Two-Server Oblivious Transfer for Quantum Messages

Oblivious transfer is considered as a cryptographic primitive task for quantum information processing over quantum network. Although it is possible with two servers, any existing protocol works only with classical messages. We propose two-server oblivious transfer protocols for quantum messages.

Unified Approach to Secret Sharing and Symmetric Private Information Retrieval with Colluding Servers in Quantum Systems

This paper unifiedly addresses two kinds of key quantum secure tasks, i.e., quantum versions of secret sharing (SS) and symmetric private information retrieval (SPIR) by using multi-target monotone span program (MMSP), which characterizes the classical linear protocols of SS and SPIR. In particular, two kinds of quantum extensions of SS are known; One is the classical-quantum (CQ) setting, in which the secret to be sent is classical information and the shares are quantum systems. The other is the quantum-quantum (QQ) setting, in which the secret to be sent is a quantum state and the shares are quantum systems. We newly introduce the third setting, i.e., the entanglement-assisted (EA) setting, which is defined by modifying the CQ setting with allowing prior entanglement between the dealer and the end-user who recovers the secret by collecting the shares. Showing that the linear version of SS with the EA setting is directly linked to MMSP, we characterize linear quantum versions of SS with the CQ ad QQ settings via MMSP. Further, we also introduce the EA setting of SPIR, which is shown to link to MMSP. In addition, we discuss the relation with the quantum version of maximum distance separable (MDS) codes.

On the Capacity of Quantum Private Information Retrieval from MDS-Coded and Colluding Servers

In quantum private information retrieval (QPIR), a user retrieves a classical file from multiple servers by downloading quantum systems without revealing the identity of the file. The QPIR capacity is the maximal achievable ratio of the retrieved file size to the total download size. In this paper, the capacity of QPIR from MDS-coded and colluding servers is studied. Two classes of QPIR, called stabilizer QPIR and dimension squared QPIR induced from classical strongly linear PIR are defined, and the related QPIR capacities are derived. For the non-colluding case, the general QPIR capacity is derived when the number of files goes to infinity. The capacities of symmetric and non-symmetric QPIR with coded and colluding servers are proved to coincide, being double to their classical counterparts. A general statement on the converse bound for QPIR with coded and colluding servers is derived showing that the capacities of stabilizer QPIR and dimension squared QPIR induced from any class of PIR are upper bounded by twice the classical capacity of the respective PIR class. The proposed capacity-achieving scheme combines the star-product scheme by Freij-Hollanti et al. and the stabilizer QPIR scheme by Song et al. by employing (weakly) self-dual Reed--Solomon codes.