Pub Date : 2026-01-16DOI: 10.22331/q-2026-01-16-1967
Tzu-Hsuan Huang, Yeong-Luh Ueng
Recent research has shown that syndrome-based belief propagation using layered scheduling (sLBP) can not only accelerate the convergence rate but also improve the error rate performance by breaking the quantum trapping sets for quantum low-density parity-check (QLDPC) codes, showcasing a result distinct from classical error correction codes. In this paper, we consider edge-wise informed dynamic scheduling (IDS) for QLDPC codes based on syndrome-based residual belief propagation (sRBP). However, the construction of QLDPC codes and the identical prior intrinsic information assignment will result in an equal residual in many edges, causing a performance limitation for sRBP. Two heuristic strategies, including edge pool design and error pre-correction, are introduced to tackle this obstacle and quantum trapping sets. Then, a novel sRBP equipped with a predict-and-reduce-error mechanism (PRE-sRBP) is proposed, which can provide over one order of performance gain on the considered bicycle codes and symmetric hypergraph (HP) code under similar iterations compared to sLBP.
{"title":"Informed Dynamic Scheduling for QLDPC Codes","authors":"Tzu-Hsuan Huang, Yeong-Luh Ueng","doi":"10.22331/q-2026-01-16-1967","DOIUrl":"https://doi.org/10.22331/q-2026-01-16-1967","url":null,"abstract":"Recent research has shown that syndrome-based belief propagation using layered scheduling (sLBP) can not only accelerate the convergence rate but also improve the error rate performance by breaking the quantum trapping sets for quantum low-density parity-check (QLDPC) codes, showcasing a result distinct from classical error correction codes. In this paper, we consider edge-wise informed dynamic scheduling (IDS) for QLDPC codes based on syndrome-based residual belief propagation (sRBP). However, the construction of QLDPC codes and the identical prior intrinsic information assignment will result in an equal residual in many edges, causing a performance limitation for sRBP. Two heuristic strategies, including edge pool design and error pre-correction, are introduced to tackle this obstacle and quantum trapping sets. Then, a novel sRBP equipped with a predict-and-reduce-error mechanism (PRE-sRBP) is proposed, which can provide over one order of performance gain on the considered bicycle codes and symmetric hypergraph (HP) code under similar iterations compared to sLBP.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"57 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145972329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-16DOI: 10.22331/q-2026-01-16-1968
L. Spagnoli, A. Roggero, N. Wiebe
We show in this paper that a strong and easy connection exists between quantum error correction and Lattice Gauge Theories (LGT) by using the Gauge symmetry to construct an efficient error-correcting code for Abelian $mathbb{Z_2}$ LGTs. We identify the logical operations on this gauge covariant code and show that the corresponding Hamiltonian can be expressed in terms of these logical operations while preserving the locality of the interactions. Furthermore, we demonstrate that these substitutions actually give a new way of writing the LGT as an equivalent hardcore boson model. Finally we demonstrate a method to perform fault-tolerant time evolution of the Hamiltonian within the gauge covariant code using both product formulas and qubitization approaches. This opens up the possibility of inexpensive end to end dynamical simulations that save physical qubits by blurring the lines between simulation algorithms and quantum error correcting codes.
{"title":"Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes","authors":"L. Spagnoli, A. Roggero, N. Wiebe","doi":"10.22331/q-2026-01-16-1968","DOIUrl":"https://doi.org/10.22331/q-2026-01-16-1968","url":null,"abstract":"We show in this paper that a strong and easy connection exists between quantum error correction and Lattice Gauge Theories (LGT) by using the Gauge symmetry to construct an efficient error-correcting code for Abelian $mathbb{Z_2}$ LGTs. We identify the logical operations on this gauge covariant code and show that the corresponding Hamiltonian can be expressed in terms of these logical operations while preserving the locality of the interactions. Furthermore, we demonstrate that these substitutions actually give a new way of writing the LGT as an equivalent hardcore boson model. Finally we demonstrate a method to perform fault-tolerant time evolution of the Hamiltonian within the gauge covariant code using both product formulas and qubitization approaches. This opens up the possibility of inexpensive end to end dynamical simulations that save physical qubits by blurring the lines between simulation algorithms and quantum error correcting codes.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"124 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145972370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-16DOI: 10.22331/q-2026-01-16-1966
Caroline L. Jones, Stefan L. Ludescher, Albert Aloy, Markus P. Müller
We demonstrate a fundamental relation between the structures of physical space and of quantum theory: the set of quantum correlations in a rotational prepare-and-measure scenario can be derived from covariance alone, without assuming quantum physics. To show this, we consider a semi-device-independent randomness generation scheme where one of two spatial rotations is performed on an otherwise uncharacterized preparation device, and one of two possible measurement outcomes is subsequently obtained. An upper bound on a theory-independent notion of spin is assumed for the transmitted physical system. It turns out that this determines the set of quantum correlations and the amount of certifiable randomness in this setup exactly. Interestingly, this yields the basis of a theory-independent protocol for the secure generation of random numbers. Our results support the conjecture that the symmetries of space and time determine at least part of the probabilistic structure of quantum theory.
{"title":"Theory-independent randomness generation from spatial symmetries","authors":"Caroline L. Jones, Stefan L. Ludescher, Albert Aloy, Markus P. Müller","doi":"10.22331/q-2026-01-16-1966","DOIUrl":"https://doi.org/10.22331/q-2026-01-16-1966","url":null,"abstract":"We demonstrate a fundamental relation between the structures of physical space and of quantum theory: the set of quantum correlations in a rotational prepare-and-measure scenario can be derived from covariance alone, without assuming quantum physics. To show this, we consider a semi-device-independent randomness generation scheme where one of two spatial rotations is performed on an otherwise uncharacterized preparation device, and one of two possible measurement outcomes is subsequently obtained. An upper bound on a theory-independent notion of spin is assumed for the transmitted physical system. It turns out that this determines the set of quantum correlations and the amount of certifiable randomness in this setup exactly. Interestingly, this yields the basis of a theory-independent protocol for the secure generation of random numbers. Our results support the conjecture that the symmetries of space and time determine at least part of the probabilistic structure of quantum theory.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"19 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145972326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-14DOI: 10.22331/q-2026-01-14-1964
Adina Goldberg
In the flavour of categorical quantum mechanics, we extend nonlocal games to allow quantum questions and answers, using quantum sets (special symmetric dagger Frobenius algebras) and the quantum functions of Musto, Reutter, and Verdon. Equations are presented using a diagrammatic calculus for tensor categories. To this quantum question and answer setting, we extend the standard definitions, including strategies, correlations, and synchronicity, and we use these definitions to extend results about synchronicity. We extend the graph homomorphism (isomorphism) game to quantum graphs, and show it is synchronous (bisynchronous) and connect its perfect (bi)strategies to quantum graph homomorphisms (isomorphisms). Our extended definitions agree with the existing quantum games literature, except in the case of synchronicity.
{"title":"Quantum games and synchronicity","authors":"Adina Goldberg","doi":"10.22331/q-2026-01-14-1964","DOIUrl":"https://doi.org/10.22331/q-2026-01-14-1964","url":null,"abstract":"In the flavour of categorical quantum mechanics, we extend nonlocal games to allow quantum questions and answers, using quantum sets (special symmetric dagger Frobenius algebras) and the quantum functions of Musto, Reutter, and Verdon. Equations are presented using a diagrammatic calculus for tensor categories. To this quantum question and answer setting, we extend the standard definitions, including strategies, correlations, and synchronicity, and we use these definitions to extend results about synchronicity. We extend the graph homomorphism (isomorphism) game to quantum graphs, and show it is synchronous (bisynchronous) and connect its perfect (bi)strategies to quantum graph homomorphisms (isomorphisms). Our extended definitions agree with the existing quantum games literature, except in the case of synchronicity.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"8 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-14DOI: 10.22331/q-2026-01-14-1965
Marius A. Oancea, Thomas B. Mieling, Giandomenico Palumbo
The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor, which unifies the Berry curvature and the quantum metric. In this work, we use the differential-geometric framework of vector bundles to analyze the properties of parameter-dependent quantum states and generalize the quantum geometric tensor to this setting. This construction is based on a general connection on a Hermitian vector bundle, which defines a notion of quantum state transport in parameter space, and a sub-bundle projector, which constrains the set of accessible quantum states. We show that the sub-bundle geometry is similar to that of submanifolds in Riemannian geometry and is described by generalized Gauss-Codazzi-Mainardi equations. This leads to a novel definition of the quantum geometric tensor that contains an additional curvature contribution. To illustrate our results, we describe the sub-bundle geometry arising in the semiclassical treatment of Dirac fields propagating in curved spacetime and show how the quantum geometric tensor, with its additional curvature contributions, is obtained in this case. As a concrete example, we consider Dirac fermions confined to a hyperbolic plane and demonstrate how spatial curvature influences the quantum geometry. This work sets the stage for further exploration of quantum systems in curved geometries, with applications in both high-energy physics and condensed matter systems.
{"title":"Quantum geometric tensors from sub-bundle geometry","authors":"Marius A. Oancea, Thomas B. Mieling, Giandomenico Palumbo","doi":"10.22331/q-2026-01-14-1965","DOIUrl":"https://doi.org/10.22331/q-2026-01-14-1965","url":null,"abstract":"The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor, which unifies the Berry curvature and the quantum metric. In this work, we use the differential-geometric framework of vector bundles to analyze the properties of parameter-dependent quantum states and generalize the quantum geometric tensor to this setting. This construction is based on a general connection on a Hermitian vector bundle, which defines a notion of quantum state transport in parameter space, and a sub-bundle projector, which constrains the set of accessible quantum states. We show that the sub-bundle geometry is similar to that of submanifolds in Riemannian geometry and is described by generalized Gauss-Codazzi-Mainardi equations. This leads to a novel definition of the quantum geometric tensor that contains an additional curvature contribution. To illustrate our results, we describe the sub-bundle geometry arising in the semiclassical treatment of Dirac fields propagating in curved spacetime and show how the quantum geometric tensor, with its additional curvature contributions, is obtained in this case. As a concrete example, we consider Dirac fermions confined to a hyperbolic plane and demonstrate how spatial curvature influences the quantum geometry. This work sets the stage for further exploration of quantum systems in curved geometries, with applications in both high-energy physics and condensed matter systems.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"81 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145968854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-14DOI: 10.22331/q-2026-01-14-1963
Sridhar Prabhu, Vladimir Kremenetski, Saeed A. Khan, Ryotatsu Yanagimoto, Peter L. McMahon
Conventionally in quantum sensing, the goal is to estimate one or more unknown parameters that are assumed to be deterministic – that is, they do not change between shots of the quantum-sensing protocol. We instead consider the setting where the parameters are stochastic: each shot of the quantum-sensing protocol senses parameter values that come from independent random draws. In this work, we explore three examples where the stochastic parameters are correlated and show how using entanglement provides a benefit in classification or estimation tasks: (1) a two-parameter classification task, for which there is an advantage in the low-shot regime; (2) an $N$-parameter estimation task and a classification variant of it, for which an entangled sensor requires just a constant number (independent of $N$) shots to achieve the same accuracy as an unentangled sensor using exponentially many (${sim}2^N$) shots; (3) classifying the magnetization of a spin chain in thermal equilibrium, where the individual spins fluctuate but the total spin in one direction is conserved – this gives a practical setting in which stochastic parameters are correlated in a way that an entangled sensor can be designed to exploit. We also present a theoretical framework for assessing, for a given choice of entangled sensing protocol and distributions to discriminate between, how much advantage the entangled sensor would have over an unentangled sensor. Our work motivates the further study of sensing correlated stochastic parameters using entangled quantum sensors – and since classical sensors by definition cannot be entangled, our work shows the possibility for entangled quantum sensors to achieve an exponential advantage in sample complexity over classical sensors, in contrast to the typical quadratic advantage.
{"title":"Exponential advantage in quantum sensing of correlated parameters","authors":"Sridhar Prabhu, Vladimir Kremenetski, Saeed A. Khan, Ryotatsu Yanagimoto, Peter L. McMahon","doi":"10.22331/q-2026-01-14-1963","DOIUrl":"https://doi.org/10.22331/q-2026-01-14-1963","url":null,"abstract":"Conventionally in quantum sensing, the goal is to estimate one or more unknown parameters that are assumed to be deterministic – that is, they do not change between shots of the quantum-sensing protocol. We instead consider the setting where the parameters are stochastic: each shot of the quantum-sensing protocol senses parameter values that come from independent random draws. In this work, we explore three examples where the stochastic parameters are correlated and show how using entanglement provides a benefit in classification or estimation tasks: (1) a two-parameter classification task, for which there is an advantage in the low-shot regime; (2) an $N$-parameter estimation task and a classification variant of it, for which an entangled sensor requires just a constant number (independent of $N$) shots to achieve the same accuracy as an unentangled sensor using exponentially many (${sim}2^N$) shots; (3) classifying the magnetization of a spin chain in thermal equilibrium, where the individual spins fluctuate but the total spin in one direction is conserved – this gives a practical setting in which stochastic parameters are correlated in a way that an entangled sensor can be designed to exploit. We also present a theoretical framework for assessing, for a given choice of entangled sensing protocol and distributions to discriminate between, how much advantage the entangled sensor would have over an unentangled sensor. Our work motivates the further study of sensing correlated stochastic parameters using entangled quantum sensors – and since classical sensors by definition cannot be entangled, our work shows the possibility for entangled quantum sensors to achieve an exponential advantage in sample complexity over classical sensors, in contrast to the typical quadratic advantage.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"37 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-14DOI: 10.22331/q-2026-01-14-1962
Qilin Li, Atharva Vidwans, Yazhen Wang, Micheline B. Soley
We establish a unified statistical framework that underscores the crucial role statistical inference plays in Quantum Amplitude Estimation (QAE), a task essential to fields ranging from chemistry to finance and machine learning. We use this framework to harness Bayesian statistics for improved measurement efficiency with rigorous interval estimates at all iterations of Iterative Quantum Amplitude Estimation. We demonstrate the resulting method, Bayesian Iterative Quantum Amplitude Estimation (BIQAE), accurately and efficiently estimates both quantum amplitudes and molecular ground-state energies to high accuracy, and show in analytic and numerical sample complexity analyses that BIQAE outperforms all other QAE approaches considered. Both rigorous mathematical proofs and numerical simulations conclusively indicate Bayesian statistics is the source of this advantage, a finding that invites further inquiry into the power of statistics to expedite the search for quantum utility.
{"title":"Harnessing Bayesian Statistics to Accelerate Iterative Quantum Amplitude Estimation","authors":"Qilin Li, Atharva Vidwans, Yazhen Wang, Micheline B. Soley","doi":"10.22331/q-2026-01-14-1962","DOIUrl":"https://doi.org/10.22331/q-2026-01-14-1962","url":null,"abstract":"We establish a unified statistical framework that underscores the crucial role statistical inference plays in Quantum Amplitude Estimation (QAE), a task essential to fields ranging from chemistry to finance and machine learning. We use this framework to harness Bayesian statistics for improved measurement efficiency with rigorous interval estimates at all iterations of Iterative Quantum Amplitude Estimation. We demonstrate the resulting method, Bayesian Iterative Quantum Amplitude Estimation (BIQAE), accurately and efficiently estimates both quantum amplitudes and molecular ground-state energies to high accuracy, and show in analytic and numerical sample complexity analyses that BIQAE outperforms all other QAE approaches considered. Both rigorous mathematical proofs and numerical simulations conclusively indicate Bayesian statistics is the source of this advantage, a finding that invites further inquiry into the power of statistics to expedite the search for quantum utility.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"15 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-08DOI: 10.22331/q-2026-01-08-1960
Roy Araiza, Yidong Chen, Marius Junge, Peixue Wu
We introduce a new framework for quantifying the complexity of quantum channels, grounded in a suitably chosen resource set. This class of convex functions is designed to analyze the complexity of both open and closed quantum systems. By leveraging Lipschitz norms inspired by quantum optimal transport theory, we rigorously establish the fundamental properties of this complexity measure. The flexibility in selecting the resource set allows us to derive effective lower bounds for gate complexities and simulation costs of both Hamiltonian simulations and dynamics of open quantum systems. Additionally, we demonstrate that this complexity measure exhibits linear growth for random quantum circuits and finite-dimensional quantum simulations, up to the Brown-Susskind threshold.
{"title":"Resource-Dependent Complexity of Quantum Channels","authors":"Roy Araiza, Yidong Chen, Marius Junge, Peixue Wu","doi":"10.22331/q-2026-01-08-1960","DOIUrl":"https://doi.org/10.22331/q-2026-01-08-1960","url":null,"abstract":"We introduce a new framework for quantifying the complexity of quantum channels, grounded in a suitably chosen resource set. This class of convex functions is designed to analyze the complexity of both open and closed quantum systems. By leveraging Lipschitz norms inspired by quantum optimal transport theory, we rigorously establish the fundamental properties of this complexity measure. The flexibility in selecting the resource set allows us to derive effective lower bounds for gate complexities and simulation costs of both Hamiltonian simulations and dynamics of open quantum systems. Additionally, we demonstrate that this complexity measure exhibits linear growth for random quantum circuits and finite-dimensional quantum simulations, up to the Brown-Susskind threshold.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"25 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145919798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-08DOI: 10.22331/q-2026-01-08-1961
Uta Isabella Meyer, Ivan Šupić, Frédéric Grosshans, Damian Markham
Self-testing identifies quantum states and correlations that exhibit nonlocality, distinguishing them, up to local transformations, from other quantum states. Due to their strong nonlocality, it is known that all graph states can be self-tested in the standard setting – where parties are not allowed to communicate. Recently it has been shown that graph states display nonlocal correlations even when bounded classical communication on the underlying graph is permitted, a feature that has found applications in proving a circuit-depth separation between classical and quantum computing. In this work, we develop self testing in the framework of bounded classical communication, and we show that certain graph states can be robustly self-tested even allowing for communication. In particular, we provide an explicit self-test for the circular graph state and the honeycomb cluster state – the latter known to be a universal resource for measurement based quantum computation. Since communication generally obstructs self-testing of graph states, we further provide a procedure to robustly self-test any graph state from larger ones that exhibit nonlocal correlations in the communication scenario.
{"title":"Self-Testing Graph States Permitting Bounded Classical Communication","authors":"Uta Isabella Meyer, Ivan Šupić, Frédéric Grosshans, Damian Markham","doi":"10.22331/q-2026-01-08-1961","DOIUrl":"https://doi.org/10.22331/q-2026-01-08-1961","url":null,"abstract":"Self-testing identifies quantum states and correlations that exhibit nonlocality, distinguishing them, up to local transformations, from other quantum states. Due to their strong nonlocality, it is known that all graph states can be self-tested in the standard setting – where parties are not allowed to communicate. Recently it has been shown that graph states display nonlocal correlations even when bounded classical communication on the underlying graph is permitted, a feature that has found applications in proving a circuit-depth separation between classical and quantum computing. In this work, we develop self testing in the framework of bounded classical communication, and we show that certain graph states can be robustly self-tested even allowing for communication. In particular, we provide an explicit self-test for the circular graph state and the honeycomb cluster state – the latter known to be a universal resource for measurement based quantum computation. Since communication generally obstructs self-testing of graph states, we further provide a procedure to robustly self-test any graph state from larger ones that exhibit nonlocal correlations in the communication scenario.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"34 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145919882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-07DOI: 10.22331/q-2026-01-07-1959
Matthias Salzger, John H. Selby
There has been a recent surge of interest within the field of quantum foundations regarding incorporating ideas from general relativity and quantum gravity. However, many quantum information tools remain agnostic to the underlying spacetime. For instance, whenever we draw a quantum circuit the effective spacetime imposed by the connectivity of the physical qubits which will realize this circuit is not taken into account. In this work, we aim to address this limitation by extending the framework of process theories to include a background spacetime structure. We introduce the notion of process implementations, i.e., decompositions of a process. A process is then embeddable if and only if one of its implementations can be embedded in such a way that all the component processes are localized and all wires follow timelike paths. While conceptually simple, checking for embeddability is generally computationally intractable. We therefore work towards simplifying this problem as much as possible, identifying a canonical subset of implementations that determine both the embeddability of a process and the causal structures distinguishable at least in some process theory. Notably, we discover countably infinite ''zigzag'' causal structures beyond those typically considered. While these can be ignored in classical theory, they seem to be essential in quantum theory, as the quantum CNOT gate can be implemented by all zigzag structures but not in a standard causal structure, except in the trivial undecomposed way. These zigzags could be significant for quantum causal modeling and the study of novel quantum resources.
{"title":"A decompositional framework for process theories in spacetime","authors":"Matthias Salzger, John H. Selby","doi":"10.22331/q-2026-01-07-1959","DOIUrl":"https://doi.org/10.22331/q-2026-01-07-1959","url":null,"abstract":"There has been a recent surge of interest within the field of quantum foundations regarding incorporating ideas from general relativity and quantum gravity. However, many quantum information tools remain agnostic to the underlying spacetime. For instance, whenever we draw a quantum circuit the effective spacetime imposed by the connectivity of the physical qubits which will realize this circuit is not taken into account. In this work, we aim to address this limitation by extending the framework of process theories to include a background spacetime structure. We introduce the notion of process implementations, i.e., decompositions of a process. A process is then embeddable if and only if one of its implementations can be embedded in such a way that all the component processes are localized and all wires follow timelike paths. While conceptually simple, checking for embeddability is generally computationally intractable. We therefore work towards simplifying this problem as much as possible, identifying a canonical subset of implementations that determine both the embeddability of a process and the causal structures distinguishable at least in some process theory. Notably, we discover countably infinite ''zigzag'' causal structures beyond those typically considered. While these can be ignored in classical theory, they seem to be essential in quantum theory, as the quantum CNOT gate can be implemented by all zigzag structures but not in a standard causal structure, except in the trivial undecomposed way. These zigzags could be significant for quantum causal modeling and the study of novel quantum resources.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"14 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145919797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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