Yusuf Alnawakhtha

Certifying the existence of entanglement between two parties is a fundamental problem in quantum information science. In this work, we develop a protocol for verifying that two parties located at specified positions share an entangled quantum state. We accomplish this by embedding the CHSH game in a quantum position verification protocol. This provides a form of entanglement testing that not only ensures that provers passing the protocol share entanglement, but that they are also located where they claim to be. This prevents parties from passing the verification test by simply forwarding the input of the verification protocol to other parties that share entanglement. The protocol has low requirements on the quantum computational abilities of honest provers---namely, it only requires the honest provers to manipulate two qubits each. It achieves security against adversaries located at incorrect positions that share at most a logarithmic amount of quantum memory with respect to the size of the classical input.

Trapdoor claw-free functions (TCFs) are immensely valuable in cryptographic interactions between a classical client and a quantum server. Typically, a protocol has the quantum server prepare a superposition of two-bit strings of a claw and then measure it using Pauli-X or Z measurements. In this paper, we demonstrate a new technique that uses the entire range of qubit measurements from the XY-plane. We show the advantage of this approach in two applications. First, building on (Brakerski et al. 2018, Kalai et al. 2022), we show an optimized two-round proof of quantumness whose security can be expressed directly in terms of the hardness of the LWE (learning with errors) problem. Second, we construct a one-round protocol for blind remote preparation of an arbitrary state on the XY-plane up to a Pauli-Z correction.