Making Quantum Local Verifiers Simulable with Potential Applications to Zero-Knowledge

Recently Chen and Movassagh proposed the quantum Merkle tree, which is a quantum analogue of the well-known classical Merkle tree. It gives a succinct verification protocol for quantum state commitment. Although they only proved security against semi-honest provers, they conjectured its general security. Using the proposed quantum Merkle tree, they gave a quantum analogue of Kilian's succinct argument for NP, which is based on probabilistically checkable proofs (PCPs). A nice feature of Kilian's argument is that it can be extended to a zero-knowledge succinct argument for NP, if the underlying PCP is zero-knowledge. Hence, a natural question is whether one can also make the quantum succinct argument by Chen and Movassagh zero-knowledge as well. This work makes progress on this problem. We generalize the recent result of Broadbent and Grilo to show that any local quantum verifier can be made simulable with a minor reduction in completeness and soundness. Roughly speaking, a local quantum verifier is simulable if in the yes case, the local views of the verifier can be computed without knowing the actual quantum proof; it can be seen as the quantum analogue of the classical zero-knowledge PCPs. Hence we conjecture that applying the proposed succinct quantum argument of Chen and Movassagh to a simulable local verifier is indeed zero-knowledge

Spatial-Aware Object Embeddings for Zero-Shot Localization and Classification of Actions

We aim for zero-shot localization and classification of human actions in video. Where traditional approaches rely on global attribute or object classification scores for their zero-shot knowledge transfer, our main contribution is a spatial-aware object embedding. To arrive at spatial awareness, we build our embedding on top of freely available actor and object detectors. Relevance of objects is determined in a word embedding space and further enforced with estimated spatial preferences. Besides local object awareness, we also embed global object awareness into our embedding to maximize actor and object interaction. Finally, we exploit the object positions and sizes in the spatial-aware embedding to demonstrate a new spatio-temporal action retrieval scenario with composite queries. Action localization and classification experiments on four contemporary action video datasets support our proposal. Apart from state-of-the-art results in the zero-shot localization and classification settings, our spatial-aware embedding is even competitive with recent supervised action localization alternatives.Comment: ICC

Practical Relativistic Zero-Knowledge for NP

In a Multi-Prover environment, how little spatial separation is sufficient to assert the validity of an NP statement in Perfect Zero-Knowledge ? We exhibit a set of two novel Zero-Knowledge protocols for the 3-COLorability problem that use two (local) provers or three (entangled) provers and only require exchanging one edge and two bits with two trits per prover. This greatly improves the ability to prove Zero-Knowledge statements on very short distances with very basic communication gear

Practical Relativistic Zero-Knowledge for NP

In this work we consider the following problem: in a Multi-Prover environment, how close can we get to prove the validity of an NP statement in Zero-Knowledge ? We exhibit a set of two novel Zero-Knowledge protocols for the 3-COLorability problem that use two (local) provers or three (entangled) provers and only require them to reply two trits each. This greatly improves the ability to prove Zero-Knowledge statements on very short distances with very minimal equipment.Comment: Submitted to ITC 202

Dynamics of the attractive 1D Bose gas: analytical treatment from integrability

The physics of the attractive one-dimensional Bose gas (Lieb-Liniger model) is investigated with techniques based on the integrability of the system. Combining a knowledge of particle quasi-momenta to exponential precision in the system size with determinant representations of matrix elements of local operators coming from the Algebraic Bethe Ansatz, we obtain rather general analytical results for the zero-temperature dynamical correlation functions of the density and field operators. Our results thus provide quantitative predictions for possible future experiments in atomic gases or optical waveguides.Comment: 26 pages, 5 figure