Pub Date : 2024-10-10DOI: 10.22331/q-2024-10-10-1499
Yifan Hong, David T. Stephen, Aaron J. Friedman
We constrain a broad class of teleportation protocols using insights from locality. In the "standard" teleportation protocols we consider, all outcome-dependent unitaries are Pauli operators conditioned on linear functions of the measurement outcomes. We find that all such protocols involve preparing a "resource state" exhibiting symmetry-protected topological (SPT) order with Abelian protecting symmetry $mathcal{G}_{k}= (mathbb{Z}_2 times mathbb{Z}_2)^k$. The $k$ logical states are teleported between the edges of the chain by measuring the corresponding $2k$ string order parameters in the bulk and applying outcome-dependent Paulis. Hence, this single class of nontrivial SPT states is both necessary and sufficient for the standard teleportation of $k$ qubits. We illustrate this result with several examples, including the cluster state, variants thereof, and a nonstabilizer hypergraph state.
{"title":"Quantum teleportation implies symmetry-protected topological order","authors":"Yifan Hong, David T. Stephen, Aaron J. Friedman","doi":"10.22331/q-2024-10-10-1499","DOIUrl":"https://doi.org/10.22331/q-2024-10-10-1499","url":null,"abstract":"We constrain a broad class of teleportation protocols using insights from locality. In the \"standard\" teleportation protocols we consider, all outcome-dependent unitaries are Pauli operators conditioned on linear functions of the measurement outcomes. We find that all such protocols involve preparing a \"resource state\" exhibiting symmetry-protected topological (SPT) order with Abelian protecting symmetry $mathcal{G}_{k}= (mathbb{Z}_2 times mathbb{Z}_2)^k$. The $k$ logical states are teleported between the edges of the chain by measuring the corresponding $2k$ string order parameters in the bulk and applying outcome-dependent Paulis. Hence, this single class of nontrivial SPT states is both necessary and sufficient for the standard teleportation of $k$ qubits. We illustrate this result with several examples, including the cluster state, variants thereof, and a nonstabilizer hypergraph state.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"8 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142398271","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 : 2024-10-04DOI: 10.22331/q-2024-10-04-1493
Teague Tomesh, Nicholas Allen, Daniel Dilley, Zain Saleem
The computational capabilities of near-term quantum computers are limited by the noisy execution of gate operations and a limited number of physical qubits. Hybrid variational algorithms are well-suited to near-term quantum devices because they allow for a wide range of tradeoffs between the amount of quantum and classical resources used to solve a problem. This paper investigates tradeoffs available at both the algorithmic and hardware levels by studying a specific case – applying the Quantum Approximate Optimization Algorithm (QAOA) to instances of the Maximum Independent Set (MIS) problem. We consider three variants of the QAOA which offer different tradeoffs at the algorithmic level in terms of their required number of classical parameters, quantum gates, and iterations of classical optimization needed. Since MIS is a constrained combinatorial optimization problem, the QAOA must respect the problem constraints. This can be accomplished by using many multi-controlled gate operations which must be decomposed into gates executable by the target hardware. We study the tradeoffs available at this hardware level, combining the gate fidelities and decomposition efficiencies of different native gate sets into a single metric called the $textit{gate decomposition cost}$.
近期量子计算机的计算能力受限于门操作的噪声执行和有限的物理量子比特。混合变分算法非常适合近期量子设备，因为它们允许在解决问题所使用的量子资源和经典资源之间进行广泛的权衡。本文通过研究一个具体案例--将量子近似优化算法（QAOA）应用于最大独立集（MIS）问题实例--来探讨算法和硬件层面的权衡。我们考虑了量子近似优化算法的三种变体，它们在算法层面上提供了不同的权衡，包括所需的经典参数数量、量子门数量以及经典优化的迭代次数。由于 MIS 是一个有约束的组合优化问题，因此 QAOA 必须尊重问题的约束条件。这可以通过使用许多多控制门操作来实现，而这些操作必须分解成目标硬件可执行的门。我们将不同本机门电路集的门保真度和分解效率合并成一个称为 $textit{gate decomposition cost}$的单一指标，研究在这一硬件层面上的权衡。
{"title":"Quantum-classical tradeoffs and multi-controlled quantum gate decompositions in variational algorithms","authors":"Teague Tomesh, Nicholas Allen, Daniel Dilley, Zain Saleem","doi":"10.22331/q-2024-10-04-1493","DOIUrl":"https://doi.org/10.22331/q-2024-10-04-1493","url":null,"abstract":"The computational capabilities of near-term quantum computers are limited by the noisy execution of gate operations and a limited number of physical qubits. Hybrid variational algorithms are well-suited to near-term quantum devices because they allow for a wide range of tradeoffs between the amount of quantum and classical resources used to solve a problem. This paper investigates tradeoffs available at both the algorithmic and hardware levels by studying a specific case – applying the Quantum Approximate Optimization Algorithm (QAOA) to instances of the Maximum Independent Set (MIS) problem. We consider three variants of the QAOA which offer different tradeoffs at the algorithmic level in terms of their required number of classical parameters, quantum gates, and iterations of classical optimization needed. Since MIS is a constrained combinatorial optimization problem, the QAOA must respect the problem constraints. This can be accomplished by using many multi-controlled gate operations which must be decomposed into gates executable by the target hardware. We study the tradeoffs available at this hardware level, combining the gate fidelities and decomposition efficiencies of different native gate sets into a single metric called the $textit{gate decomposition cost}$.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"10 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142374153","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 : 2024-10-04DOI: 10.22331/q-2024-10-04-1491
Quanlong Wang, Richie Yeung, Mark Koch
ZX-calculus has proved to be a useful tool for quantum technology with a wide range of successful applications. Most of these applications are of an algebraic nature. However, other tasks that involve differentiation and integration remain unreachable with current ZX techniques. Here we elevate ZX to an analytical perspective by realising differentiation and integration entirely within the framework of ZX-calculus. We explicitly illustrate the new analytic framework of ZX-calculus by applying it in context of quantum machine learning for the analysis of barren plateaus.
{"title":"Differentiating and Integrating ZX Diagrams with Applications to Quantum Machine Learning","authors":"Quanlong Wang, Richie Yeung, Mark Koch","doi":"10.22331/q-2024-10-04-1491","DOIUrl":"https://doi.org/10.22331/q-2024-10-04-1491","url":null,"abstract":"ZX-calculus has proved to be a useful tool for quantum technology with a wide range of successful applications. Most of these applications are of an algebraic nature. However, other tasks that involve differentiation and integration remain unreachable with current ZX techniques. Here we elevate ZX to an analytical perspective by realising differentiation and integration entirely within the framework of ZX-calculus. We explicitly illustrate the new analytic framework of ZX-calculus by applying it in context of quantum machine learning for the analysis of barren plateaus.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"20 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142374152","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 : 2024-10-04DOI: 10.22331/q-2024-10-04-1492
Roberto Rubboli, Ryuji Takagi, Marco Tomamichel
We prove that the stabilizer fidelity is multiplicative for the tensor product of an arbitrary number of single-qubit states. We also show that the relative entropy of magic becomes additive if all the single-qubit states but one belong to a symmetry axis of the stabilizer octahedron. We extend the latter results to include all the $alpha$-$z$ Rényi relative entropy of magic. This allows us to identify a continuous set of magic monotones that are additive for single-qubit states. We also show that all the monotones mentioned above are additive for several standard two and three-qubit states subject to depolarizing noise. Finally, we obtain closed-form expressions for several states and tighter lower bounds for the overhead of probabilistic one-shot magic state distillation.
{"title":"Mixed-state additivity properties of magic monotones based on quantum relative entropies for single-qubit states and beyond","authors":"Roberto Rubboli, Ryuji Takagi, Marco Tomamichel","doi":"10.22331/q-2024-10-04-1492","DOIUrl":"https://doi.org/10.22331/q-2024-10-04-1492","url":null,"abstract":"We prove that the stabilizer fidelity is multiplicative for the tensor product of an arbitrary number of single-qubit states. We also show that the relative entropy of magic becomes additive if all the single-qubit states but one belong to a symmetry axis of the stabilizer octahedron. We extend the latter results to include all the $alpha$-$z$ Rényi relative entropy of magic. This allows us to identify a continuous set of magic monotones that are additive for single-qubit states. We also show that all the monotones mentioned above are additive for several standard two and three-qubit states subject to depolarizing noise. Finally, we obtain closed-form expressions for several states and tighter lower bounds for the overhead of probabilistic one-shot magic state distillation.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"223 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142374151","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 : 2024-10-03DOI: 10.22331/q-2024-10-03-1490
Nicola Pranzini, Guillermo García-Pérez, Esko Keski-Vakkuri, Sabrina Maniscalco
The Born rule describes the probability of obtaining an outcome when measuring an observable of a quantum system. As it can only be tested by measuring many copies of the system under consideration, it does not hold for non-replicable systems. For these systems, we give a procedure to predict the future statistics of measurement outcomes through Repeated Measurements (RM). This is done by extending the validity of quantum mechanics to those systems admitting no replicas; we prove that if the statistics of the results acquired by performing RM on such systems is sufficiently similar to that obtained by the Born rule, the latter can be used effectively. We apply our framework to a repeatedly measured Unruh-DeWitt detector interacting with a massless scalar quantum field, which is an example of a system (detector) interacting with an uncontrollable environment (field) for which using RM is necessary. Analysing what an observer learns from the RM outcomes, we find a regime where history-dependent RM probabilities are close to the Born ones. Consequently, the latter can be used for all practical purposes. Finally, we numerically study inertial and accelerated detectors, showing that an observer can see the Unruh effect via RM.
{"title":"Repeated measurements on non-replicable systems and their consequences for Unruh-DeWitt detectors","authors":"Nicola Pranzini, Guillermo García-Pérez, Esko Keski-Vakkuri, Sabrina Maniscalco","doi":"10.22331/q-2024-10-03-1490","DOIUrl":"https://doi.org/10.22331/q-2024-10-03-1490","url":null,"abstract":"The Born rule describes the probability of obtaining an outcome when measuring an observable of a quantum system. As it can only be tested by measuring many copies of the system under consideration, it does not hold for non-replicable systems. For these systems, we give a procedure to predict the future statistics of measurement outcomes through Repeated Measurements (RM). This is done by extending the validity of quantum mechanics to those systems admitting no replicas; we prove that if the statistics of the results acquired by performing RM on such systems is sufficiently similar to that obtained by the Born rule, the latter can be used effectively. We apply our framework to a repeatedly measured Unruh-DeWitt detector interacting with a massless scalar quantum field, which is an example of a system (detector) interacting with an uncontrollable environment (field) for which using RM is necessary. Analysing what an observer learns from the RM outcomes, we find a regime where history-dependent RM probabilities are close to the Born ones. Consequently, the latter can be used for all practical purposes. Finally, we numerically study inertial and accelerated detectors, showing that an observer can see the Unruh effect via RM.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"49 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142374150","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 : 2024-10-02DOI: 10.22331/q-2024-10-02-1488
Mathias B. M. Svendsen, Marcel Cech, Max Schemmer, Beatriz Olmos
We establish the concept of topological pumping in one-dimensional systems with long-range couplings and apply it to the transport of a photon in quantum optical systems. In our theoretical investigation, we introduce an extended version of the Rice-Mele model with all-to-all couplings. By analyzing its properties, we identify the general conditions for topological pumping and theoretically and numerically demonstrate topologically protected and dispersionless transport of a photon on a one-dimensional emitter chain. As concrete examples, we investigate three different popular quantum optics platforms, namely Ryd-berg atom lattices, dense lattices of atoms excited to low-lying electronic states, and atoms coupled to waveguides, using experimentally relevant parameters. We observe that despite the long-ranged character of the dipole-dipole interactions, topological pumping facilitates the transport of a photon with a fidelity per cycle which can reach 99.9%. Moreover, we find that the photon pumping process remains topologically protected against local disorder in the coupling parameters.
{"title":"Topological photon pumping in quantum optical systems","authors":"Mathias B. M. Svendsen, Marcel Cech, Max Schemmer, Beatriz Olmos","doi":"10.22331/q-2024-10-02-1488","DOIUrl":"https://doi.org/10.22331/q-2024-10-02-1488","url":null,"abstract":"We establish the concept of topological pumping in one-dimensional systems with long-range couplings and apply it to the transport of a photon in quantum optical systems. In our theoretical investigation, we introduce an extended version of the Rice-Mele model with all-to-all couplings. By analyzing its properties, we identify the general conditions for topological pumping and theoretically and numerically demonstrate topologically protected and dispersionless transport of a photon on a one-dimensional emitter chain. As concrete examples, we investigate three different popular quantum optics platforms, namely Ryd-berg atom lattices, dense lattices of atoms excited to low-lying electronic states, and atoms coupled to waveguides, using experimentally relevant parameters. We observe that despite the long-ranged character of the dipole-dipole interactions, topological pumping facilitates the transport of a photon with a fidelity per cycle which can reach 99.9%. Moreover, we find that the photon pumping process remains topologically protected against local disorder in the coupling parameters.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"8 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142362860","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}
Quantum phase estimation is one of the most powerful quantum primitives. This work proposes a new approach for the problem of multiple eigenvalue estimation: Quantum Multiple Eigenvalue Gaussian filtered Search (QMEGS). QMEGS leverages the Hadamard test circuit structure and only requires simple classical postprocessing. QMEGS is the first algorithm to simultaneously satisfy the following two properties: (1) It can achieve the Heisenberg-limited scaling without relying on any spectral gap assumption. (2) With a positive energy gap and additional assumptions on the initial state, QMEGS can estimate all dominant eigenvalues to $epsilon$ accuracy utilizing a significantly reduced circuit depth compared to the standard quantum phase estimation algorithm. In the most favorable scenario, the maximal runtime can be reduced to as low as $log(1/epsilon)$. This implies that QMEGS serves as an efficient and versatile approach, achieving the best-known results for both gapped and gapless systems. Numerical results validate the efficiency of our proposed algorithm in various regimes.
{"title":"Quantum Multiple Eigenvalue Gaussian filtered Search: an efficient and versatile quantum phase estimation method","authors":"Zhiyan Ding, Haoya Li, Lin Lin, HongKang Ni, Lexing Ying, Ruizhe Zhang","doi":"10.22331/q-2024-10-02-1487","DOIUrl":"https://doi.org/10.22331/q-2024-10-02-1487","url":null,"abstract":"Quantum phase estimation is one of the most powerful quantum primitives. This work proposes a new approach for the problem of multiple eigenvalue estimation: Quantum Multiple Eigenvalue Gaussian filtered Search (QMEGS). QMEGS leverages the Hadamard test circuit structure and only requires simple classical postprocessing. QMEGS is the first algorithm to simultaneously satisfy the following two properties: (1) It can achieve the Heisenberg-limited scaling without relying on any spectral gap assumption. (2) With a positive energy gap and additional assumptions on the initial state, QMEGS can estimate all dominant eigenvalues to $epsilon$ accuracy utilizing a significantly reduced circuit depth compared to the standard quantum phase estimation algorithm. In the most favorable scenario, the maximal runtime can be reduced to as low as $log(1/epsilon)$. This implies that QMEGS serves as an efficient and versatile approach, achieving the best-known results for both gapped and gapless systems. Numerical results validate the efficiency of our proposed algorithm in various regimes.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"23 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142363015","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 : 2024-10-02DOI: 10.22331/q-2024-10-02-1489
Yuan Liu, Ho Yiu Chung, Ravishankar Ramanathan
Investigations of the boundary of the quantum correlation set have gained increased attention in recent years. This is done through the derivation of quantum Bell inequalities, which are related to Tsirelson's problem and have significant applications in device-independent (DI) information processing. However, determining quantum Bell inequalities is a notoriously difficult task and only isolated examples are known. In this paper, we present families of (almost-)quantum Bell inequalities and highlight four foundational and DI applications. Firstly, it is known that quantum correlations on the non-signaling boundary are of crucial importance in the task of DI randomness extraction from weak sources. In the practical Bell scenario of two players with two $k$-outcome measurements, we derive quantum Bell inequalities that demonstrate a separation between the quantum boundary and certain portions of the boundaries of the no-signaling polytope of dimension up to $4k-8$, extending previous results from nonlocality distillation and the collapse of communication complexity. Secondly as an immediate by-product, we give a general proof of Aumann’s Agreement theorem for quantum systems as well as the almost-quantum correlations, which implies Aumann’s agreement theorem is a reasonable physical principle in the context of epistemics to pick out both quantum theory and almost-quantum correlations from general no-signaling theories. Thirdly, we present a family of quantum Bell inequalities in the two players with $m$ binary measurements scenarios, that we prove serve to self-test the two-qubit singlet and the corresponding $2m$ measurements. Interestingly, this claim generalizes the result for $m=2$ discovered by Tsirelson-Landau-Masanes and shows an improvement over the state-of-the-art Device-Independent Randomness-Amplification (DIRA). Lastly, we use our quantum Bell inequalities to derive the general form of the principle of no advantage in nonlocal computation, which is an information-theoretic principle that serves to characterize the quantum correlation set.
近年来，对量子相关集边界的研究越来越受到关注。量子贝尔不等式与齐雷尔森问题有关，在设备无关（DI）信息处理中有着重要应用。然而，确定量子贝尔不等式是一项众所周知的艰巨任务，目前只知道一些孤立的例子。在本文中，我们介绍了（近）量子贝尔不等式族，并重点介绍了四个基础性和 DI 应用。首先，众所周知，非信号边界上的量子相关性对于从弱信号源中提取 DI 随机性至关重要。在两个参与者有两个 $k$ 结果测量的实际贝尔场景中，我们推导出量子贝尔不等式，证明量子边界与维度高达 $4k-8$ 的无信号多面体边界的某些部分之间存在分离，扩展了之前从非位置性蒸馏和通信复杂性坍缩中得出的结果。其次，作为直接的副产品，我们给出了量子系统以及近量子关联的奥曼一致定理的一般证明，这意味着奥曼一致定理是认识论背景下从一般无信号理论中挑出量子理论和近量子关联的合理物理原理。第三，我们提出了一个量子贝尔不等式族，在两个玩家带$m$二元测量的情况下，我们证明这个不等式族可以自我测试双量子比特单子和相应的$2m$测量。有趣的是，这一主张概括了齐雷尔松-朗道-马萨尼斯发现的 $m=2$ 结果，并显示了对最先进的设备无关随机性放大（DIRA）的改进。最后，我们利用量子贝尔不等式推导出了非局部计算中无优势原理的一般形式，这是一个信息论原理，用于描述量子相关集的特征。
{"title":"(Almost-)Quantum Bell Inequalities and Device-Independent Applications","authors":"Yuan Liu, Ho Yiu Chung, Ravishankar Ramanathan","doi":"10.22331/q-2024-10-02-1489","DOIUrl":"https://doi.org/10.22331/q-2024-10-02-1489","url":null,"abstract":"Investigations of the boundary of the quantum correlation set have gained increased attention in recent years. This is done through the derivation of quantum Bell inequalities, which are related to Tsirelson's problem and have significant applications in device-independent (DI) information processing. However, determining quantum Bell inequalities is a notoriously difficult task and only isolated examples are known. In this paper, we present families of (almost-)quantum Bell inequalities and highlight four foundational and DI applications. Firstly, it is known that quantum correlations on the non-signaling boundary are of crucial importance in the task of DI randomness extraction from weak sources. In the practical Bell scenario of two players with two $k$-outcome measurements, we derive quantum Bell inequalities that demonstrate a separation between the quantum boundary and certain portions of the boundaries of the no-signaling polytope of dimension up to $4k-8$, extending previous results from nonlocality distillation and the collapse of communication complexity. Secondly as an immediate by-product, we give a general proof of Aumann’s Agreement theorem for quantum systems as well as the almost-quantum correlations, which implies Aumann’s agreement theorem is a reasonable physical principle in the context of epistemics to pick out both quantum theory and almost-quantum correlations from general no-signaling theories. Thirdly, we present a family of quantum Bell inequalities in the two players with $m$ binary measurements scenarios, that we prove serve to self-test the two-qubit singlet and the corresponding $2m$ measurements. Interestingly, this claim generalizes the result for $m=2$ discovered by Tsirelson-Landau-Masanes and shows an improvement over the state-of-the-art Device-Independent Randomness-Amplification (DIRA). Lastly, we use our quantum Bell inequalities to derive the general form of the principle of no advantage in nonlocal computation, which is an information-theoretic principle that serves to characterize the quantum correlation set.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"111 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142363013","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 : 2024-09-26DOI: 10.22331/q-2024-09-26-1486
Joshua Eglinton, Federico Carollo, Igor Lesanovsky, Kay Brandner
Microscopic thermal machines promise to play an important role in future quantum technologies. Making such devices widely applicable will require effective strategies to channel their output into easily accessible storage systems like classical degrees of freedom. Here, we develop a self-consistent theoretical framework that makes it possible to model such quantum-classical hybrid devices in a thermodynamically consistent manner. Our approach is based on the assumption that the quantum part of the device is subject to strong decoherence and dissipation induced by a thermal reservoir. Due to the ensuing separation of time scales between slowly evolving classical and fast relaxing quantum degrees of freedom, the dynamics of the hybrid system can be described by means of adiabatic-response theory. We show that, upon including fluctuations in a minimally consistent way, the resulting equations of motion can be equipped with a first and second law, both on the ensemble level and on the level of individual trajectories of the classical part of the system, where thermodynamic quantities like heat and work become stochastic variables. As an application of our theory, we work out a physically transparent model of a quantum-classical hybrid engine, whose working system consists of a chain of Rydberg atoms, which is confined in an optical cavity and driven by periodic temperature variations. We demonstrate through numerical simulations that the engine can sustain periodic oscillations of a movable mirror, which acts as a classical load, against external friction and extract the full distributions of input heat and output work. By making the statistics of thermodynamic processes in quantum-classical hybrid systems accessible without the need to further specify a measurement protocol, our work contributes to bridging the long-standing gap between classical and quantum stochastic thermodynamics.
{"title":"Stochastic Thermodynamics at the Quantum-Classical Boundary: A Self-Consistent Framework Based on Adiabatic-Response Theory","authors":"Joshua Eglinton, Federico Carollo, Igor Lesanovsky, Kay Brandner","doi":"10.22331/q-2024-09-26-1486","DOIUrl":"https://doi.org/10.22331/q-2024-09-26-1486","url":null,"abstract":"Microscopic thermal machines promise to play an important role in future quantum technologies. Making such devices widely applicable will require effective strategies to channel their output into easily accessible storage systems like classical degrees of freedom. Here, we develop a self-consistent theoretical framework that makes it possible to model such quantum-classical hybrid devices in a thermodynamically consistent manner. Our approach is based on the assumption that the quantum part of the device is subject to strong decoherence and dissipation induced by a thermal reservoir. Due to the ensuing separation of time scales between slowly evolving classical and fast relaxing quantum degrees of freedom, the dynamics of the hybrid system can be described by means of adiabatic-response theory. We show that, upon including fluctuations in a minimally consistent way, the resulting equations of motion can be equipped with a first and second law, both on the ensemble level and on the level of individual trajectories of the classical part of the system, where thermodynamic quantities like heat and work become stochastic variables. As an application of our theory, we work out a physically transparent model of a quantum-classical hybrid engine, whose working system consists of a chain of Rydberg atoms, which is confined in an optical cavity and driven by periodic temperature variations. We demonstrate through numerical simulations that the engine can sustain periodic oscillations of a movable mirror, which acts as a classical load, against external friction and extract the full distributions of input heat and output work. By making the statistics of thermodynamic processes in quantum-classical hybrid systems accessible without the need to further specify a measurement protocol, our work contributes to bridging the long-standing gap between classical and quantum stochastic thermodynamics.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"35 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142321724","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 : 2024-09-26DOI: 10.22331/q-2024-09-26-1485
Yìlè Yīng, Marina Maciel Ansanelli, Andrea Di Biagio, Elie Wolfe, David Schmid, Eric Gama Cavalcanti
Nonclassical causal modeling was developed in order to explain violations of Bell inequalities while adhering to relativistic causal structure and $faithfulness$---that is, avoiding fine-tuned causal explanations. Recently, a no-go theorem that can be viewed as being stronger than Bell's theorem has been derived, based on extensions of the Wigner's friend thought experiment: the Local Friendliness (LF) no-go theorem. Here we show that the LF no-go theorem poses formidable challenges for the field of causal modeling, even when nonclassical and/or cyclic causal explanations are considered. We first recast the LF inequalities, one of the key elements of the LF no-go theorem, as special cases of monogamy relations stemming from a statistical marginal problem. We then further recast LF inequalities as causal compatibility inequalities stemming from a $nonclassical$ causal marginal problem, for a causal structure implied by well-motivated causal-metaphysical assumptions. We find that the LF inequalities emerge from this causal structure even when one allows the latent causes of observed events to admit post-quantum descriptions, such as in a generalized probabilistic theory or in an even more exotic theory. We further prove that $no$ nonclassical causal model can explain violations of LF inequalities without violating the No Fine-Tuning principle. Finally, we note that these obstacles cannot be overcome even if one appeals to $cyclic$ causal models, and we discuss potential directions for further extensions of the causal modeling framework.
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