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arXiv:2603.07930

Quantum information advantage based on Bell inequalities

Rahul Jain, Srijita Kundu

quant-phcs.CCSubmitted Mar 9, 2026• Announced Mar 10, 2026• 0 citations
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Abstract

Recently, Kretschmer et al. [KGD+25] presented an experimental demonstration of a proposed quantum information advantage protocol. We present an alternate proposal based on a relation derived from parallel-repeated CHSH games. Our memory measure is based on an information measure and is different from [KGD+25], where they count the number of qubits. Our proposal has an efficient verifier and a noise-robust quantum prover which is arguably much more efficient compared to [KGD+25].

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Recently, Kretschmer et al. [KGD+25] presented an experimental demonstration of a proposed quantum information advantage protocol.
We present an alternate proposal based on a relation derived from parallel-repeated CHSH games. Our memory measure is based on an information measure and is different from [KGD+25], where they count the number of qubits. Our proposal has an efficient verifier and a noise-robust quantum prover which is arguably much more efficient compared to [KGD+25].
Achieving quantum computational advantage requires solving a classically intractable problem on a quantum device. Natural proposals rely upon the intrinsic hardness of classically simulating quantum mechanics; however, verifying the output is itself classically intractable. On the other hand, certain quantum algorithms (e.g. prime factorization via Shor's algorithm) are efficiently verifiable, but require more resources than what is available on near-term devices. One way to bridge the gap between verifiability and implementation is to use "interactions" between a prover and a verifier. By leveraging cryptographic functions, such protocols enable the classical verifier to enforce consistency in a quantum prover's responses across multiple rounds of interaction. In this work, we demonstrate the first implementation of an interactive quantum advantage protocol, using an ion trap quantum computer. We execute two complementary protocols -- one based upon the learning with errors problem and another where the cryptographic construction implements a computational Bell test. To perform multiple rounds of interaction, we implement mid-circuit measurements on a subset of trapped ion qubits, with subsequent coherent evolution. For both protocols, the performance exceeds the asymptotic bound for classical behavior; maintaining this fidelity at scale would conclusively demonstrate verifiable quantum advantage.
In the recent years self-testing has grown into a rich and active area of study with applications ranging from practical verification of quantum devices to deep complexity theoretic results. Self-testing allows a classical verifier to deduce which quantum measurements and on what state are used, for example, by provers Alice and Bob in a nonlocal game. Hence, self-testing as well as its noise-tolerant cousin – robust self-testing – are desirable features for a nonlocal game to have.Contrary to what one might expect, we have a rather incomplete understanding of if and how self-testing could fail to hold. In particular, could it be that every 2-party nonlocal game or Bell inequality with a quantum advantage certifies the presence of a specific quantum state? Also, is it the case that every self-testing result can be turned robust with enough ingeniuty and effort? We answer these questions in the negative by providing simple and fully explicit counterexamples. To this end, given two nonlocal games G1 and G2 , we introduce the (G1∨G2) -game, in which the players get pairs of questions and choose which game they want to play. The players win if they choose the same game and win it with the answers they have given. Our counterexamples are based on this game and we believe this class of games to be of independent interest.
Bell's theorem is an important milestone in the development of quantum mechanics. It draws a line between concepts such as realism and locality on the one hand and quantum mechanics on the other. Experimentally veried violations of Bell inequalities can yield important information about what assumptions can be made about physical reality. Experiments have been conducted for over 40 years, but have left loopholes open in their executions. It is of great interest to close these loopholes, and in order to do so, further experiments are needed. The objective of this project is to investigate the underlying, previous work in the eld and to formulate a proposal for a new experiment. To do this, the derivations of the original Bell inequality and the CHSH inequality are presented along with previously conducted experiments. Also presented is the EPR paradox from which sprung the original Bell inequality.
In the field of quantum information theory one investigates the properties of information carriers which are subject to the laws of quantum mechanics. The differences between quantum mechanics and the laws that govern macroscopic information carriers lead to new opportunities and challenges in information processing. One of these differences is the entanglement of particles, which leads to strong correlations of measurement outcomes. This allows the violation of so-called Bell inequalities in quantum mechanics, which is impossible in ``classical'' theories. I investigated the possible amount of violation for an important class of Bell inequalities. In doing so I found a simple mathematical expression for an upper bound and studied the achievability of that bound. The approach provides a basic understanding of the considered Bell inequalities, which allows to construct new inequalities with interesting properties. In particular one can understand how Bell inequalities allow to bound the dimension of a quantum system. Changing a Bell inequality with invariant quantum value proved useful in optimizing them with respect to the violation. The distribution of entangled systems across large distances is achieved by sending photons. However, since they are absorbed in long fibers, quantum repeater become necessary for distances larger than approximately 200 km. Several approaches to counter the losses are known. In the long term error correction codes are very promising. Here the information is encoded into many photons, such that some losses can be compensated. I contributed to the analysis of this approach by showing how it naturally generalizes to networks of quantum repeaters. The formalism of graph states is useful in this context. A complete performance analysis of a quantum repeater contains many sources of errors and their propagation inside the circuit. I extended this analysis compared to the literature. At the moment it is not clear which types of quantum repeaters will prevail. My comparison of different theoretical proposals helps towards answering this question.
In many quantum information applications, a minimum detection efficiency must be exceeded to ensure success. Protocols depending on the violation of a Bell inequality, for instance, may be subject to the so-called detection loophole: Imperfect detectors may yield spurious violations, which consequently cannot be used to ensure, say, quantum cryptographic security. Hence, we investigate the possibility of giving lower bounds on detector efficiency even if an adversary has full control over both the source and the detectors. To this end, we present a technique to systematically derive Bell inequalities free from the detection loophole using only the observed measurements statistics. The violation of these inequalities certifies that the detectors used exceed a certain minimal efficiency.
Nonlocal games play a crucial role in quantum information theory and have numerous applications in certification and cryptographic protocols. Kalai et al. (STOC 2023) introduced a procedure to compile a nonlocal game into a single-prover interactive proof, using a quantum homomorphic encryption scheme, and showed that their compilation method preserves the classical bound of the game. Natarajan and Zhang (FOCS 2023) then showed that the quantum bound is preserved for the specific case of the CHSH game. Extending the proof techniques of Natarajan and Zhang, we show that the compilation procedure of Kalai et al. preserves the quantum bound for two classes of games: bipartite XOR games and a higher dimensional generalization of CHSH (the SATWAP inequality), that we refer to as d-outcome CHSH games. We also establish that, for any pair of qubit measurements, there exists a compiled XOR game such that its near-optimal winning probability serves as a robust selftest for that particular pair of measurements. Finally, we derive computational self-testing of three anticommuting qubit observables, based on the compilation of the nonlocal game corresponding to the so-called elegant Bell inequality.