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      A general framework for the composition of quantum homomorphic encryption \& quantum error correction

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          Abstract

          Two essential primitives for universal, cloud-based quantum computation with security based on the laws of quantum mechanics, are quantum homomorphic encryption with information-theoretic security and quantum error correction. The former enables information-theoretic security of outsourced quantum computation, while the latter allows reliable and scalable quantum computations in the presence of errors. Previously these ingredients have been considered in isolation from one another. By establishing group-theoretic requirements that these two ingredients must satisfy, we provide a general framework for composing them. Namely, a quantum homomorphic encryption scheme enhanced with quantum error correction can directly inherit its properties from its constituent quantum homomorphic encryption and quantum error correction schemes. We apply our framework to both discrete- and continuous-variable models for quantum computation, such as Pauli-key and permutation-key encryptions in the qubit model, and displacement-key encryptions in a continuous-variable model based on Gottesman-Kitaev-Preskill codes.

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          Author and article information

          Journal
          21 April 2022
          Article
          2204.10471
          4e2cf095-05ed-48f1-a55b-3d113f750b1c

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          13 pages, Two columns
          quant-ph cs.CR

          Quantum physics & Field theory,Security & Cryptology
          Quantum physics & Field theory, Security & Cryptology

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