Stephanie Wehner

Remote state preparation (RSP) allows one party to remotely prepare a known quantum state on another party's qubit using entanglement. This can be used in quantum networks to perform applications such as blind quantum computing or long-distance quantum key distribution (QKD) with quantum repeaters. Devices to perform RSP, referred to as a client, ideally have low hardware requirements, such as only sending photonic qubits. A weak coherent pulse source offers a practical alternative to true single-photon sources and is already widely used in QKD. Here, we introduce two new protocols to the previously known protocol for RSP with a weak-coherent-pulse-based device. The known technique uses a double-click (DC) protocol, where a photon from both the server and the client needs to reach an intermediate Bell state measurement. Here, we add to that a single-click (SC) RSP protocol, which requires only one photon to reach the Bell state measurement, allowing for better performance in certain regimes. In addition, we introduce a double-single-click (DSC) protocol, where the SC protocol is repeated twice, and a CNOT gate is applied between the resulting qubits. DSC mitigates the need for phase stabilization in certain regimes, lowering technical complexity while still improving performance compared to DC in some regimes. We compare these protocols in terms of fidelity and rate, finding that SC consistently achieves higher rates than DC and, interestingly, does not suffer from an inherently lower fidelity than the DC, as is the case for entanglement generation. Although SC provides stronger performance, DSC can still show performance improvements over DC, and it may have reduced technical complexity compared to SC. Lastly, we show how these protocols can be used in long-distance QKD using quantum repeaters.

Verifiable hybrid secret sharing (VHSS) is a task in which a secret quantum state must be split among n parties, such that they can only recover the secret if a sufficient number of parties cooperate, while small coalitions of parties learn nothing. Each party may hold classical and/or quantum shares, and the parties must be able to collectively verify that their shares can later be used to reconstruct a valid quantum state. Here, we explore the resource efficiency of VHSS protocols, critical for implementation in near-term quantum networks. Lipinska et al. [PRA 102(2):022405, 2020] recently introduced a protocol that required a reduced number of qubits per party. Building on this, we further optimize their protocol and reduce the quantum communication overhead. While the scaling with the number of parties remains unchanged, our improvements yield orders-of-magnitude reductions in the time required to successfully distribute and verify a quantum secret.