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arXiv:2512.02284

Quantum-Classical Separation in Bounded-Resource Tasks Arising from Measurement Contextuality

Shashwat Kumar, Eliott Rosenberg, Alejandro Grajales Dau, Rodrigo Cortinas, Dmitri Maslov, Richard Oliver, Adam Zalcman, Matthew Neeley, Alice Pagano, Aaron Szasz, Ilya Drozdov, Zlatko Minev, Craig Gidney, Noureldin Yosri, Stijn J. de Graaf, Aniket Maiti, Dmitry Abanin, Rajeev Acharya, Laleh Aghababaie Beni, Georg Aigeldinger, Ross Alcaraz, Sayra Alcaraz, Trond I. Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Walt Askew, Nikita Astrakhantsev, Juan Atalaya, Ryan Babbush, Brian Ballard, Joseph C. Bardin, Hector Bates, Andreas Bengtsson, Martin Bigdeli, Alexander Bilmes, Simon Bilodeau, Felix Borjans, Alexandre Bourassa, Jenna Bovaird, Dylan Bowers, Leon Brill, Peter Brooks, Michael Broughton, David A. Browne, Brett Buchea, Bob B. Buckley, Tim Burger, Brian Burkett, Nicholas Bushnell, Jamal Busnaina, Anthony Cabrera, Juan Campero, Hung-Shen Chang, Silas Chen, Zijun Chen, Ben Chiaro, Liang-Ying Chih, Jahan Claes, Agnetta Y. Cleland, Bryan Cochrane, Matt Cockrell, Josh Cogan, Roberto Collins, Paul Conner, Harold Cook, William Courtney, Alexander L. Crook, Ben Curtin, Sayan Das, Laura De Lorenzo, Sean Demura, Agustin Di Paolo, Paul Donohoe, Andrew Dunsworth, Valerie Ehimhen, Alec Eickbusch, Aviv Moshe Elbag, Lior Ella, Mahmoud Elzouka, David Enriquez, Catherine Erickson, Vinicius S. Ferreira, Marcos Flores, Leslie Flores Burgos, Ebrahim Forati, Jeremiah Ford, Austin G. Fowler, Brooks Foxen, Masaya Fukami, Alan Wing Lun Fung, Lenny Fuste, Suhas Ganjam, Gonzalo Garcia, Christopher Garrick, Robert Gasca, Helge Gehring, Élie Genois, William Giang, Dar Gilboa, James E. Goeders, Ed Gonzales, Raja Gosula, Dietrich Graumann, Joel Grebel, Alex Greene, Jonathan A. Gross, Jose Guerrero, Tan Ha, Steve Habegger, Tanner Hadick, Monica Hansen, Matthew P. Harrigan, Sean D. Harrington, Jeanne Hartshorn, Stephen Heslin, Paula Heu, Oscar Higgott, Reno Hiltermann, Jeremy Hilton, Hsin-Yuan Huang, Mike Hucka, Ashley Huff, William J. Huggins, Evan Jeffrey, Shaun Jevons, Zhang Jiang, Xiaoxuan Jin, Cody Jones, Chaitali Joshi, Pavol Juhas, Andreas Kabel, Dvir Kafri, Hui Kang, Amir H. Karamlou, Ryan Kaufman, Kostyantyn Kechedzhi, Trupti Khaire, Tanuj Khattar, Mostafa Khezri, Seon Kim, Paul V. Klimov, Can M. Knaut, Bryce Kobrin, Alexander N. Korotkov, Fedor Kostritsa, John Mark Kreikebaum, Ryuho Kudo, Ben Kueffler, Arun Kumar, Vladislav D. Kurilovich, Vitali Kutsko, David Landhuis, Tiano Lange-Dei, Brandon W. Langley, Pavel Laptev, Kim-Ming Lau, Loïck Le Guevel, Emma Leavell, Justin Ledford, Joy Lee, Kenny Lee, Brian J. Lester, Wendy Leung, Lily L Li, Wing Yan Li, Alexander T. Lill, William P. Livingston, Matthew T. Lloyd, Aditya Locharla, Daniel Lundahl, Aaron Lunt, Sid Madhuk, Ashley Maloney, Salvatore Mandrà, Leigh S. Martin, Orion Martin, Eric Mascot, Paul Masih Das, Cameron Maxfield, Jarrod R. McClean, Matt McEwen, Seneca Meeks, Anthony Megrant, Kevin C. Miao, Reza Molavi, Sebastian Molina, Shirin Montazeri, Charles Neill, Michael Newman, Anthony Nguyen, Murray Nguyen, Chia-Hung Ni, Murphy Yuezhen Niu, Logan Oas, William D. Oliver, Raymond Orosco, Kristoffer Ottosson, Sherman Peek, David Peterson, Alex Pizzuto, Rebecca Potter, Orion Pritchard, Michael Qian, Chris Quintana, Ganesh Ramachandran, Arpit Ranadive, Matthew J. Reagor, Rachel Resnick, David M. Rhodes, Daniel Riley, Gabrielle Roberts, Roberto Rodriguez, Emma Ropes, Emma Rosenfeld, Dario Rosenstock, Elizabeth Rossi, David A. Rower, Kannan Sankaragomathi, Murat Can Sarihan, Kevin J. Satzinger, Sebastian Schroeder, Henry F. Schurkus, Aria Shahingohar, Michael J. Shearn, Aaron Shorter, Noah Shutty, Vladimir Shvarts, Volodymyr Sivak, Spencer Small, W. Clarke Smith, David A. Sobel, Barrett Spells, Sofia Springer, George Sterling, Jordan Suchard, Alexander Sztein, Madeline Taylor, Jothi Priyanka Thiruraman, Douglas Thor, Dogan Timucin, Eifu Tomita, Alfredo Torres, M. Mert Torunbalci, Hao Tran, Abeer Vaishnav, Justin Vargas, Sergey Vdovichev, Guifre Vidal, Catherine Vollgraff Heidweiller, Meghan Voorhees, Steven Waltman, Jonathan Waltz, Shannon X. Wang, Brayden Ware, James D. Watson, Travis Weidel, Theodore White, Kristi Wong, Bryan W. K. Woo, Christopher J. Wood, Maddy Woodson, Cheng Xing, Z. Jamie Yao, Ping Yeh, Bicheng Ying, Juhwan Yoo, Elliot Young, Grayson Young, Ran Zhang, Yaxing Zhang, Ningfeng Zhu, Nicholas Zobrist, Zhenjie Zou, Shruti Puri, Erik Lucero, Julian Kelly, Sergio Boixo, Yu Chen, Vadim Smelyanskiy, Hartmut Neven, Pedram Roushan, Michel Devoret

quant-phcs.ETSubmitted Dec 1, 2025• Announced Dec 3, 2025• 0 citations
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Abstract

The prevailing view is that quantum phenomena can be harnessed to tackle certain problems beyond the reach of classical approaches. Quantifying this capability as a quantum-classical separation and demonstrating it on current quantum processors has remained elusive. Using a superconducting qubit processor, we show that quantum contextuality enables certain tasks to be performed with success probabilities beyond classical limits. With a few qubits, we illustrate quantum contextuality with the magic square game, as well as quantify it through a Kochen--Specker--Bell inequality violation. To examine many-body contextuality, we implement the N-player GHZ game and separately solve a 2D hidden linear function problem, exceeding classical success rate in both. Our work proposes novel ways to benchmark quantum processors using contextuality-based algorithms.

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Nonlocality and contextuality are at the root of conceptual puzzles in quantum mechanics, and they are key resources for quantum advantage in information-processing tasks.Bell nonlocality is best understood as the incompatibility between quantum correlations and the classical theory of causality, applied to relativistic causal structure.Contextuality, on the other hand, is on a more controversial foundation.In this work, I provide a common conceptual ground between nonlocality and contextuality as violations of classical causality.First, I show that Bell inequalities can be derived solely from the assumptions of no signaling and no fine-tuning of the causal model.This removes two extra assumptions from a recent result from Wood and Spekkens and, remarkably, does not require any assumption related to independence of measurement settings-unlike all other derivations of Bell inequalities.I then introduce a formalism to represent contextuality scenarios within causal models and show that all classical causal models for violations of a Kochen-Specker inequality require fine-tuning.Thus, the quantum violation of classical causality goes beyond the case of spacelike-separated systems and already manifests in scenarios involving single systems.

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The prevailing view is that quantum phenomena can be harnessed to tackle certain problems beyond the reach of classical approaches. Quantifying this capability as a quantum-classical separation and demonstrating it on current quantum processors has remained elusive. Using a superconducting qubit processor, we show that quantum contextuality enables certain tasks to be performed with success probabilities beyond classical limits. With a few qubits, we illustrate quantum contextuality with the magic square game, as well as quantify it through a Kochen--Specker--Bell inequality violation. To examine many-body contextuality, we implement the N-player GHZ game and separately solve a 2D hidden linear function problem, exceeding classical success rate in both. Our work proposes novel ways to benchmark quantum processors using contextuality-based algorithms.
Nonlocal games provide application-level benchmarks for quantum hardware whose classical performance bounds are information-theoretic, holding against all classical strategies regardless of computational resources. We implement a 14-vertex graph coloring game, the smallest graph exhibiting a quantum-classical separation for this game type, on four trapped-ion quantum processors across three institutions. One system achieved a win rate that surpasses the classical bound with statistical significance, marking the first violation of a classical bound in a graph coloring nonlocal game on quantum hardware. The remaining systems achieved win rates comparable to the best superconducting processors evaluated on the same game, further illustrating the potential of nonlocal games as cross-architecture quantum benchmarks.
Soon after the dawn of quantum error correction, DiVincenzo and Peres observed that stabilizer codewords could give rise to simple proofs of quantumness via contextuality. This discovery can be recast in the language of nonlocal games: every nnn-qubit stabilizer state defines a specific "stabilizer-testing" nnn-player nonlocal game, which quantum players can win with probability one. If quantum players can moreover outperform all possible classical players, then the state is contextual. However, the classical values of stabilizer-testing games are largely unknown for scalable examples beyond the nnn-qubit GHZ state. We introduce several new methods for upper-bounding the classical values of these games. We first prove a general coding-theory bound for all stabilizer-testing games: if the classical value pcl∗<1p_{\mathrm{cl}}^* < 1pcl∗​<1, then pcl∗≤7/8p_{\mathrm{cl}}^* \leq 7/8pcl∗​≤7/8, i.e., there is no classical strategy that can perform as well as the optimal quantum strategy even in an asymptotic sense. We then show how to tighten this bound for the most common scalable examples, namely GHZ, toric-code and cyclic cluster states. In particular, we establish an asymptotically tight upper bound for cyclic cluster states using transfer-matrix methods. This leads to the striking conclusion that measuring an exponentially small fidelity to the cyclic cluster state will suffice to witness its contextuality.
Contextuality is arguably the fundamental property that makes quantum mechanics different from classical physics. It is responsible for quantum computational speedups in both magic-state-injection-based and measurement-based models of computation, and can be directly probed in a many-body setting by multiplayer nonlocal quantum games. Here, we discuss a family of games that can be won with certainty when performing single-site Pauli measurements on a state that is a codeword of a Calderbank-Shor-Steane (CSS) error-correcting quantum code. We show that these games require deterministic computation of a code-dependent Boolean function, and that the classical probability of success is upper bounded by a generalized notion of nonlinearity/nonquadraticity. This success probability quantifies the state's contextuality, and is computed via the function's (generalized) Walsh-Hadamard spectrum. To calculate this, we introduce an efficient, many-body-physics-inspired method that involves identifying the symmetries of an auxiliary hypergraph state. We compute the classical probability of success for several paradigmatic CSS codes and relate it to both classical statistical mechanics models and to strange correlators of symmetry-protected topological states. We also consider CSS submeasurement games, which can only be won with certainty by sharing the appropriate codeword up to local isometries. These games therefore enable self-testing, which we illustrate explicitly for the 2D toric code. We also discuss how submeasurement games enable an extensive notion of contextuality in many-body states.
Quantum entanglement is the defining feature of composite quantum systems, underpinning correlations beyond classical randomness and enabling quantum communication, cryptography, and error correction. Surveys treat entanglement, Bell nonlocality, contextuality, and decoherence in isolation or narrow subcommunities. This review advances a unified perspective analysing these phenomena as distinct but interrelated manifestations of nonclassical correlations with an operational structure. We organise bipartite entanglement through separability criteria, Schmidt decomposition, and partial-transpose techniques, and develop tools for nonlocal correlations based on Bell inequalities, Tsirelson’s bound, nonlocal games, and self-testing, emphasising device-independent protocols. We then examine contextuality and magic states as resources for quantum computational advantage beyond entanglement, clarifying their relationship to nonlocality. Finally, we characterise decoherence as environment-induced entanglement selecting classical records, and use this perspective to specify which aspects of the measurement problem it addresses and which require interpretational or dynamical extensions. Integrating these dimensions, the review clarifies how notions of nonclassicality relate, diverge, and underpin quantum technologies.
An ontological model of an operational theory is considered to be universally noncontextual if both preparation and measurement noncontextuality assumptions are satisfied in that model. In this report, we first generalize the logical proofs of quantum preparation and measurement contextuality for qubit system for any odd number of preparations and measurements. Based on the logical proof, we derive testable universally non-contextual inequalities violated by quantum theory. We then propose a class of two-party communication games and show that the average success probability of winning such games is solely linked to suitable Bell expression whose local bound is greater than universal non-contextual bound. Thus, for a given state, even if quantum theory does not exhibit non-locality, it may still reveal non-classicality by violating the universal non-contextual bound. Further, we consider a different communication game to demonstrate that for a given choices of observables in quantum theory, even if there is no logical proof of preparation and measurement contextuality exist, the universal quantum contextuality can be revealed through that communication game. Such a game thus test a weaker form of universal non-contextuality with minimal assumption.
Nonlocality and contextuality are at the root of conceptual puzzles in quantum mechanics, and they are key resources for quantum advantage in information-processing tasks.Bell nonlocality is best understood as the incompatibility between quantum correlations and the classical theory of causality, applied to relativistic causal structure.Contextuality, on the other hand, is on a more controversial foundation.In this work, I provide a common conceptual ground between nonlocality and contextuality as violations of classical causality.First, I show that Bell inequalities can be derived solely from the assumptions of no signaling and no fine-tuning of the causal model.This removes two extra assumptions from a recent result from Wood and Spekkens and, remarkably, does not require any assumption related to independence of measurement settings-unlike all other derivations of Bell inequalities.I then introduce a formalism to represent contextuality scenarios within causal models and show that all classical causal models for violations of a Kochen-Specker inequality require fine-tuning.Thus, the quantum violation of classical causality goes beyond the case of spacelike-separated systems and already manifests in scenarios involving single systems.