Samson Abramsky
Contextuality is a key feature of quantum mechanics. We present the sheaf-theoretic approach to contextuality introduced by Abramsky and Brandenburger, and show how it covers a range of logical and physical phenomena "at the borders of paradox".
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Contextuality is a key feature of quantum mechanics that provides an important non-classical resource for quantum information and computation. Abramsky and Brandenburger used sheaf theory to give a general treatment of contextuality in quantum theory [New Journal of Physics 13 (2011) 113036]. However, contextual phenomena are found in other fields as well, for example database theory. In this paper, we shall develop this unified view of contextuality. We provide two main contributions: firstly, we expose a remarkable connection between contexuality and logical paradoxes; secondly, we show that…
While quantum computers are expected to yield considerable advantages over classical devices, the precise features of quantum theory enabling these advantages remain unclear. Contextuality--the denial of a notion of classical physical reality--has emerged as a promising hypothesis. Magic states are quantum resources critical for practically achieving universal quantum computation. They exhibit the standard form of contextuality that is known to enable probabilistic advantages in a variety of computational and communicational tasks. Strong contextuality is an extremal form of contextuality desc…
Many seemingly paradoxical effects are known in the predictions for outcomes of measurements made on pre- and post-selected quantum systems. A class of such effects, which we call ``logical pre- and post-selection paradoxes'', bear a striking resemblance to proofs of the Bell-Kochen-Specker theorem, which suggests that they demonstrate the contextuality of quantum mechanics. Despite the apparent similarity, we show that such effects can occur in noncontextual hidden variable theories, provided measurements are allowed to disturb the values of the hidden variables.
We describe a joint cohomological framework for measurement-based quantum computation (MBQC) and the corresponding contextuality proofs. The central object in this framework is an element in the second cohomology group of the chain complex describing a given MBQC. It contains the function computed, up to gauge equivalence, and at the same time is a contextuality witness. The present cohomological description only applies to temporally flat MBQCs, and we outline an approach for extending it to the temporally ordered case.
Many seemingly paradoxical effects are known in the predictions for outcomes of intermediate measurements made on pre- and post-selected quantum systems. Despite appearances, these effects do not demonstrate the impossibility of a noncontextual hidden variable theory, since an explanation in terms of measurement-disturbance is possible. Nonetheless, we show that for every paradoxical effect wherein all the pre- and post- selected probabilities are 0 or 1 and the pre- and post-selected states are nonorthogonal, there is an associated proof of contextuality. This proof is obtained by considering…
A refined Frauchiger--Renner paradox based on strong contextuality
本文通过识别逻辑语境性（Hardy 型）是 Frauchiger-Renner 悖论的关键要素，并基于强语境性的 GHZ-Mermin 场景提出了一个更强的悖论（GHZ-FR 悖论），该悖论无需后选择或量子建模观察者的推理。
This short note is an introduction to the slides from our talks given in 2018 during the Advanced School of Quantum Foundations and Quantum Computation in Joao Pessoa , Brazil. In these talks, addressed to participants with a limited knowledge of quantum foundations, we defined locality, causality, randomness, counterfactual definiteness and we explained EPR-Bohm paradoxes. In particular we discussed in great detail various Bell-type inequalities and the implications of their violation in spin polarisation correlation experiments. Finally we explained why and how the predictive completeness of…
Contextuality and nonlocality are non-classical properties exhibited by quantum statistics whose implications profoundly impact both foundations and applications of quantum theory. In this paper we provide some insights into logical contextuality and inequality-free proofs. The former can be understood as the possibility version of contextuality, while the latter refers to proofs of quantum contextuality/nonlocality that are not based on violations of some noncontextuality (or Bell) inequality. The present work aims to build a bridge between these two concepts from what we call possibilistic p…
Algebraic paradoxes in adaptive quantum computation
该研究解决了自适应测量量子计算中代数语境性的开放问题，证明自适应$\boldsymbol{\boldsymbol{Z}_2}$线性MBQC协议计算非仿射布尔函数时会出现代数悖论，可通过上同调检测，为量子优势的代数分析提供了关键方法。
A Logical Formalism of Hardy-type Paradox
该研究针对哈迪型悖论引入统一逻辑形式主义，证明其存在与逻辑语境性等价，推广了相关场景的工作，并分析了KCBS场景中的逻辑哈迪型悖论，发现特定设置下有一种悖论，成功概率约为10.56%。
The two state vector formalism (TSVF) was proposed by Aharonov, Bergmann, and Lebowitz (ABL) to provide a way for the counterfactual assignment of the probabilities of outcomes of contemplated but unperformed measurements on quantum systems. This formalism underlies various aspects of foundations of quantum theory and has been used significantly in the development of weak values and several proofs of quantum contextuality. We consider the application of TSVF, with pre- and post-selection (PPS) and the corresponding ABL rule, as a means to unearth quantum contextuality. We use the principle of …
Any theory that admits a Wigner's Friend type multi-agent paradox is logically contextual
本研究证明任何允许维格纳朋友型多智能体悖论的理论必然具有逻辑情境性，并揭示量子弗劳希格-伦纳悖论为逻辑情境性证明，同时构建了无需贝尔非局域性的新悖论。
Many features of single-partite quantum walks can be simulated by classical waves. However, it was recently experimentally shown that some temporal sequences of measurements on a quantum walker do not admit a classical description in terms of macro-realistic theories. Here, we extend this observation and present pre- and post-selection scenarios in quantum walks leading to logical paradoxes. Such paradoxes were recently shown to be equivalent to proofs of contextuality, therefore we provide an additional argument for non-classicality of a quantum walk model. The assumptions behind the claims o…
Hardy's Paradox for Yu-Oh Set Constructed by Logically Contextual Quantum States
本文基于 Yu-Oh 集构造 Hardy's paradox，通过逻辑上下文纯态系统枚举并证明混合态不具有逻辑上下文性，进一步构建了 12 个成功概率为 11.1% 的 Hardy's paradox。
The notion of contextuality, which emerges from a theorem established by Simon Kochen and Ernst Specker (1960-1967) and by John Bell (1964-1966), is certainly one of the most fundamental aspects of quantum weirdness. If it is a questioning on scholastic philosophy and a study of contrafactual logic that led Specker to his demonstration with Kochen, it was a criticism of von Neumann's "proof" that led John Bell to the result. A misinterpretation of this famous "proof" will lead them to diametrically opposite conclusions. Over the last decades, remarkable theoretical progresses have been made on…
We establish a strong link between two apparently unrelated topics: the study of conflicting information in the formal framework of valuation algebras, and the phenomena of non-locality and contextuality. In particular, we show that these peculiar features of quantum theory are mathematically equivalent to a general notion of \emph{disagreement} between information sources. This result vastly generalises previously observed connections between contextuality, relational databases, constraint satisfaction problems, and logical paradoxes, and gives further proof that contextual behaviour is not a…
A Quantum Gödelian Hunch
本文提出量子理论的悖论性源于类哥德尔不完备性的不可判定性的直觉，通过量子互文性、测量问题两个案例，结合说谎者悖论逻辑结构与元互文性概念展开论证，并探讨了时间从自相矛盾中涌现的可能。
Exploring the boundary of quantum correlations with a time-domain optical processor
本文推导出语境覆盖数为3且达到量子理论下界的GHZ型悖论，并通过时域光纤光学平台在37维装置中成功演示，为利用时分复用光学系统探索高维量子关联铺平了道路。
A kind of paradoxical effects has been demonstrated that the pigeonhole principle, i.e., if three pigeons are put in two pigeonholes then at least two pigeons must stay in the same hole, fails in certain quantum mechanical scenario. Here we shall show how to associate a proof of Kochen-Specker theorem with a quantum pigeonhole effect and vise versa, e.g., from state-independent proofs of Kochen-Specker theorem some kind of state-independent quantum pigeonhole effects can be demonstrated. In particular, a state-independent version of the quantum Cheshire cat, which can be rendered as a kind of …
Contextuality, Coherences, and Quantum Cheshire Cats
本文运用语境性理论分析量子柴郡猫悖论，揭示其源于三种测量间的逻辑矛盾，并指出该现象体现的是前选择和后选择系统中禁戒态间的相干性效应，而非粒子属性脱离实体。
Exploring Quantum Contextuality with the Quantum Moebius-Escher-Penrose hypergraph
本文提出量子莫比乌斯-埃舍尔-彭罗斯超图，通过量子与经典双重嵌入对比，揭示语境性及其与经典逻辑的关联。
One fascinating way of revealing the quantum nonlocality is the all-versus-nothing test due to Greenberger, Horne, and Zeilinger (GHZ) known as GHZ paradox. So far genuine multipartite and multilevel GHZ paradoxes are known to exist only in systems containing an odd number of particles. Here we shall construct GHZ paradoxes for an arbitrary number (greater than 3) of particles with the help of qudit graph states on a special kind of graphs, called as GHZ graphs. Based on the GHZ paradox arising from a GHZ graph, we derive a Bell inequality with two $d$-outcome observables for each observer, wh…
Contextuality is a key signature of quantum non-classicality, which has been shown to play a central role in enabling quantum advantage for a wide range of information-processing and computational tasks. We study the logic of contextuality from a structural point of view, in the setting of partial Boolean algebras introduced by Kochen and Specker in their seminal work. These contrast with traditional quantum logic à la Birkhoff and von Neumann in that operations such as conjunction and disjunction are partial, only being defined in the domain where they are physically meaningful. We study how …
The discovery of quantum key distribution by Bennett and Brassard (BB84) bases on the fundamental quantum feature: incompatibility of measurements of quantum non-commuting observables. In 1991 Ekert showed that cryptographic key can be generated at a distance with help of entangled (correlated) quantum particles. Recently Barrett, Hardy and Kent showed that the non-locality used by Ekert is itself a good resource of cryptographic key even beyond quantum mechanics. Their result paved the way to new generation of quantum cryptographic protocols - secure even if the devices are built by the very …
How Quantum Contextuality disappears in the Classical Limit
本文研究了量子上下文性在经典极限中的消失问题，通过分析KCBS和Peres-Mermin实验方案在去极化通道中的动态，揭示开放系统如何抑制上下文性所需的相关性，导致经典化。
The discovery of quantum key distribution by Bennett and Brassard (BB84) bases on the fundamental quantum feature: incompatibility of measurements of quantum non-commuting observables. In 1991 Ekert showed that cryptographic key can be generated at a distance with help of entangled (correlated) quantum particles. Recently Barrett, Hardy and Kent showed that the non-locality used by Ekert is itself a good resource of cryptographic key even beyond quantum mechanics. Their result paved the way to new generation of quantum cryptographic protocols - secure even if the devices are built by the very …
Sequential propagation of a single photon through five measurement contexts in a three-path interferometer
本文提出一种三维路径干涉仪，按顺序实现证明量子语境性所需的五个测量语境，并通过弱测量中的条件流解释路径看似被相消干涉阻断的悖论，表明弱值有助于连接波动传播与局域粒子探测。
The formalism of abstracted quantum mechanics is applied in a model of the generalized Liar Paradox. Here, the Liar Paradox, a consistently testable configuration of logical truth properties, is considered a dynamic conceptual entity in the cognitive sphere. Basically, the intrinsic contextuality of the truth-value of the Liar Paradox is appropriately covered by the abstracted quantum mechanical approach. The formal details of the model are explicited here for the generalized case. We prove the possibility of constructing a quantum model of the m-sentence generalizations of the Liar Paradox. T…
Quantum pre- and post-selection (PPS) paradoxes occur when counterfactual inferences are made about different measurements that might have been performed, between two measurements that are actually performed. The 3 box paradox is the paradigm example of such a paradox, where a ball is placed in one of three boxes and it is inferred that it would have been found, with certainty, both in box 1 and in box 2 had either box been opened on their own. Precisely what is at stake in PPS paradoxes has been unclear, and classical models have been suggested which are supposed to mimic the essential featur…
We present a logical type of proof of contextuality for a two-qubit state. We formulate a paradox that cannot be verified by a two-qubit system with local measurements while it is possible by using entanglement measurements. With our scheme we achieve $p_{\rm Hardy} \approx 0.167$, which is the highest probability obtained for a system of similar dimension. Our approach uses graph theory and the global exclusivity principle to give an interpretation of logical type of proofs of quantum correlations. We review the Hardy paradox and find connection to the KCBS inequality. We apply the same metho…
Most of the paradoxical, for the classical intuition, features of quantum theory were formulated for situations which involve a fixed number of particles. While one can now find a formulation of Bell's theorem for quantum fields, a Kochen-Specker-type reasoning is usually formulated for just one particle, or like in the case of Peres-Mermin square for two. A question emerges. Is it possible to formulate a contextuality proof for situation in which the numbers of particles are fundamentally undefined? We address this problem for bosonic fields. We introduce a representation of the $\mathfrak{su…
Empirical evidence has confirmed that quantum effects occur frequently also outside the microscopic domain, while quantum structures satisfactorily model various situations in several areas of science, including biological, cognitive and social processes. In this paper, we elaborate a quantum mechanical model which faithfully describes the 'Ellsberg paradox' in economics, showing that the mathematical formalism of quantum mechanics is capable to represent the 'ambiguity' present in this kind of situations, because of the presence of 'contextuality'. Then, we analyze the data collected in a con…
Foundational puzzles on quantum universality: From Wigner's friend to black holes
本论文探讨量子理论中的测量问题与黑洞信息悖论，提出扩展维格纳的朋友论证及统一悖论，并分析叠加黑洞的探测器响应，深化对量子实在性和引力的理解。
Algorithmic Idealism II: Reassessment of Competing Theories
本文提出算法唯心主义作为统一框架，将身份视为信息构造、实在视为算法转换过程，以解决经典形而上学、量子力学与计算理论之间的悖论，并为数字化世界中的存在理解提供更优模型。
An Introduction to the Foundations and Interpretations of Quantum Mechanics
本文综述量子力学关键概念与诠释发展，从公设到测量、非定域性及经典涌现，分析哥本哈根、德布罗意-玻姆、多世界等诠释如何回应量子理论对物理实在本质的启示。
We present an information-theoretic interpretation of quantum formalism based on a Bayesian framework and devoid of any extra axiom or principle. Quantum information is construed as a technique for analyzing a logical system subject to classical constraints, based on a question-and-answer procedure. The problem is posed from a particular batch of queries while the constraints are represented by the truth table of a set of Boolean functions. The Bayesian inference technique consists in assigning a probability distribution within a real-valued probability space to the joint set of queries in ord…
We understand emergent quantum mechanics in the sense that quantum mechanics describes processes of physical emergence relating an assumed sub-quantum physics to macroscopic boundary conditions. The latter can be shown to entail top-down causation, in addition to usual bottom-up scenarios. With this example it is demonstrated that definitions of "realism" in the literature are simply too restrictive. A prevailing manner to define realism in quantum mechanics is in terms of pre-determination independent of the measurement. With our counter-example, which actually is ubiquitous in emergent, or s…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。