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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
Preservation of entanglement in local noisy channels
Priya Ghosh, Kornikar Sen, Ujjwal Sen
- Year
- 2022
- Journal
- arXiv preprint
- DOI
- arXiv:2209.04422
- arXiv
- 2209.04422
Entanglement subject to noise can not be shielded against decaying. But, in case of many noisy channels, the degradation can be partially prevented by using local unitary operations. We consider the effect of local noise on shared quantum states and evaluate the amount of entanglement that can be preserved from deterioration. The amount of saved entanglement not only depends on the strength of the channel but also on the type of the channel, and in particular, it always vanishes for the depolarizing channel. The main motive of this work is to analyze the reason behind this dependency of saved entanglement by inspecting properties of the corresponding channels. In this context, we quantify and explore the biasnesses of channels towards the different states on which they act. We postulate that all biasness measures must vanish for depolarizing channels, and subsequently introduce a few measures of biasness. We also consider the entanglement capacities of channels. We observe that the joint behaviour of the biasness quantifiers and the entanglement capacity explains the nature of saved entanglement. Furthermore, we find a pair of upper bounds on saved entanglement which are noticed to imitate the graphical nature of the latter.
Open paper