arXiv subjects

Lucas Tendick

Publications and source records attributed to Lucas Tendick.

14 recordsLinked to original sources

arXiv2026

Fermions are fundamentally more nonlocal than Bosons

Bell's theorem shows that entangled quantum particles can exhibit correlations that classical particles cannot reproduce without an additional nonlocal resource, such as communication. In this sense, quantum particles are fundamentally more nonlocal than classical ones, and entanglement becomes unavoidable in physics. Here we prove the analogous result within quantum theory itself: indistinguishable fermions transmitted through a quantum network can generate correlations that distinguishable particles or indistinguishable bosons cannot reproduce without additional communication. In the same sense, fermions are fundamentally more nonlocal than bosons or distinguishable particles, motivating fermionic anticommutation and indistinguishability as unavoidable operational resources. Our result further implies that fermions can strictly surpass all qubit-based protocols for certain distributed computing tasks, demonstrating that a complete understanding of information processing requires going beyond qubits to fermionic information carriers - febits.

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arXiv2026

Coordination Requires a Common Cause in Quantum Theory

We propose a novel causal principle that is a genuinely multipartite extension of Reichenbach's common cause principle, namely, the coordination principle: parties in a network can achieve perfect randomized coordination--in particular, agree on a uniformly random output--only if they all share a common cause. We show that this principle does not follow from the standard no-signaling and independence principles by providing an explicit theory satisfying all these principles while violating the coordination principle. Strikingly, we prove that the coordination principle holds, however, in quantum theory for four parties, and derive noise-tolerant Bell-like inequalities that certify a common cause. We then extend these results to a genuinely quantum coordination task, showing that the four-partite GHZ state requires a quantum common cause which can also be certified by experimentally accessible Bell-like inequalities. A companion paper generalizes these results for N parties, proving that the coordination principle is satisfied in general for quantum theory.

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arXiv2026

A missing causal principle: Coordination

We introduce the coordination principle, which states that perfect coordination, in the form of agreement on a uniformly random output, among N parties is possible only if they share a common cause. This principle is purely causal and can be viewed as a multipartite generalization of Reichenbach's common cause principle. We prove that quantum information theory satisfy the coordination principle in any network, and derive noise-tolerant Bell-like inequalities that certify the presence of a common cause. We further show that the principle is not a consequence of no-signaling and independence alone by constructing a concrete operational probabilistic theory that obeys both principles while still allowing perfect coordination without a common cause. This possibility arises only in fully general causal scenarios with intermediate transformations between preparations and measurements. We also formulate a genuinely quantum coordination task, showing that the preparation of a multipartite GHZ state requires a quantum common cause, which can be certified by Bell-like inequalities which are experimentally testable. Finally, we discuss the open problem of finding a quantitative, noise-tolerant version of the coordination principle that constrains approximate coordination in any reasonable causal theory. This work is the extended version of the more compact letter and provides all the technical details of the proofs.

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arXiv2026

Can every set of incompatible measurements lead to genuine multipartite steering?

Measurement incompatibility and bipartite quantum steering are known to display a strong connection: a set of measurements is incompatible if and only if it can lead to bipartite steering. Despite such a close link between these concepts in bipartite scenarios, little is known in the multipartite setting, where notions of genuine multipartite correlations play major roles. In this work we prove that, as in the bipartite case, incompatibility is also necessary and sufficient for genuine multipartite steering in any multipartite scenario with a single uncharacterised party. Interestingly, genuine multipartite steering can be extracted from any set of incompatible measurements using states which are not SLOCC equivalent, such as GHZ and W states. In contrast, we prove that this result does not hold in scenarios with more than one uncharacterised party, by presenting a set of incompatible measurements that can never lead to genuine multipartite steering in these cases. In order to obtain our main results, we introduce methods tailored for multipartite correlations, paving the way to understanding the role of measurement incompatibility beyond bipartite scenarios.

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arXiv2025

Quantitative quantum soundness for all multipartite compiled nonlocal games

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 providing quantitative upper bounds for all multipartite compiled nonlocal games via a new sequential NPA-like hierarchy. In particular, finite-level convergence yields quantitative quantum soundness with respect to the commuting quantum value, and flat optimality yields the same with respect to the tensor-product quantum value. 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.

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arXiv2025

Quantitative Quantum Soundness for Bipartite Compiled Bell Games via the Sequential NPA Hierarchy

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 bipartite compiled Bell games via a newly formalized convergent sequential Navascu\'es-Pironio-Ac\'in (NPA) hierarchy: any polynomial-time prover's score is controlled by a finite-level hierarchy value, and finite-level convergence gives a negligible gap to the commuting quantum value, or to the tensor-product quantum value under flat optimality. 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 such finite-level certificates, 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.

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arXiv2025

Strict hierarchy between $n$-wise measurement simulability, compatibility structures, and multi-copy compatibility

The incompatibility of quantum measurements, i.e. the fact that certain observable quantities cannot be measured jointly is widely regarded as a distinctive quantum feature with important implications for the foundations and the applications of quantum information theory. While the standard incompatibility of multiple measurements has been the focus of attention since the inception of quantum theory, its generalizations, such as measurement simulability, $n$-wise incompatibility, and mulit-copy incompatibility have only been proposed recently. Here, we point out that all these generalizations are differing notions of the question of how many measurements are genuinely contained in a measurement device. We then show, that all notions do differ not only in their operational meaning but also mathematically in the set of measurement assemblages they describe. We then fully resolve the relations between these different generalizations, by showing a strict hierarchy between these notions. Hence, we provide a general framework for generalized measurement incompatibility. Finally, we consider the implications our results have for recent works using these different notions.

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arXiv2025

Unlimited quantum correlation advantage from bound entanglement

Entangled states that cannot be distilled to maximal entanglement are called bound entangled and they are often viewed as too weak to break the limitations of classical models. Here, we show a strongly contrasting result: that bound entangled states, when deployed as resources between two senders who communicate with a receiver, can generate correlation advantages of unlimited magnitude. The proof is based on using many copies of a bound entangled state to assist quantum communication. We show that in order to simulate the correlations predicted by bound entanglement, one requires in the many-copy limit either an entanglement visibility that tends to zero or a diverging amount of overhead communication. This capability of bound entanglement is unlocked by only using elementary single-qubit operations. The result shows that bound entanglement can be a scalable resource for breaking the limitations of physical models without access to entanglement.

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arXiv2024

Distributed Quantum Advantage for Local Problems

We present the first local problem that shows a super-constant separation between the classical randomized LOCAL model of distributed computing and its quantum counterpart. By prior work, such a separation was known only for an artificial graph problem with an inherently global definition [Le Gall et al. 2019]. We present a problem that we call iterated GHZ, which is defined using only local constraints. Formally, it is a family of locally checkable labeling problems [Naor and Stockmeyer 1995]; in particular, solutions can be verified with a constant-round distributed algorithm. We show that in graphs of maximum degree $\Delta$, any classical (deterministic or randomized) LOCAL model algorithm will require $\Omega(\Delta)$ rounds to solve the iterated GHZ problem, while the problem can be solved in $1$ round in quantum-LOCAL. We use the round elimination technique to prove that the iterated GHZ problem requires $\Omega(\Delta)$ rounds for classical algorithms. This is the first work that shows that round elimination is indeed able to separate the two models, and this also demonstrates that round elimination cannot be used to prove lower bounds for quantum-LOCAL. To apply round elimination, we introduce a new technique that allows us to discover appropriate problem relaxations in a mechanical way; it turns out that this new technique extends beyond the scope of the iterated GHZ problem and can be used to e.g. reproduce prior results on maximal matchings [FOCS 2019, PODC 2020] in a systematic manner.

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arXiv2024

Quantum correlations cannot be reproduced with a finite number of measurements in any no-signaling theory

We show, for any finite $n \geq 2$, that there exist quantum correlations obtained from performing $n$ dichotomic quantum measurements in a bipartite Bell scenario, which cannot be reproduced by mixtures of measurement devices with at most $(n-1)$ incompatible measurements across different partitions in any no-signaling theory. That is, it requires any no-signaling theory an unbounded number of measurements to reproduce the predictions of quantum theory. We prove our results by showing that there exist linear Bell inequalities that have to be obeyed by any no-signaling theory involving only $(n-1)$-wise incompatible measurements and show explicitly how these can be violated in quantum theory. Finally, we discuss the relation of our work to previous works ruling out alternatives to quantum theory with some kind of bounded degree of freedom and consider the experimental verifiability of our results.

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arXiv2023

Distributed quantum incompatibility

Incompatible, i.e. non-jointly measurable quantum measurements are a necessary resource for many information processing tasks. It is known that increasing the number of distinct measurements usually enhances the incompatibility of a measurement scheme. However, it is generally unclear how large this enhancement is and on what it depends. Here, we show that the incompatibility which is gained via additional measurements is upper and lower bounded by certain functions of the incompatibility of subsets of the available measurements. We prove the tightness of some of our bounds by providing explicit examples based on mutually unbiased bases. Finally, we discuss the consequences of our results for the nonlocality that can be gained by enlarging the number of measurements in a Bell experiment.

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arXiv2022

Distance-based resource quantification for sets of quantum measurements

The advantage that quantum systems provide for certain quantum information processing tasks over their classical counterparts can be quantified within the general framework of resource theories. Certain distance functions between quantum states have successfully been used to quantify resources like entanglement and coherence. Perhaps surprisingly, such a distance-based approach has not been adopted to study resources of quantum measurements, where other geometric quantifiers are used instead. Here, we define distance functions between sets of quantum measurements and show that they naturally induce resource monotones for convex resource theories of measurements. By focusing on a distance based on the diamond norm, we establish a hierarchy of measurement resources and derive analytical bounds on the incompatibility of any set of measurements. We show that these bounds are tight for certain projective measurements based on mutually unbiased bases and identify scenarios where different measurement resources attain the same value when quantified by our resource monotone. Our results provide a general framework to compare distance-based resources for sets of measurements and allow us to obtain limitations on Bell-type experiments.

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arXiv2021

Quantifying necessary quantum resources for nonlocality

Nonlocality is one of the most important resources for quantum information protocols. The observation of nonlocal correlations in a Bell experiment is the result of appropriately chosen measurements and quantum states. We quantify the minimal purity to achieve a certain Bell value for any Bell operator. Since purity is the most fundamental resource of a quantum state, this enables us also to quantify the necessary coherence, discord, and entanglement for a given violation of two-qubit correlation inequalities. Our results shine new light on the CHSH inequality by showing that for a fixed Bell violation an increase in the measurement resources does not always lead to a decrease of the minimal state resources.

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arXiv2019

Activation of nonlocality in bound entanglement

We discuss the relation between entanglement and nonlocality in the hidden nonlocality scenario. Hidden nonlocality signifies nonlocality that can be activated by applying local filters to a particular state that admits a local hidden-variable model in the Bell scenario. We present a fully-biseparable three-qubit bound entangled state with a local model for the most general (non-sequential) measurements. This proves for the first time that bound entangled states can admit a local model for general measurements. We furthermore show that the local model breaks down when suitable local filters are applied. Our results demonstrate the first example of activation of nonlocality in bound entanglement. Hence, we show that genuine hidden nonlocality does not imply entanglement distillability.

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