# Commitments to Quantum States

@article{Gunn2022CommitmentsTQ, title={Commitments to Quantum States}, author={Sam Gunn and Nathan Ju and Fermi Ma and Mark Zhandry}, journal={Electron. Colloquium Comput. Complex.}, year={2022}, volume={TR22} }

What does it mean to commit to a quantum state? In this work, we propose a simple answer: a commitment to quantum messages is binding if, after the commit phase, the committed state is hidden from the sender’s view. We accompany this new definition with several instantiations. We build the first non-interactive succinct quantum state commitments, which can be seen as an analogue of collision-resistant hashing for quantum messages. We also show that hiding quantum state commitments (QSCs) are…

## One Citation

### Quantum Merkle Trees

- Computer Science, MathematicsArXiv
- 2021

Using the quantum Merkle tree, a succinct quantum argument for the Gap-k-Local-Hamiltonian problem is proposed and it is proved it is secure against semi-honest provers in QHROM and conjecture its general security.

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It is shown that recent Bulletproofs-like protocols based on lattices satisfy these properties, and are hence sound against quantum adversaries, and a new quantum rewinding strategy is devised, which applies to any protocol satisfying natural multi-round generalizations of special soundness and collapsing.

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This work gives a classical commit-and-open protocol which is post-quantum secure if and only if the commitment scheme used is collapse binding, and establishes that a variety of “weaker” post-Quantum computational binding notions are in fact equivalent to collapse binding.

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- Computer Science, MathematicsArXiv
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Using the quantum Merkle tree, a succinct quantum argument for the Gap-k-Local-Hamiltonian problem is proposed and it is proved it is secure against semi-honest provers in QHROM and conjecture its general security.

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This work constructs, assuming the existence of pseudorandom state generators that map a λ-bit seed to a ω(log λ)-qubit state, (a) statistically binding and computationally hiding commitments and (b) pseudo one-time encryption schemes that are sufficient to construct maliciously secure multiparty computation protocols in the dishonest majority setting.

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This work shows that non-interactive quantum commitments (for classical messages) with computational hiding and statistical binding exist if pseudorandom quantum states exist, and considers digital signatures, which are other fundamental primitives in cryptography.

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This work constructs a non-interactive quantum commitment scheme which is classically statistically-binding and has a classical opening, based on the existence of any post-quantum one-way function, and shows that it is impossible to achieve classical binding for statistically hiding commitments, regardless of assumption or round complexity.