Compare Papers
Paper 1
Quantum soundness of testing tensor codes
Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, Henry Yuen
- Year
- 2021
- Journal
- arXiv preprint
- DOI
- arXiv:2111.08131
- arXiv
- 2111.08131
A locally testable code is an error-correcting code that admits very efficient probabilistic tests of membership. Tensor codes provide a simple family of combinatorial constructions of locally testable codes that generalize the family of Reed-Muller codes. The natural test for tensor codes, the axis-parallel line vs. point test, plays an essential role in constructions of probabilistically checkable proofs. We analyze the axis-parallel line vs. point test as a two-prover game and show that the test is sound against quantum provers sharing entanglement. Our result implies the quantum-soundness of the low individual degree test, which is an essential component of the MIP* = RE theorem. Our proof also generalizes to the infinite-dimensional commuting-operator model of quantum provers.
Open paperPaper 2
Entanglement at the interplay between single- and many-bodyness
Jose Reslen
- Year
- 2022
- Journal
- arXiv preprint
- DOI
- arXiv:2209.04287
- arXiv
- 2209.04287
The tensor network representation of the ground state of a Bethe chain is analytically obtained and studied in relation to its entanglement distribution. Block entanglement displays a maximum at the interplay between single- and many-bodyness. In systems of two fermions, tensor networks describing ground states of interacting Hamiltonians cannot be written as a sequence of next-neighbor unitaries applied on an uncorrelated state, but need four-next-neighbor unitaries in addition. This differs from the idea that the ground state can be obtained as a sequence of next-neighbor operations applied on a tensor network. The work uncovers the transcendence of the notion of many-bodyness in the implementation of protocols based on matrix product states.
Open paper