Xiangling Xu

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 demonstrating the quantitative quantum soundness of the KLVY compiler for all multipartite nonlocal games that admit finite-dimensional optimal strategies and, more generally, by providing quantitative upper bounds 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. This NPA-like hierarchy can be seen to complement previous multipartite generalizations of the S-G-HJW purification theorem, which takes a central role in quantum information, nonlocality, and contextuality. 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.

Compiling Bell games under cryptographic assumptions replaces the need for physical separation, allowing nonlocality to be probed with a single untrusted device. While Kalai et al. (STOC'23) showed that this compilation preserves quantum advantages, its quantitative quantum soundness has remained an open problem. We address this gap with two primary contributions. First, we establish the first quantitative quantum soundness bounds for every bipartite compiled Bell game whose optimal quantum strategy is finite-dimensional: any polynomial-time prover's score in the compiled game is negligibly close to the game's ideal quantum value. More generally, for all bipartite games we show that the compiled score cannot significantly exceed the bounds given by a newly formalized convergent sequential Navascués-Pironio-Acín (NPA) hierarchy. Second, we provide a full characterization of this sequential NPA hierarchy, establishing it as a robust numerical tool that is of independent interest. Finally, for games without finite-dimensional optimal strategies, we explore the necessity of NPA approximation error for quantitatively bounding their compiled scores, linking these considerations to the complexity conjecture $\mathrm{MIP}^{\mathrm{co}}=\mathrm{coRE}$ and open challenges such as quantum homomorphic encryption correctness for "weakly commuting" quantum registers.

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 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 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.

Feynman [1] remarked that the spin–statistics theorem is one of the few principles in physics that can be simply stated yet whose proof requires the full machinery of relativistic quantum field theory. A central implication of this theorem is that fermions cannot be composite bosons. This naturally raises the question: can this fact admit an elementary, non-relativistic proof? Bell’s theorem [2] provides a paradigm for such elementary arguments: under the minimal assumption of causality, it rules out classical (local hidden-variable) explanations of quantum correlations. In particular, it shows that quantum systems such as qubits — carried, for instance, by bosons — cannot be simulated by classical bits, and that bosonic correlations cannot arise from compositions of classical particles. Inspired by this framework, we introduce a fermionic thought experiment whose outcome shows that fermions cannot be composite bosons through reasoning analogous to Bell’s theorem. The thought experiment is formulated in the setting of distributed quantum networks and draws on concepts from distributed computing. Within this framework, we prove the existence of fermionic correlations that admit no local hidden-qubit model and are strictly stronger than Bell nonlocal correlations achievable with qubits. This shows that standard quantum information theory is insufficient to represent information carried by indistinguishable fermions in distributed settings. The assumptions remain minimal: causality is preserved, and the distributed parties have no knowledge of the network topology. Our result therefore provides an information-theoretic, non-relativistic proof of the fundamental fermion–boson distinction implied by the spin–statistics theorem. References: [1] R. P. Feynman, The Character of Physical Law, MIT Press (1965). [2] J. S. Bell, “On the Einstein–Podolsky–Rosen paradox,” Physics (1964).