Terahertz-Bandwidth Quantum Teleportation

• The paper presents a continuous-variable protocol that leverages ultrabroadband two-mode squeezing to achieve quantum state transfer with fidelities exceeding classical limits.
• It utilizes broadband optical parametric amplifiers and spectral-temporal multiplexing to generate and channel over 23 parallel teleportation links across THz bandwidths.
• The approach enables high-throughput quantum communication and computing, with potential aggregate rates up to 1 Tbit/s integrated into telecom networks.

Terahertz-bandwidth quantum teleportation refers to the continuous-variable (CV) quantum teleportation protocol implemented over an optical bandwidth spanning up to several terahertz (THz). Such protocols exploit the intrinsic ultrafast timescales and broad spectral range of photonic modes to effectuate quantum state transfer between distant nodes at rates far exceeding the classic MHz–GHz constraints imposed by conventional electronics. This approach underpins high-throughput quantum information processing and is a cornerstone for quantum communication, measurement-based quantum computing (MBQC), and scalable photonic quantum networks (Eldan et al., 2023, Suzuki et al., 16 Apr 2026).

1. Theoretical Framework for CV Quantum Teleportation

Terahertz-bandwidth quantum teleportation is fundamentally based on the continuous-variable teleportation protocol first proposed by Braunstein and Kimble, employing quadrature entanglement (EPR states) and beam-splitter mixing, with feedforward displacement based on measurement outcomes. For a single temporal or spectral mode, the canonical quadratures are defined as

$$\hat x_j = \frac{\hat a_j + \hat a_j^\dagger}{\sqrt2},\quad \hat p_j = \frac{\hat a_j - \hat a_j^\dagger}{i\sqrt2}$$

with $\left[\hat x_j,\hat p_k\right] = i\delta_{jk}$.

An ideal EPR state $|\mathrm{EPR}\rangle_{12}$ is characterized by perfect correlations $\hat x_1-\hat x_2\to0$ and $\hat p_1+\hat p_2\to0$ in the limit of infinite two-mode squeezing $r\to\infty$. In the CV teleportation protocol, an unknown input state ($\hat x_{\rm in}, \hat p_{\rm in}$) is mixed with mode 1 of the EPR pair on a balanced beam splitter. A joint ("Bell") measurement yields

$$\hat x_- = \frac{\hat x_{\rm in}-\hat x_1}{\sqrt2},\quad \hat p_+ = \frac{\hat p_{\rm in}+\hat p_1}{\sqrt2}$$

which, after transmission of the measurement results and with gain $g=1$, are used to displace mode 2: $$\hat D_2(x_-,p_+): \hat x_2\rightarrow \hat x_2 + x_-,\quad \hat p_2\rightarrow \hat p_2 + p_+$$

Combining all elements, the Heisenberg-picture input-output map is

$\left[\hat x_j,\hat p_k\right] = i\delta_{jk}$0

In the case of finite squeezing, excess vacuum noise appears in each output quadrature.

The teleportation fidelity for an input coherent state $\left[\hat x_j,\hat p_k\right] = i\delta_{jk}$1 is

$\left[\hat x_j,\hat p_k\right] = i\delta_{jk}$2

where $\left[\hat x_j,\hat p_k\right] = i\delta_{jk}$3 and $\left[\hat x_j,\hat p_k\right] = i\delta_{jk}$4 are the output variances above the vacuum level. The protocol strictly surpasses the classical limit ($\left[\hat x_j,\hat p_k\right] = i\delta_{jk}$5 when no entanglement is used) when EPR correlations are present (Suzuki et al., 16 Apr 2026).

2. Generation of Broadband Entangled Resources

To realize terahertz-bandwidth teleportation, broadband EPR-like resource states must be generated over a wide optical spectrum. This is achieved using a broadband optical parametric amplifier (OPA), typically composed of a periodically poled lithium niobate (PPLN) crystal pumped at a frequency $\left[\hat x_j,\hat p_k\right] = i\delta_{jk}$6, which supports spontaneous parametric down-conversion (SPDC) spanning up to tens of THz. Each frequency pair $\left[\hat x_j,\hat p_k\right] = i\delta_{jk}$7 forms a two-mode squeezed vacuum state with squeezing parameter $\left[\hat x_j,\hat p_k\right] = i\delta_{jk}$8. The quantum statistics of each mode pair are captured by the Wigner function with covariance matrix: $\left[\hat x_j,\hat p_k\right] = i\delta_{jk}$9 This multimode EPR state underpins multiplexed teleportation, with each spectral-temporal channel acting as an independent teleportation link (Eldan et al., 2023).

3. Spectral and Temporal Multiplexing

The continuous output of the broadband OPA can be partitioned into $|\mathrm{EPR}\rangle_{12}$0 spectral channels of width $|\mathrm{EPR}\rangle_{12}$1, using a combination of diffraction gratings, lenses, and Fourier-domain pulse shapers. This slicing enables the encoding, processing, and measurement of quantum information in parallel across all channels.

A spatial light modulator (SLM) or electro-optic modulator array imprints independent amplitude and phase profiles onto each channel and can also compensate dispersion accrued in transmission fibers. Channel widths of $|\mathrm{EPR}\rangle_{12}$2100 GHz (0.8 nm) have been demonstrated, with isolation between channels $|\mathrm{EPR}\rangle_{12}$399.5% and the ability to scale down to $|\mathrm{EPR}\rangle_{12}$410 GHz per channel using advanced gratings and modulators, allowing for $|\mathrm{EPR}\rangle_{12}$5–$|\mathrm{EPR}\rangle_{12}$6 channels over standard telecommunications bands (Eldan et al., 2023).

4. Ultrafast All-Optical Implementation

The principal bottleneck in previous teleportation implementations was the electronic feedforward for Bell measurement outcomes, limited to $|\mathrm{EPR}\rangle_{12}$7100 MHz bandwidth in direct-detection systems. Recent work has circumvented this by performing the Bell measurement and transmission of outcomes entirely in the optical domain using phase-sensitive amplifiers (PSAs), specifically in cavity-free 45 mm PPLN ridge waveguides with a $|\mathrm{EPR}\rangle_{12}$81 ps nonlinear response.

Schematically, after the Bell-type mixing and high-speed homodyne detection, the real-time outcomes are encoded back into the optical field by injecting the local oscillator and pump beam into a secondary OPA. The resulting idler acquires an optical displacement proportional to the measurement result, enabling feedforward displacements at rates determined by the OPA's intrinsic response ($|\mathrm{EPR}\rangle_{12}$91 THz) rather than electronic bandwidth constraints. Real-time teleportation of vacuum states and dynamic coherent 42 ps wavepackets has been demonstrated with this approach (Suzuki et al., 16 Apr 2026).

5. Experimental Realizations and Performance

Performance metrics are determined by teleportation fidelity and channel throughput. In the frequency domain, Suzuki et al. measured raw output noise for vacuum-input teleportation over $\hat x_1-\hat x_2\to0$01 THz sidebands as 1.77 dB (x) and 1.73 dB (p) above shot noise, corresponding to reconstructed intrinsic fidelities of $\hat x_1-\hat x_2\to0$1 for the vacuum state and $\hat x_1-\hat x_2\to0$2 for 42 ps coherent-state wavepackets. Both values exceed the classical (0.5) and no-cloning (2/3) boundaries. All operations are performed in all-fiber, telecom-compatible architectures, using 1545.32 nm signal and 772.66 nm pump wavelengths.

Multiplexed platforms have realized $\hat x_1-\hat x_2\to0$323 parallel channels of CV-QKD in a proof-of-principle experiment, with projected scalability to 1000+ channels, limited by available spectral shaping and detection hardware. Inter-channel crosstalk suppression to $\hat x_1-\hat x_2\to0$40.05% has been achieved, and individual channel rates are currently limited only by SLM refresh ($\hat x_1-\hat x_2\to0$5100 Hz), with clear upgradability to GHz-class refresh rates. Parametric gain per OPA is set low ($\hat x_1-\hat x_2\to0$6) to operate deeply in the quantum regime ($\hat x_1-\hat x_2\to0$7 per channel per window) (Eldan et al., 2023).

Key metrics are summarized below:

Parameter	Achieved Value (2023–2026)	Remarks
Teleportation bandwidth	$\hat x_1-\hat x_2\to0$81 THz (demonstrated)	Platform bandwidth $\hat x_1-\hat x_2\to0$96 THz available
Teleportation fidelity	$\hat p_1+\hat p_2\to0$0	Well above classical/no-cloning limits
Parallel channels	$\hat p_1+\hat p_2\to0$1 (CV-QKD, proof-of-principle)	Scalable to $\hat p_1+\hat p_2\to0$2 in principle
Wavepacket duration	42 ps	Temporal multiplexing of $\hat p_1+\hat p_2\to0$3 modes

6. Implications for Quantum Technology

Terahertz-bandwidth CV quantum teleportation establishes the possibility of quantum information transfer and processing at speeds governed by optical nonlinear response times rather than conventional electronics. In time-division MBQC schemes, shrinking mode durations from nanoseconds to picoseconds increases the encoded qu-mode count per optical loop from $\hat p_1+\hat p_2\to0$4 to $\hat p_1+\hat p_2\to0$5 or more. Aggregate teleportation rates of $\hat p_1+\hat p_2\to0$6 states/s (1 Tbit/s for qubit-encoded Gaussian states) are plausible, with all-photonic quantum processing speeds outpacing classical hardware on absolute time scales.

All spectral and temporal channels can coexist within the existing telecom infrastructure, as the demonstrated operations use standard fiber-compatible wavelengths and modules. The operational bandwidths meet or exceed those anticipated for future 6G networks, facilitating direct integration with advanced quantum internet and quantum repeater protocols that can coexist with classical dense wavelength-division multiplexed (DWDM) traffic (Eldan et al., 2023, Suzuki et al., 16 Apr 2026).

A plausible implication is that these methods support the construction of scalable, high-capacity quantum networks and enable quantum computers operating at genuine THz clock rates, fundamentally circumventing electronic scaling bottlenecks associated with Moore's law.

7. Outlook and Prospects

Further advances are expected in both the spectral density of channels (e.g., by reducing the channel width using finer-resolution dispersive optics and high-speed modulators) and in the degree of squeezing ($\hat p_1+\hat p_2\to0$7 dB) accessible using multi-pass OPOs. Combining high-speed SLMs, acousto-optic deflectors, and low-loss fiber/free-space transmission, platforms may scale to 1000+ channels with potential aggregate throughputs at the terabit-per-second level. Given telecom compatibility, direct integration into existing fiber networks is feasible, supporting both quantum communication and distributed quantum computing.

In summary, terahertz-bandwidth quantum teleportation leverages ultrabroadband two-mode squeezing, spectral-temporal multiplexing, and all-optical measurement chains to achieve ultrafast, high-dimensional quantum state transfer. This establishes a technical foundation for large-scale optical quantum information processing, high-capacity quantum networks, and future photonic quantum computing systems (Eldan et al., 2023, Suzuki et al., 16 Apr 2026).