-coupling limit,

$^{3+}$31

Readout is performed with another weak microwave pulse that swaps the magnon state to the cavity output for microwave tomography.

The proposal gives closed-form fidelities for coherent, single-photon, and squeezed-vacuum inputs, and numerical results for cat states. For coherent-state inputs, the fidelity exceeds the classical continuous-variable benchmark of $^{3+}$32 across the full plotted range of $^{3+}$33 for both Gaussian and distilled resources, with substantially higher fidelity for the distilled case. For single-photon inputs, distillation raises the fidelity and lowers the $^{3+}$34 threshold required to surpass $^{3+}$35. For squeezed inputs, fidelity decreases with the squeezing parameter $^{3+}$36, but distillation maintains quantum teleportation over a broader $^{3+}$37 range. For cat states, the distilled resource preserves Wigner-function negativity and interference fringes more faithfully and sustains fidelity above $^{3+}$38 for larger amplitudes $^{3+}$39 than the Gaussian resource.

6. Conceptual distinctions, limitations, and network significance

A recurring misconception is to treat all photon-to-magnon teleportation protocols as equivalent instances of optical-to-ferromagnetic-magnon transfer. The rare-earth–crystal experiment does not teleport to a ferromagnetic magnon; it teleports to a collective optical excitation in a solid-state ensemble. It is nevertheless closely related to the spin-wave picture because the excitation is delocalized over many ions with a controlled phase profile. The authors explicitly identify longer-distance operation with the long-lived spin states of Pr$^{3+}$40, dynamical decoupling, and on-demand readout as the route to the genuine spin-wave regime (Lago-Rivera et al., 2022).

The proposals in YIG address a different interface. In the discrete-variable case, teleportation relies on heralded single-excitation Stokes scattering, linear-optical Bell-state analysis, and dual-rail storage across two macroscopic spheres (Fan et al., 2023). In the continuous-variable case, teleportation is deterministic once the EPR resource has been prepared, but high fidelity depends on non-Gaussian distillation because bare optomagnonic coupling is weak in present devices (Lu et al., 16 Jul 2025). These are not alternative descriptions of the same apparatus; they are distinct architectures with different target excitations, resource states, measurement models, and dominant noise channels.

The main limiting factors are correspondingly different. In the AFC experiment, the key issues are entangled-resource fidelity, Hong–Ou–Mandel indistinguishability, weak-coherent input statistics, reduced AFC efficiency at longer storage times, phase noise between time bins, and residual detector background. In the discrete-variable YIG proposal, thermal magnon occupation is the critical fidelity limiter, and the heralding rate remains low because operation is in the $^{3+}$41 regime with only two Bell states resolved by linear optics. In the continuous-variable YIG proposal, weak optomagnonic coupling, optical loss, detection inefficiency, and imperfect heralding in the subtraction stages bound performance, while pulsed operation is used precisely to avoid instability and suppress thermalization.

From the standpoint of quantum-network integration, the demonstrated telecom compatibility of the $^{3+}$42 nm idler and input qubit is the strongest near-term systems result. The experiment combines standard telecom fiber, active feed-forward, and temporal multiplexing, directly addressing two-way signaling latency in repeater-like settings. Practical scaling, as stated in the literature, requires higher memory efficiency through improved AFC preparation and impedance-matching cavities, spin-wave storage with dynamical decoupling and on-demand readout, and larger multiplexing dimensionality in time, frequency, and space (Lago-Rivera et al., 2022). In the YIG setting, the corresponding scaling path is based on triple-resonance optimization, improved outcoupling, stronger effective interaction under pulsed driving, low-temperature operation, and microwave control of magnon subtraction and displacement (Fan et al., 2023, Lu et al., 16 Jul 2025).

Taken together, the field comprises one experimentally established telecom-to-solid-state collective-excitation teleporter and two optomagnonic routes toward genuine photon-to-magnon teleportation in ferrimagnetic media, one discrete-variable and one continuous-variable. The unifying theme is the conversion of a flying optical qubit or qumode into a matter-based collective excitation while preserving nonclassical state information through Bell-measurement conditioning and feed-forward.