Elham Kashefi

Quantum state purification is the functionality that, given multiple copies of an unknown state, outputs a state with increased purity. This is an essential building block for the near- and middle-term quantum ecosystems before the availability of full fault tolerance, where one may want to obtain purified quantum states instead of expectation values. We propose an effective state purification gadget with a moderate quantum overhead by projecting multiple noisy quantum inputs to their symmetry subspace defined by a set of projectors forming a subgroup of the symmetry group. This provides a state purification performance scaling inverse-linearly to the number of state copies given a fixed stochastic error rate, which drastically improves the implementation overhead in previous works. Our method may find its application in designing robust verification protocols for quantum outputs before the availability of fully fault-tolerant computing.

Known protocols for the secure delegation of quantum computations from a client to a server in an information-theoretic setting require quantum communication. In this work, we investigate methods to reduce the communication overhead. First, we establish an impossibility result by proving that local processes on the server side cannot increase the number of qubits required for the computation. We develop a series of no-go results that prohibit such a process within an information-theoretic framework. Second, we present a possibility result by introducing the notion of selectively blind quantum computing (SBQC), a protocol that minimizes the number of encrypted qubits in the computation when delegating one computation from a pre-known set of computations. This approach, which we term can reduce communication costs drastically depending on the type of the possible computations and the differences between them.

Authentication is a fundamental building block of secure quantum networks, essential for quantum cryptographic protocols and often debated as a key limitation of quantum key distribution (QKD) in security standards. Most quantum-safe authentication schemes rely on small pre-shared keys or post-quantum computational assumptions. In this work, we introduce a new authentication approach that combines hardware assumptions, particularly Physical Unclonable Functions (PUFs), along with fundamental quantum properties of non-local states, such as local indistinguishability, to achieve a provable security in an entanglement-based protocol. We propose two protocols for different scenarios in entanglement-enabled quantum networks. The first protocol, referred to as the offline protocol, requires pre-distributed entangled states but no quantum communication during the process of authentication. It enables a server to authenticate clients at any time with only minimal classical communication. The second, an online protocol, requires quantum communication but only necessitates entangled state generation on the Prover’s side. For this, we introduce a novel hardware module, the Hybrid Entangled PUF (HEPUF). Both protocols use weakly secure, off-the-shelf classical PUFs as their hardware module, yet we prove that quantum properties such as local indistinguishability enable exponential security for authentication, even in a single round. We provide a full security analysis for both protocols and establish them as the first entanglement-based extension of hardware-based quantum authentication. These protocols are suitable for implementation across various platforms, particularly photonics-based ones, and offer a practical and flexible solution to the long-standing challenge of authentication in quantum communication networks.

With the advent of delegated quantum computing as a service, verifying quantum computations is becoming a question of great importance. Existing information theoretically Secure Delegated Quantum Computing (SDQC) protocols require the client to possess the ability to perform either trusted state preparations or measurements. Whether it is possible to verify universal quantum computations with information-theoretic security without trusted preparations or measurements was an open question so far. In this paper, we settle this question in the affirmative by presenting a modular, composable, and efficient way to turn known verification schemes into protocols that rely only on trusted gates.

With the recent availability of cloud quantum computing services, the question of verifying quantum computations delegated by a client to a quantum server is becoming of practical interest. While Verifiable Blind Quantum Computing (VBQC) has emerged as one of the key approaches to address this challenge, current protocols still need to be optimised before they are truly practical. To this end, we establish a fundamental correspondence between error-detection and verification and provide sufficient conditions to both achieve security in the Abstract Cryptography framework and optimise resource overheads of all known VBQC-based protocols. As a direct application, we demonstrate how to systematise the search for new efficient and robust verification protocols for BQP computations. While we have chosen Measurement-Based Quantum Computing (MBQC) as the working model for the presentation of our results, one could expand the domain of applicability of our framework via direct known translation between the circuit model and MBQC.

Secure multi-party computation (SMPC) protocols allow several parties that distrust each other to collectively compute a function on their inputs. In this paper, we introduce a protocol that lifts classical SMPC to quantum SMPC in a composably and statistically secure way, even for a single honest party. Unlike previous quantum SMPC protocols, our proposal only requires very limited quantum resources from all but one party; it suffices that the weak parties, i.e. the clients, are able to prepare single-qubit states in the X-Y plane. The novel quantum SMPC protocol is constructed in a naturally modular way, and relies on a new technique for quantum verification that is of independent interest. This verification technique requires the remote preparation of states only in a single plane of the Bloch sphere. In the course of proving the security of the new verification protocol, we also uncover a fundamental invariance that is inherent to measurement-based quantum computing.

We show the security of multi-user key establishment on a single line of quantum communication. More precisely, we consider a quantum communication architecture where the qubit generation and measurement happen at the two ends of the line, whilst intermediate parties are limited to single-qubit unitary transforms. This network topology has been previously introduced to implement quantum-assisted secret-sharing protocols for classical data, as well as the key establishment, and secure computing. This architecture has numerous advantages. The intermediate nodes are only using simplified hardware, which makes them easier to implement. Moreover, key establishment between arbitrary pairs of parties in the network does not require key routing through intermediate nodes. This is in contrast with quantum key distribution networks for which non- adjacent nodes need intermediate ones to route keys, thereby revealing these keys to intermediate parties and consuming previously established ones to secure the routing process. Our main result is to show the security of key establishment on quantum line networks. We show the security using the framework of abstract cryptography. This immediately makes the security composable, showing that the keys can be used for encryption or other tasks.