# QMA-hardness of Consistency of Local Density Matrices with Applications to Quantum Zero-Knowledge

@article{Broadbent2020QMAhardnessOC, title={QMA-hardness of Consistency of Local Density Matrices with Applications to Quantum Zero-Knowledge}, author={Anne Broadbent and Alex Bredariol Grilo}, journal={2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)}, year={2020}, pages={196-205} }

We provide several advances to the understanding of the class of Quantum Merlin-Arthur proof systems (QMA), the quantum analogue of NP. Our central contribution is proving a longstanding conjecture that the Consistency of Local Density Matrices (CLDM) problem is QMA-hard under Karp reductions. The input of CLDM consists of local reduced density matrices on sets of at most $k$ qubits, and the problem asks if there is an n-qubit global quantum state that is locally consistent with all of the k… Expand

#### 9 Citations

Electronic Structure in a Fixed Basis is QMA-complete

- Computer Science, Physics
- ArXiv
- 2021

It is proved that this electronic-structure problem, when restricted to a fixed single-particle basis and fixed number of electrons, is QMA-complete, which is equivalent to being NP-complete for the ElectronicStructure Hamiltonian in a fixed basis. Expand

Classically Verifiable (Dual-Mode) NIZK for QMA with Preprocessing

- Computer Science
- ArXiv
- 2021

This construction has the so-called dual-mode property, which means that there are two computationally indistinguishable modes of generating CRS, and it has information theoretical soundness in one mode and information theoretical zero-knowledge property in the other. Expand

Classically Verifiable NIZK for QMA with Preprocessing

- Physics, Computer Science
- 2021

We propose three constructions of classically verifiable non-interactive zero-knowledge proofs and arguments (CV-NIZK) for QMA in various preprocessing models. 1. We construct a CV-NIZK for QMA in… Expand

Jordan products of quantum channels and their compatibility

- Medicine, Physics
- Nature communications
- 2021

Given two quantum channels, we examine the task of determining whether they are compatible—meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel… Expand

Non-Destructive Zero-Knowledge Proofs on Quantum States, and Multi-Party Generation of Authorized Hidden GHZ States

- Computer Science, Physics
- ArXiv
- 2021

This work proposes a different approach, and starts the study of Non-Destructive Zero-Knowledge Proofs on Quantum States, and shows how it can prove useful to distribute a GHZ state between different parties, in such a way that only parties knowing a secret can be part of this GHZ. Expand

Preparation and verification of tensor network states

- Physics
- 2021

Esther Cruz, Flavio Baccari, Jordi Tura, 2 Norbert Schuch, 3 and J. Ignacio Cirac Max-Planck-Institute of Quantum Optics, Hans-Kopfermann-Straße 1, 85748 Garching, Germany, and Munich Center for… Expand

Self-Testing of a Single Quantum Device Under Computational Assumptions

- Computer Science
- ITCS
- 2021

A protocol is constructed that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a change of basis applied to both the device's state and measurements. Expand

The Round Complexity of Quantum Zero-Knowledge

- Computer Science
- IACR Cryptol. ePrint Arch.
- 2021

This is the first protocol for constant-round statistical zero-knowledge arguments for QMA, and matches the best round complexity known for the corresponding protocols for NP with security against classical adversaries. Expand

A Black-Box Approach to Post-Quantum Zero-Knowledge in Constant Round

- Computer Science, Physics
- IACR Cryptol. ePrint Arch.
- 2020

A new quantum rewinding technique is introduced that enables a simulator to extract a committed message of a malicious verifier while simulating verifier's internal state in an appropriate sense. Expand

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