Telecloning -- the combination of quantum teleportation and cloning -- offers a powerful mechanism to disseminate unknown quantum states to multiple spatially separated recipients with optimal fidelity. Despite its conceptual importance for quantum networks, an experimental demonstration of symmetric qubit quantum telecloning remains elusive, particularly due to the challenges of generating multipartite entangled resource states and implementing stable multi-photon interference across distributed nodes. Here, we realize the optimal 1 to 2 symmetric quantum telecloning using a scalable silicon photonic platform. We implement a six-photon protocol using two independent, fiber-linked photonic chips: one generating a heralded input state and the other preparing a four-photon entangled resource state. By performing an interchip Bell-state measurement, we successfully distribute the input state into two optimal clones at remote nodes. We observe an interchip cloning fidelity of 78.45 $\pm$ 1.39%, exceeding the classical limit of 2/3 by 8 standard deviations. Our results demonstrate the robust generation and manipulation of complex multi-photon states between integrated chips, providing a foundational building block for large-scale multi-party quantum networks.
Telecloning -- the combination of quantum teleportation and cloning -- offers a powerful mechanism to disseminate unknown quantum states to multiple spatially separated recipients with optimal fidelity. Despite its conceptual importance for quantum networks, an experimental demonstration of symmetric qubit quantum telecloning remains elusive, particularly due to the challenges of generating multipartite entangled resource states and implementing stable multi-photon interference across distributed nodes. Here, we realize the optimal 1 to 2 symmetric quantum telecloning using a scalable silicon photonic platform. We implement a six-photon protocol using two independent, fiber-linked photonic chips: one generating a heralded input state and the other preparing a four-photon entangled resource state. By performing an interchip Bell-state measurement, we successfully distribute the input state into two optimal clones at remote nodes. We observe an interchip cloning fidelity of 78.45 ± 1.39%, exceeding the classical limit of 2/3 by 8 standard deviations. Our results demonstrate the robust generation and manipulation of complex multi-photon states between integrated chips, providing a foundational building block for large-scale multi-party quantum networks.
Symmetric N→M telecloning and remote quantum state inference
Teleporting unknown quantum states between distant nodes of a network is a significant feature of quantum communication. Few studies, however, have been conducted on N→M telecloning, in which N copies of an unknown quantum state are optimally teleported to M≥N receivers. Previous work requires global POVMs on all copies and auxiliaries; here, we show that symmetric N→M telecloning can be probabilistically performed using only sequential (or parallel) Bell state measurements (BSMs), allowing the copies to be spatially separated. When successful, the fidelity of each receiver's reduced state saturates the bound imposed by the no-cloning theorem, with the probability of success being independent of M. In the case of an `unsuccessful' BSM, we show that the teleportation fidelity is likely to remain high, with the measurement outcome also providing information about the closest Pauli eigenbasis to the unknown state being telecloned. In this sense, each receiver can remotely infer the unknown quantum state with a level of confidence that scales with the number of copies, even if the fidelity of their own reduced state is sub-optimal. We additionally analyze the required resources to ensure the classical-communication fidelity bound is surpassed, both in terms of two-qubit inseparability and varying classes of multipartite entanglement. Surprisingly, we uncover that, at a given iteration of the protocol, pairwise entanglement is not always necessary to increase the teleportation fidelity and is never required to beat the classical bound for N≥2.
Large-scale quantum computers possess the capacity to effectively tackle practical problems that can be insurmountable for classical computers. The main challenge in building these quantum computers is to realize scalable modules for remote qubits and entanglement. By assembling small, specialized parts into a larger architecture, the modular approach mitigates complexity and uncertainty. Such a distributed architecture requires non-local quantum gate operations between remote qubits. An essential method for implementing such operations, known as quantum gate teleportation, requires only local operations, classical communication, and shared entanglement. Till today, the quantum gate teleportation using a photonic chip has remained elusive. Here, we experimentally demonstrate the quantum teleportation of an on-chip controlled-NOT (CNOT) gate, implemented via a silicon polarization directional coupler. Assisted with the scalable silicon chip platform, high-fidelity local quantum logic gates, linear optical components, post-selected entanglement, and coincidence measurements from photonic qubits, we first measure and characterize our teleported chip-scale CNOT gate with an average truth table fidelity of 93.1 ± 0.3%. Second, for different input polarization states, we obtain an average quantum state fidelity of 87.0 ± 2.2% with our teleported on-chip CNOT gate. Third, we use our non-local CNOT gate for remote entanglement creation of four Bell states, with an average quantum state fidelity of 86.2 ± 0.8%. Fourth, we fully characterize our teleported on-chip CNOT gate with a quantum process fidelity of 83.1 ± 2.0%, and an average non-local CNOT gate fidelity of 86.5 ± 2.2%. Our teleported photonic on-chip quantum logic gate could be extended both to multiple qubits and chip-scale modules towards fault-tolerant and large-scale distributed quantum computation.
Due to the no-cloning theorem, generating perfect quantum clones of an arbitrary unknown quantum state is not possible, however approximate quantum clones can be constructed. Quantum telecloning is a protocol that originates from a combination of quantum teleportation and quantum cloning. Here we present 1 → 2 and 1 → 3 quantum telecloning circuits, with and without ancilla, that are theoretically optimal (meaning the clones have the highest fidelity allowed by quantum mechanics), universal (meaning the clone fidelity is independent of the state being cloned), and symmetric (meaning the clones all have the same fidelity). We implement these circuits on gate model IBMQ and Quantinuum NISQ hardware and quantify the clone fidelities using parallel single qubit state tomography. Quantum telecloning using mid-circuit measurement with classical feed-forward control (i.e. real time if statements) is demonstrated on the Quantinuum H1-2 device. Two alternative implementations of quantum telecloning, deferred measurement and post selection, are demonstrated on ibmq_montreal, where mid-circuit measurements with real time if statements are not available. Our results show that NISQ devices can achieve near-optimal quantum telecloning fidelity; for example the Quantinuum H1-2 device running the telecloning circuits without ancilla achieved a mean clone fidelity of 0.824 with standard deviation of 0.024 for two clone circuits and 0.765 with standard deviation of 0.022 for three clone circuits. The theoretical fidelity limits are 0.83ˉ for two clones and 0.7ˉ for three clones. This demonstrates the viability of performing experimental analysis of quantum information networks and quantum cryptography protocols on NISQ computers.
Long-range quantum entanglement is essential for building large-scale quantum networks and unconditionally secure cryptographic systems based on quantum key distribution (QKD). While photonic integrated circuits offer a highly scalable platform, the fragility of phase coherence between spatial modes has prevented the distribution of path-encoded entanglement over long distances. Here, we report chip-to-chip distribution of path-encoded entangled states over 80 km between fully integrated silicon photonic transmitter and receiver chips. Telecom-band entangled photon pairs are generated via spontaneous four-wave mixing in on-chip spiral waveguides and distributed between chips over a dual-core, actively stabilized fiber link. Upon distribution, we measure a Bell state fidelity of 85.7±0.2%. Implementing the BBM92 protocol with the same source, we obtain a secure key rate of 2.03 bit/s in the infinite-key regime. These results establish silicon photonic chips as a viable platform for long-distance path-encoded entanglement-based quantum key distribution, paving the way toward scalable, device-independent quantum networks.
Quantum information can not be perfectly cloned, but approximate copies of quantum information can be generated. Quantum telecloning combines approximate quantum cloning, more typically referred as quantum cloning, and quantum teleportation. Quantum telecloning allows approximate copies of quantum information to be constructed by separate parties, using the classical results of a Bell measurement made on a prepared quantum telecloning state. Quantum telecloning can be implemented as a circuit on quantum computers using a classical co-processor to compute classical feed forward instructions using if statements based on the results of a mid-circuit Bell measurement in real time. We present universal, symmetric, optimal1→Mtelecloning circuits, and experimentally demonstrate these quantum telecloning circuits forM=2up toM=10, natively executed with real time classical control systems on IBM Quantum superconducting processors, known as dynamic circuits. We perform the cloning procedure on many different message states across the Bloch sphere, on 7 IBM Quantum processors, optionally using the error suppression technique X-X sequence digital dynamical decoupling. Two circuit optimizations are utilized, one which removes ancilla qubits forM=2,3, and one which reduces the total number of gates in the circuit but still uses ancilla qubits. Parallel single qubit tomography with MLE density matrix reconstruction is used in order to compute the mixed state density matrices of the clone qubits, and clone quality is measured using quantum fidelity. These results present one of the largest and most comprehensive NISQ computer experimental analyses on (single qubit) quantum telecloning to date. The clone fidelity sharply decreases to 0.5 forM>5, but forM=2we are able to achieve a mean clone fidelity of up to 0.79 using dynamical decoupling.
Abstract Quantum teleportation transfers unknown quantum states from one node in a quantum network to another. It is one of the crucial architectures in quantum information processing. The teleportation of high-dimensional quantum states remains challenging due to the difficulties in executing high-dimensional Bell state measurement. Here, we propose a Quantum Autoencoder-Facilitated Teleportation (QAFT) protocol for high-dimensional quantum teleportation, and report the first demonstration of QAFT on qutrits using an integrated photonic platform for future scalability. The key strategy is to reduce the dimension of the input states by erasing redundant information and reconstruct its initial state after chip-to-chip teleportation. Machine learning is applied in training the autoencoder to facilitate the teleportation of any state from a particular high-dimensional subspace and achieve the reconstruction of the unknown state (by the decoder) with high fidelities (~ 0.971). Experimentally, we teleport unknown qutrits by generating, transferring and manipulating photons, and training quantum autoencoders on a silicon chip. A teleportation fidelity of ~ 0.894 is demonstrated. Our scheme opens pathway towards quantum internet and cryptography to transfer unmeasured states in a quantum computer. It also lays the groundwork for machine learning technologies in quantum networks and quantum computations.