Lattice-Based Quantum Advantage from Rotated Measurements
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866916316782264320 |
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| author | Alnawakhtha, Yusuf Mantri, Atul Miller, Carl A. Wang, Daochen |
| author_facet | Alnawakhtha, Yusuf Mantri, Atul Miller, Carl A. Wang, Daochen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_10143 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Lattice-Based Quantum Advantage from Rotated Measurements Alnawakhtha, Yusuf Mantri, Atul Miller, Carl A. Wang, Daochen Quantum Physics Cryptography and Security Emerging Technologies 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. |
| title | Lattice-Based Quantum Advantage from Rotated Measurements |
| topic | Quantum Physics Cryptography and Security Emerging Technologies |
| url | https://arxiv.org/abs/2210.10143 |