Marc-Olivier Renou | LIP6 - QI Team

Quantitative quantum soundness for all multipartite compiled nonlocal games

Mon, 09 Mar 2026 00:00:00 +0000

Compiled nonlocal games transfer the power of Bell-type multi-prover tests into a single-device setting by replacing spatial separation with cryptography. Concretely, the KLVY compiler (STOC'23) maps any multi-prover game to an interactive single-prover protocol, using quantum homomorphic encryption. A crucial security property of such compilers is quantum soundness, which ensures that a dishonest quantum prover cannot exceed the original game’s quantum value. For practical cryptographic implementations, this soundness must be quantitative, providing concrete bounds, rather than merely asymptotic. While quantitative quantum soundness has been established for the KLVY compiler in the bipartite case, it has only been shown asymptotically for multipartite games. This is a significant gap, as multipartite nonlocality exhibits phenomena with no bipartite analogue, and the difficulty of enforcing space-like separation makes single-device compilation especially compelling. This work closes this gap by showing the quantitative quantum soundness of the KLVY compiler for all multipartite nonlocal games. On the way, we introduce an NPA-like hierarchy for quantum instruments and prove its completeness, thereby characterizing correlations from operationally-non-signaling sequential strategies. We further develop novel geometric arguments for the decomposition of sequential strategies into their signaling and non-signaling parts, which might be of independent interest.

Any Physical Theory of Nature Must Be Boundlessly Multipartite Nonlocal

Thu, 13 Jan 2022 13:00:00 +0200

Quantum correlations are obtained when multiple parties perform independent measurements on a shared quantum state. For instance, (a) depicts quantum correlations arising from Alice, Bob and Charlie each performing measurements on the quantum state Q.

Bell’s seminal theorem proves that certain correlations predicted by quantum theory resist explanation in terms of any local theory based on shared randomness (for instance when the quantum state is replaced with a dice in (a)). But what about alternative explanations for quantum correlations, in terms of an exotic bipartite resources E of an undiscovered causal theory generalising quantum theory and shared randomness, as in (b)?

In our work we find that no such exotic causal theory can account for all quantum correlations, thus generalizing Bell’s theorem. We propose a concrete experiment as in figure a, which achieves correlations impossible to simulate with figure b scenario. This certifies the fact that No Bipartite-Nonlocal Causal Theory Can Explain Nature’s Quantum Correlations. It also opens a new technological challenge to experimentalists toward the realisation of our proposed experiment.

We generalise this result to more general causal theory based on k-partite (and not only bipartite) systems and shared randomness.

On a more practical aspect, our work questions the standard notion of genuine multipartite nonlocality and propose a stricter redefinition of it, more compatible with the notion of no-signalling.