Remote state preparation (RSP) is a central primitive in quantum cryptography, enabling classical parties to remotely construct quantum states using only classical communication. As a result, RSP serves as a key building block in numerous protocols involving classical clients and quantum servers, allowing classical parties to leverage the advantages offered by powerful quantum computers. All known constructions of RSP rely on strong cryptographic assumptions, typically variants of trapdoor claw-free functions (TCFs).
In this work, we initiate the study of a weaker form of remote state preparation, which we call eavesdropper-blind remote state preparation (EB-RSP). Informally, EB-RSP requires blindness only against external observers who see the transcript of the honest protocol, rather than against the quantum server itself. Despite this relaxed adversarial model, the resulting notion remains sufficient for useful cryptographic applications. In particular, we show that two-message EB-RSP already suffices to construct quantum public-key encryption with classical public keys and quantum ciphertexts. We then construct two-message EB-RSP protocols from specific one-way group actions, yielding a first step toward RSP-type primitives based on assumptions that do not rely on trapdoors. Finally, we observe that existing RSP constructions are likely naturally adaptable to the two-message EB-RSP notion; we demonstrate this explicitly for a concrete TCF-based RSP construction.
Remote state preparation (RSP) is a central primitive in quantum cryptography, enabling classical parties to remotely construct quantum states using only classical communication. As a result, RSP serves as a key building block in numerous protocols involving classical clients and quantum servers, allowing classical parties to leverage the advantages offered by powerful quantum computers. All known constructions of RSP rely on strong cryptographic assumptions, typically variants of trapdoor claw-free functions (TCFs).
In this work, we initiate the study of a weaker form of remote state preparation, which we call eavesdropper-blind remote state preparation (EB-RSP). Informally, EB-RSP requires blindness only against external observers who see the transcript of the honest protocol, rather than against the quantum server itself. Despite this relaxed adversarial model, the resulting notion remains sufficient for useful cryptographic applications. In particular, we show that two-message EB-RSP already suffices to construct quantum public-key encryption with classical public keys and quantum ciphertexts. We then construct two-message EB-RSP protocols from specific one-way group actions, yielding a first step toward RSP-type primitives based on assumptions that do not rely on trapdoors. Finally, we observe that existing RSP constructions are likely naturally adaptable to the two-message EB-RSP notion; we demonstrate this explicitly for a concrete TCF-based RSP construction.
Classical client remote state preparation (CC − RSP) is a primitive where a fully classical party (client) can instruct the preparation of a sequence of random quantum states on some distant party (server) in a way that the description is known to the client but remains hidden from the server. This primitive has many applications, most prominently, it makes blind quantum computing possible for classical clients. In this work, we give a protocol for classical client remote state preparation, that requires minimal resources. The protocol is proven secure against honest-but-curious servers and any malicious third party in a game-based security framework. We provide an instantiation of a trapdoor (approximately) 2-regular family of functions whose security is based on the hardness of the Learning-With-Errors problem, including a first analysis of the set of usable parameters. We also run an experimentation on IBM’s quantum cloud using a toy function. This is the first proof-of-principle experiment of classical client remote state preparation.
Remote state preparation with verifiability (RSPV) is an important quantum cryptographic primitive [Alexandru Gheorghiu and Thomas Vidick, 2019; Jiayu Zhang, 2022]. In this primitive, a client would like to prepare a quantum state (sampled or chosen from a state family) on the server side, such that ideally the client knows its full description, while the server holds and only holds the state itself. In this work we make several contributions on its formulations, constructions and applications. In more detail: - We first work on the definitions and abstract properties of the RSPV problem. We select and compare different variants of definitions [Bennett et al., 2001; Alexandru Gheorghiu and Thomas Vidick, 2019; Jiayu Zhang, 2022; Alexandru Gheorghiu et al., 2022], and study their basic properties (like composability and amplification). - We also study a closely related question of how to certify the server’s operations (instead of solely the states). We introduce a new notion named remote operator application with verifiability (ROAV). We compare this notion with related existing definitions [Summers and Werner, 1987; Dominic Mayers and Andrew Chi-Chih Yao, 2004; Zhengfeng Ji et al., 2021; Tony Metger and Thomas Vidick, 2021; Anand Natarajan and Tina Zhang, 2023], study its abstract properties and leave its concrete constructions for further works. - Building on the abstract properties and existing results [Zvika Brakerski et al., 2023], we construct a series of new RSPV protocols. Our constructions not only simplify existing results [Alexandru Gheorghiu and Thomas Vidick, 2019] but also cover new state families, for example, states in the form of 1/√2 (|0⟩ + |x_0⟩ + |1⟩ |x_1⟩). All these constructions rely only on the existence of weak NTCF [Zvika Brakerski et al., 2020; Navid Alamati et al., 2022], without additional requirements like the adaptive hardcore bit property [Zvika Brakerski et al., 2018; Navid Alamati et al., 2022]. - As a further application, we show that the classical verification of quantum computations (CVQC) problem [Dorit Aharonov et al., 2010; Urmila Mahadev, 2018] could be constructed from assumptions on group actions [Navid Alamati et al., 2020]. This is achieved by combining our results on RSPV with group-action-based instantiation of weak NTCF [Navid Alamati et al., 2022], and then with the quantum-gadget-assisted quantum verification protocol [Ferracin et al., 2018].
Remote state preparation with verifiability (RSPV) is an important quantum cryptographic primitive [GV19,Zha22]. In this primitive, a client would like to prepare a quantum state (sampled or chosen from a state family) on the server side, such that ideally the client knows its full description, while the server holds and only holds the state itself. In this work we make several contributions on its formulations, constructions and applications. In more detail: - We first work on the definitions and abstract properties of the RSPV problem. We select and compare different variants of definitions [GV19,GMP22,Zha22], and study their basic properties (like composability and amplification). - We also study a closely related question of how to certify the server's operations (instead of solely the states). We introduce a new notion named remote operator application with verifiability (ROAV). We compare this notion with related existing definitions [SW87,MY04,MV21,NZ23] and study its abstract properties. - Building on the abstract properties and existing results [BGKPV23], we construct a series of new RSPV protocols. Our constructions not only simplify existing results [GV19] but also cover new state families, for example, states in the form of 21(∣0⟩∣x0⟩+∣1⟩∣x1⟩). All these constructions rely only on the existence of weak NTCF [BKVV,AMR22], without additional requirements like the adaptive hardcore bit property [BCMVV,AMR22]. - As a further application, we show that the classical verification of quantum computations (CVQC) problem [ABEM,Mah18] could be constructed from assumptions on group actions [ADMP20]. This is achieved by combining our results on RSPV with group-action-based instantiation of weak NTCF [AMR22], and then with the quantum-gadget-assisted quantum verification protocol [FKD18].
Secure delegated quantum computing allows a computationally weak client to outsource an arbitrary quantum computation to an untrusted quantum server in a privacy-preserving manner. One of the promising candidates to achieve classical delegation of quantum computation is classical-client remote state preparation (RSPCC), where a client remotely prepares a quantum state using a classical channel. However, the privacy loss incurred by employing RSPCC as a sub-module is unclear. In this work, we investigate this question using the Constructive Cryptography framework by Maurer and Renner (ICS'11). We first identify the goal of RSPCC as the construction of ideal RSP resources from classical channels and then reveal the security limitations of using RSPCC. First, we uncover a fundamental relationship between constructing ideal RSP resources (from classical channels) and the task of cloning quantum states. Any classically constructed ideal RSP resource must leak to the server the full classical description (possibly in an encoded form) of the generated quantum state, even if we target computational security only. As a consequence, we find that the realization of common RSP resources, without weakening their guarantees drastically, is impossible due to the no-cloning theorem. Second, the above result does not rule out that a specific RSPCC protocol can replace the quantum channel at least in some contexts, such as the Universal Blind Quantum Computing (UBQC) protocol of Broadbent et al. (FOCS '09). However, we show that the resulting UBQC protocol cannot maintain its proven composable security as soon as RSPCC is used as a subroutine. Third, we show that replacing the quantum channel of the above UBQC protocol by the RSPCC protocol QFactory of Cojocaru et al. (Asiacrypt '19), preserves the weaker, game-based, security of UBQC.
Quantum mechanical effects have enabled the construction of cryptographic primitives that are impossible classically. For example, quantum copy-protection allows for a program to be encoded in a quantum state in such a way that the program can be evaluated, but not copied. Many of these cryptographic primitives are two-party protocols, where one party, Bob, has full quantum computational capabilities, and the other party, Alice, is only required to send random BB84 states to Bob. In this work, we show how such protocols can generically be converted to ones where Alice is fully classical, assuming that Bob cannot efficiently solve the LWE problem. In particular, this means that all communication between (classical) Alice and (quantum) Bob is classical, yet they can still make use of cryptographic primitives that would be impossible if both parties were classical. We apply this conversion procedure to obtain quantum cryptographic protocols with classical communication for unclonable encryption, copy-protection, computing on encrypted data, and verifiable blind delegated computation. The key technical ingredient for our result is a protocol for classically-instructed parallel remote state preparation of BB84 states. This is a multi-round protocol between (classical) Alice and (quantum polynomial-time) Bob that allows Alice to certify that Bob must have prepared n uniformly random BB84 states (up to a change of basis on his space). While previous approaches could only certify one- or two-qubit states, our protocol allows for the certification of an n-fold tensor product of BB84 states. Furthermore, Alice knows which specific BB84 states Bob has prepared, while Bob himself does not. Hence, the situation at the end of this protocol is (almost) equivalent to one where Alice sent n random BB84 states to Bob. This allows us to replace the step of preparing and sending BB84 states in existing protocols by our remote-state preparation protocol in a generic and modular way.
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 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 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 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. Finally, we show how these protocols can be used in long-distance QKD using quantum repeaters.