Masahito Hayashi

We study the construction of fully universal private channel coding protocols for classical-quantum channels. While earlier schemes achieved universal decoding, they relied on random encoders, preventing complete universality. We close this gap by showing that spectral expansion of a graph associated with a codebook guarantees universal channel resolvability: if the graph has a large spectral gap, the output state induced by the codewords is asymptotically indistinguishable from the target state, independent of the channel. This yields the first deterministic, channel-independent resolvability coding in the quantum regime. Combining this with universal channel coding, we construct a fully universal private coding protocol that achieves standard private information rates, highlighting the role of expander graphs in secure quantum communication.

In the quest to unlock the maximum potential of quantum sensors, it is of paramount importance to have practical measurement strategies that can estimate incompatible parameters with best precisions possible. However, it is still not known how to find practical measurements with optimal precisions, even for uncorrelated measurements over probe states. Here, we give a concrete way to find uncorrelated measurement strategies with optimal precisions. We solve this fundamental problem by introducing a framework of conic programming that unifies the theory of precision bounds for multiparameter estimates for uncorrelated and correlated measurement strategies under a common umbrella. Namely, we give precision bounds that arise from linear programs on various cones defined on a tensor product space of matrices, including a particular cone of separable matrices. Subsequently, our theory allows us to develop an efficient algorithm that calculates both upper and lower bounds for the ultimate precision bound for uncorrelated measurement strategies, where these bounds can be tight. In particular, the uncorrelated measurement strategy that arises from our theory saturates the upper bound to the ultimate precision bound. Also, we show numerically that there is a strict gap between the previous efficiently computable bounds and the ultimate precision bound.

Quantum communication is emerging as a foundational element of future secure information systems, with applications ranging from key distribution to direct message transmission. Widely used standards such as the Digital Video Broadcasting – Satellite – Second Generation Extension (DVB-S2X) can be considered for satellite-based quantum communication scenarios, where resource constraints and channel impairments must be carefully addressed. While much of the early work in quantum security focused on asymptotic analyses or relied on models rooted in classical wiretap theory, there is a growing need for frameworks that provide operational security guarantees in finite-length and non-asymptotic regimes. In this work, we address that gap by introducing a composable security metric based on the trace distance, derived from α-order Rényi information. Our model, illustrated in Fig. 1 (left), serves as a general abstraction of quantum communication systems subject to eavesdropping, which includes protocols of the family known as Quantum Direct Secure Communication (QDSC), which aim to transmit confidential messages directly over quantum channels. The proposed framework allows for precise evaluation of secrecy leakage under realistic conditions and offers an alternative to traditional key-based paradigms, thereby contributing to the broader effort of enabling keyless secure and efficient quantum communication. Our key result is a composable bound on the trace distance, which solely depends on an αparameterized mutual information term. Unlike conventional methods based on ε-smooth min-entropy, our approach avoids smoothing altogether while still ensuring composability. This leads to analytically tractable bounds and a clearer understanding of the trade-off between coding rate and secrecy. As a practical application, we apply our bounds to a one-way information flow where BPSK-modulated coherent quantum states carry secret information over lossy bosonic channels, consistent with DVB-S2X satellite links. Our results, illustrated in Fig. 1 (right) provide two-fold insights. First, we demonstrate the usefulness of our bound for practical design of reliable and secret space links. Second, we quantify the reliability-secrecy trade-off by numerically showing that the finitelength physical-layer secrecy can be guaranteed only if coding rates are appropriately adjusted.

Digital signatures are a powerful cryptographic tool widely employed across various industries for securely authenticating the identity of a signer during communication between signers and verifiers. While quantum digital signatures have been extensively studied, the security still depends on a trusted third-party. To address this limitation and enhance the applicability in real-world scenarios, here we propose a novel quantum digital signature protocol without a trusted third-party to further improve the security. We note that a quantum one-way function can work appropriately in digital signature due to the intrinsic non-cloning property for quantum states. Secret keys in the protocol are constituted by classical private keys and quantum public keys because we assume that no user is trusted in the protocol. We prove that the protocol has information-theoretical unforgeability. Moreover, it satisfies other important secure properties, including asymmetry, undeniability, and expandability.

Noisy channel is a valuable resource for cryptography. It can be used to build cryptographic primitives like bit commitment and oblivious transfer that are information-theoretically secure between two untrusting parties. Existing studies on this topic focus on the channel that does not change over successive uses. In this work, we study non-independent and identically distributed (non-i.i.d.) channels with constraint on min-entropy. The dishonest player is able to configure the channel at his will under the constraint. We devise a protocol that is complete, hiding, and binding, and give its commitment rate.

Dense coding is known as an attractive quantum information protocol. While the original study considers the noiseless setting, many subsequent studies extended this result to more general settings. However, all of them focused only on the communication speed in various noisy settings. While dense coding with the noiseless setting realizes twice communication speed, it also realizes quantum secure direct communication (QSDC) as follows.In dense coding, the sender, Alice, and the receiver, Bob, share perfect Bell states and Alice encodes her message by application of a unitary operation. Since Alice's local state is a completely mixed state, the eavesdropper, Eve, cannot obtain any information about the message even when Eve intercepts the transmitted quantum state. However, it is not easy to share a perfect Bell state. Hence, we need to consider secure communication under imperfect shared state. Specifically, we study secure direct communication by using a general preshared quantum state and a generalization of dense coding. In this scenario, Alice is allowed to apply a unitary operation on the preshared state to encode her message, and the set of allowed unitary operations forms a group. To decode the message, Bob is allowed to apply a measurement across his own system and the system he receives. In the worst scenario, we guarantee that Eve obtains no information for the message even when Eve access the joint system between the system that she intercepts and her original system of the preshared state. For a practical application, we construct a modular wiretap code by concatenating inverse universal hashing and an arbitrary error correcting code. Combining the wiretap code with error verification, we propose a concrete protocol for the private dense coding model and derive an upper bound of information leakage in the finite-length setting. We also discuss how to apply our scenario to the case with discrete Weyl-Heisenberg representation when the preshared state is unknown. In this case, Pauli encoding operation and Pauli channel are considered. Hence, our protocol can be applied many similar tasks.

Quantum private information retrieval (QPIR) for quantum messages is the protocol in which a user retrieves one of the multiple quantum states from one or multiple servers without revealing which state is retrieved. We consider QPIR in two different settings: the blind setting, in which the servers contain one copy of the message states, and the visible setting, in which the servers contain the description of the message states. One trivial solution in both settings is downloading all states from the servers and the main goal of this paper is to find more efficient QPIR protocols. First, we prove that the trivial solution is optimal for one-server QPIR in the blind setting. In one-round protocols, the same optimality holds even in the visible setting. On the other hand, when the user and the server share entanglement, we prove that there exists an efficient one-server QPIR protocol in the blind setting. Furthermore, in the visible setting, we prove that it is possible to construct symmetric QPIR protocols in which the user obtains no information of the non-targeted messages. We construct two-server symmetric QPIR protocols. Note that symmetric classical PIR is impossible without shared randomness unknown to the user.

Randomness is one of the key ingredients to information processing in practice, especially for computation and cryptography. A vast number of applications critically rely on abundant, high-quality random numbers that are generated securely. In this work we introduce a variant of randomness extraction framework, named \emph{incoherent randomness extraction} (IRE), in the context of quantum coherence theory where free incoherent operations are employed. This cryptographic framework unveils a new perspective to the study of quantum coherence distillation (QCD) by an \emph{exact} one-shot connection, that is, the maximum number of secure random bits extractable from a single instance of \emph{unstructured} quantum state is precisely equal to the maximum number of coherent bits that can be distilled from the same state. This exact relation not only sharpens our understanding on the operational equivalence between randomness and coherence, but also enables us to derive tight second order expansions (estimation of the number of extractable random bits/distillable coherent bits to the order~$o(\sqrt{n})$ where $n$ is the number of the prepared source states) of both tasks in the independent and identically distributed setting. Remarkably, the incoherent operation classes that can empower coherence distillation for generic states all lead to the same second order expansions, indicating their operational equivalence for QCD as well as IRE in both asymptotic and large block length regimes. As a by-product, we showcase a proof of the strong converse property for IRE from its second order expansion, excluding a possible tradeoff between the insecurity threshold and the rate of extractable randomness of a protocol. This also contributes to an alternative strong converse proof for QCD due to their exact one-shot correspondence.

Quantum private information retrieval (QPIR) is a protocol that a user retrieves one of f files from non- communicating n servers by downloading quantum systems without revealing the identity of the target file. As variants of the QPIR with stronger security requirements, the symmetric QPIR is a protocol that the files except for the target file are not leaked to the user, and the t-private QPIR is a protocol that the identity of the target file is kept secret even if at most t servers may collude to reveal the identity. The QPIR capacity is the maximum ratio of the one file size to the size of downloaded quantum systems, and we prove that the symmetric t-private QPIR capacity is min{1, 2(n − t)/n} for any 1 ≤ t < n. We construct a capacity-achieving QPIR protocol by the stabilizer formalism and prove the optimality of our protocol. The proposed capacity is greater than the classical counterpart.