Contextuality Research Articles

Bounding and Simulating Contextual Correlations in Quantum Theory

We introduce a hierarchy of semidefinite relaxations of the set of quantum correlations in generalised contextuality scenarios. This constitutes a simple and versatile tool for bounding the magnitude of quantum contextuality. To illustrate its utility, we use it to determine the maximal quantum violation of several noncontextuality inequalities whose maximum violations were previously unknown. We then go further and use it to prove that certain preparation-contextual correlations cannot be explained with pure states, thereby showing that mixed states are an indispensable resource for contextuality. In the second part of the paper, we turn our attention to the simulation of preparation-contextual correlations in general operational theories. We introduce the information cost of simulating preparation contextuality, which quantifies the additional, otherwise forbidden, information required to simulate contextual correlations in either classical or quantum models. In both cases, we show that the simulation cost can be efficiently bounded using a variant of our hierarchy of semidefinite relaxations, and we calculate it exactly in the simplest contextuality scenario of parity-oblivious multiplexing.

State-independent quantum contextuality with projectors of nonunit rank

Virtually all of the analysis of quantum contextuality is restricted to the case where events are represented by rank-one projectors. This restriction is arbitrary and not motivated by physical considerations. We show here that loosening the rank constraint opens a new realm of quantum contextuality and we demonstrate that state-independent contextuality (SIC) can even require projectors of nonunit rank. This enables the possibility of SIC with less than 13 projectors, which is the established minimum for the case of rank one. We prove that for any rank, at least 9 projectors are required. Furthermore, in an exhaustive numerical search we find that 13 projectors are also minimal for the cases where all projectors are uniformly of rank two or uniformly of rank three.

Quantum contextuality of YO-13 rays

Quantum contextuality, a more general quantum correlation, is an important resource for quantum computing and quantum information processing. Meanwhile, quantum contextuality plays an important role in fundamental quantum physics. Yu and Oh (YO) proposed a proof of the Kochen–Specker theorem for a qutrit with only 13 rays. Here, we further study quantum contextuality of YO-13 rays using the inequality approach. The maximum quantum violation value of the optimal noncontextuality inequality constructed by YO-13 rays is increased to 11.9776 in the four-dimensional system, which is larger than 11.6667 in the qutrit system. The result shows that the set of YO-13 rays has stronger quantum contextuality in the four-dimensional system. Moreover, we provide an all-versus-nothing proof (i.e. Hardy-like proof) to study YO-13 rays without using any inequality, which is easily applied to experimental tests. Our results will further deepen the understanding of YO-13 rays.

Classifying Space for Quantum Contextuality

We construct a topological space to study contextuality in quantum mechanics. The resulting space is a classifying space in the sense of algebraic topology. Cohomological invariants of our space correspond to physical quantities relevant to the study of contextuality. Within this framework the Wigner function of a quantum state can be interpreted as a class in the twisted $K$-theory of the classifying space.

Contextuality of quantum fluctuations characterized by conditional weak values of entangled states

The quantum fluctuations of a physical property can be observed in the measurement statistics of any measurement that is at least partially sensitive to that physical property. Quantum theory indicates that the effective distribution of values taken by the physical property depends on the specific measurement context based on which these values are determined and weak values have been identified as the contextual values describing this dependence of quantum fluctuations on the measurement context. Here, the relation between classical statistics and quantum contextuality is explored by considering systems entangled with a quantum reference. The quantum fluctuations of the system can then be steered by precise projective measurements of the reference, resulting in different contextual values of the quantum fluctuations depending on the effective state preparation context determined by the measurement of the reference. The results show that mixed-state statistics are consistent with a wide range of potential contexts, indicating that the precise definition of a context requires maximal quantum coherence in both state preparation and measurement.

Classical limits and contextuality in a scenario of multiple observers

Contextuality is regarded as a non-classical feature, challenging our everyday intuition; quantum contextuality is currently seen as a resource for many applications in quantum computation, being responsible for quantum advantage over classical analogs. In our work, we adapt the $N$-cycle scenarios with odd $N$ to multiple independent observers which measure the system sequentially. We analyze the possibility of violating the inequalities as a function of the number of observers and under different measurement protocols. We then reinterpret the results as an open quantum system where the environment is divided into fragments. In this context, the results show the emergence of non-contextuality in such a setting, bringing together the quantum behavior to our classical experience. We then compare such emergence of non-contextuality with that of objectivity under the `Environment as a Witness paradigm'.

Quantum Contextuality for Training Neural Networks

In the training process of Neural networks (NNs), the selection of hyper-parameters is crucial, which determines the final training effect of the model. Among them, the Learning rate decay (LRD) can improve the learning speed and accuracy; the Weight decay (WD) improves the over-fitting to varying degrees. However, the decay methods still have problems such as hysteresis and stiffness of parameter adjustment, so that the final model will be inferior. Based on the Quantum contextuality (QC) theory, we propose a Quantum contextuality constraint (QCC) to constrain the weights of nodes in NNs to further improve the training effect. In the simplest classification model, we combine this constraint with different methods of LRD and WD to verify that QCC can further improve the training effect on the decay method. The performance of the experiments shows that QCC can significantly improve the convergence and accuracy of the model.

Information flow in context-dependent hierarchical Bayesian inference

ABSTRACT Recent theories developing broad notions of context and its effects on inference are becoming increasingly important in fields as diverse as cognitive psychology, information science and quantum information theory and computing. Here we introduce a novel and general approach to the characterisation of contextuality using the techniques of Chu spaces and Channel Theory viewed as general theories of information flow. This involves introducing three essential components into the formulism: events, conditions and measurement systems. Incorporating these factors in relationship to conditional probabilities leads to information flows both in the setting of Chu spaces and Channel Theory. The latter provides a representation of semantic content using local logics from which conditionals can be derived. We employ these features to construct cone-cocone diagrams, commutativity of which enforces inferential coherence. With these we build a scale-free architecture incorporating a Bayesian-like hierarchical structure, in which there is an interpretation of active inference and Markov blankets. We compare this architecture with other theories of contextuality which we briefly review. We also show that this development of ideas conveniently accommodates negative probabilities, leading to the notion of signed information flow, and address how quantum contextuality can be interpreted within this model. Finally, we relate contextuality to the Frame Problem, another way of characterising a fundamental limitation on the observational and inferential capabilities of finite agents.

Quantumness of States and Unitary Operations

This paper investigates various properties that may by possessed by quantum states, which are believed to be specifically “quantum” (entanglement, nonlocality, steerability, negative conditional entropy, non-zero quantum discord, non-zero quantum super discord and contextuality) and their opposites. It also considers their “absolute” counterparts in the following sense: a given state has a given property absolutely if after an arbitrary unitary transformation it still possesses it. The known relations between the listed properties and between their absolute counterparts are summarized. It is proven that the only two-qubit state that has zero quantum discord absolutely is the maximally mixed state. Finally, related conceptual issues concerning the terms “classical” and “quantum” are discussed.

Distribution of Additive Quantum Resources

Quantum resource theories offer formal frameworks for quantification and manipulation of intrinsic resources associated in quantum systems. Each resource, such as quantum entanglement, coherence, contextuality and many others, has attracted considerable interest encompassing the characterization, quantification, and its operational application. Despite the fundamental importance of quantum resource, the development of a unified framework of resource theories has been initiated only recently, especially in the framework of additive quantum resources. Monogamy is a fundamental property of many entanglement measures, and a unified view to monogamy inequalities of bipartite entanglement in multi-party quantum systems has recently been established. By investigating the monogamy property of the additive quantum resource, general monogamy inequalities given by the α th power of additive quantum resource measures are presented: any additive resource measure satisfy the polynomial relation for α ≥ 1 and obey monogamy inequalities for α ≤ 0. However, the relation is not clear for 0 < α < 1. These relations add a fundamental item to the list of common properties based on the tensor product structure for the general quantum resources.

Articulaciones teóricas y metodológicas entre los procesos de inclusión-exclusión educativa, cohesión grupal y rendimiento

El espacio escolar es poderoso en su capacidad de instituir contenidos subjetivos que reproduzcan o transformen el ordenamiento social. Por ello, la Psicología necesita contribuir a producir instituciones escolares transformadas y transformadoras. No obstante, padece separaciones entre sus disciplinas que limitan su accionar. El artículo presenta las premisas para una mirada transdiciplinar de la escuela. Se articula un modelo que propone un modo de diagnosticar y transformar la realidad de estas instituciones a partir de tres procesos: la cohesión grupal, la inclusión-exclusión educativa y el rendimiento. El modelo emplea como unidades de análisis la institución educativa y el grupo escolar como espacio psicológico condicionado, pero también transformador. Ello permite un análisis desde la multideterminación de los procesos de la relación subjetividad-grupalidad en la contextualidad social. Coloca la responsabilidad en las instituciones y se enfoca en procesos subjetivos en relación con elementos estructurales.

Quantum logic is undecidable

We investigate the first-order theory of closed subspaces of complex Hilbert spaces in the signature $(\lor,\perp,0,1)$, where `$\perp$' is the orthogonality relation. Our main result is that already its quasi-identities are undecidable: there is no algorithm to decide whether an implication between equations and orthogonality relations implies another equation. This is a corollary of a recent result of Slofstra in combinatorial group theory. It follows upon reinterpreting that result in terms of the hypergraph approach to quantum contextuality, for which it constitutes a proof of the inverse sandwich conjecture. It can also be interpreted as stating that a certain quantum satisfiability problem is undecidable.

Quantum Contextuality and Indeterminacy.

The circumstances of measurement have more direct significance in quantum than in classical physics, where they can be neglected for well-performed measurements. In quantum mechanics, the dispositions of the measuring apparatus-plus-environment of the system measured for a property are a non-trivial part of its formalization as the quantum observable. A straightforward formalization of context, via equivalence classes of measurements corresponding to sets of sharp target observables, was recently given for sharp quantum observables. Here, we show that quantum contextuality, the dependence of measurement outcomes on circumstances external to the measured quantum system, can be manifested not only as the strict exclusivity of different measurements of sharp observables or valuations but via quantitative differences in the property statistics across simultaneous measurements of generalized quantum observables, by formalizing quantum context via coexistent generalized observables rather than only its subset of compatible sharp observables. Here, the question of whether such quantum contextuality follows from basic quantum principles is then addressed, and it is shown that the Principle of Indeterminacy is sufficient for at least one form of non-trivial contextuality. Contextuality is thus seen to be a natural feature of quantum mechanics rather than something arising only from the consideration of impossible measurements, abstract philosophical issues, hidden-variables theories, or other alternative, classical models of quantum behavior.

Sum-of-squares decompositions for a family of noncontextuality inequalities and self-testing of quantum devices

Violation of a noncontextuality inequality or the phenomenon referred to `quantum contextuality&amp;apos; is a fundamental feature of quantum theory. In this article, we derive a novel family of noncontextuality inequalities along with their sum-of-squares decompositions in the simplest (odd-cycle) sequential-measurement scenario capable to demonstrate Kochen-Specker contextuality. The sum-of-squares decompositions allow us to obtain the maximal quantum violation of these inequalities and a set of algebraic relations necessarily satisfied by any state and measurements achieving it. With their help, we prove that our inequalities can be used for self-testing of three-dimensional quantum state and measurements. Remarkably, the presented self-testing results rely on a single assumption about the measurement device that is much weaker than the assumptions considered in Kochen-Specker contextuality.

Indistinguishability and Negative Probabilities.

In this paper, we examined the connection between quantum systems’ indistinguishability and signed (or negative) probabilities. We do so by first introducing a measure-theoretic definition of signed probabilities inspired by research in quantum contextuality. We then argue that ontological indistinguishability leads to the no-signaling condition and negative probabilities.

Operator analysis of contextuality-witness measurements for multimode-entangled single-neutron interferometry

We develop an operator-based description of two types of multimode-entangled single-neutron quantum optical devices: Wollaston prisms and radio-frequency spin flippers in inclined magnetic field gradients. This treatment is similar to the approach used in quantum optics, and is convenient for the analysis of quantum contextuality measurements in certain types of neutron interferometers. We describe operationally the way multimode-entangled single-neutron states evolve in these devices, and provide expressions for the associated operators describing the dynamics, in the limit in which the neutron state space is approximated by a finite tensor product of distinguishable subsystems. We design entangled-neutron interferometers to measure entanglement witnesses for the Clauser, Horne, Shimony and Holt, and Mermin inequalities, and compare the theoretical predictions with recent experimental results. We present the generalization of these expressions to $n$ entangled distinguishable subsystems, which could become relevant in the future if it becomes possible to add neutron orbital angular momentum to the experimentally-accessible list of entangled modes. We view this work as a necessary first step towards a theoretical description of entangled neutron scattering from strongly entangled matter, and we explain why it should be possible to formulate a useful generalization of the usual Van Hove linear response theory for this case. We also briefly describe some other scientific extensions and applications which can benefit from interferometric measurements using the types of single-neutron multimode entanglement described by this analysis.

Kentsel Adaletin Temsil Edil(e)memesi Ekseninde Ekümenopolis (Ucu Olmayan Şehir) Filminin Sosyolojik Okuması

Kentlesme, modernlesme ve kapitalistlesme olgulari arasinda karsilikli baglamsallik soz konusudur. Kentin toplumsalliginda kurulan iliski dinamikligi bu anlamda deger kazanmaktadir. Ancak kurulan bu dinamizmin kentsel yasamda butunuyle devingenlik sagladigi anlamina gelmemektedir. Oysa kent, kendi toplumsal ve kulturel dokusuyla ozgunluk barindirmalidir. Sinifsal farkliliklarin catismalara sebep olmadigi kentlerin var olabilmesi bu anlamda onem tasimaktadir. Buna karsin esitsiz mekânsal ayrismalar, kamusalligin tasarlanisi ile kent politikalarini ve kentlesmedeki egemen yapinin temel nuvelerini derinden etkilemektedir Bu calisma Ekunemopolis (Ucu Olmayan Sehir) belgesel filminin siniflar arasi kutuplasmanin mekânsal ayrimlasmaya sebebiyet veren tezahurunu sosyolojik perspektifle sorgulamayi hedeflemektedir. Bunu gerceklestirebilmek amaciyla oncelikle ilgili belgeselde kent, kentlesme, kentsel dinamizm, kentsel adalet, yoksullugun gorunumu, kentsel donusum, kentin yapilandiricilari, politikacilar, yerinden edinmeyi deneyimleyenler, bu olayi tartisan mimarlar, akademisyenler ve sehir plancilarinin gorusleri uzerinden degerlendirilecektir. Calismada ayrica belgeselde sunulanin arda planini ve alt metnini anlayabilmek icin filmden belli kesitler sunulmak ve sosyolojik perspektif temel alinmaksuretiyle kentsel adaletin nasil olusturul(a)madigi elestirel bakis acisi ile analiz edilecektir.

Randomness Expansion Secured by Quantum Contextuality

The output randomness from a random number generator can be certified by observing the violation of quantum contextuality inequalities based on the Kochen-Specker theorem. Contextuality can be tested in a single quantum system, which significantly simplifies the experimental requirements to observe the violation comparing to the ones based on nonlocality tests. However, it is not yet resolved how to ensure compatibilities for sequential measurements that is required in contextuality tests. Here, we employ a modified Klyachko-Can-Binicio\u{g}lu-Shumovsky contextuality inequality, which can ease the strict compatibility requirement on measurements. On a trapped single \Ba ion system, we experimentally demonstrate violation of the contextuality inequality and realize self-testing quantum random number expansion by closing detection loopholes. We perform $1.29 \times 10^8$ trials of experiments and extract the randomness of $8.06 \times 10^5$ bits with a speed of 270 bits s$^{-1}$. Our demonstration paves the way for the practical high-speed spot-checking quantum random number expansion and other secure information processing applications.

Three-dimensional entanglement on a silicon chip

Entanglement is a counterintuitive feature of quantum physics that is at the heart of quantum technology. High-dimensional quantum states offer unique advantages in various quantum information tasks. Integrated photonic chips have recently emerged as a leading platform for the generation, manipulation and detection of entangled photons. Here, we report a silicon photonic chip that uses interferometric resonance-enhanced photon-pair sources, spectral demultiplexers and high-dimensional reconfigurable circuitries to generate, manipulate and analyse path-entangled three-dimensional qutrit states. By minimizing on-chip electrical and thermal cross-talk, we obtain high-quality quantum interference with visibilities above 96.5% and a maximally entangled-qutrit state with a fidelity of 95.5%. We further explore the fundamental properties of entangled qutrits to test quantum nonlocality and contextuality, and to implement quantum simulations of graphs and high-precision optical phase measurements. Our work paves the path for the development of multiphoton high-dimensional quantum technologies.

Certified Quantum Measurement of Majorana Fermions.

We present a quantum self-testing protocol to certify measurements of fermion parity involving Majorana fermion modes. We show that observing a set of ideal measurement statistics implies anti-commutativity of the implemented Majorana fermion parity operators, a necessary prerequisite for Majorana detection. Our protocol is robust to experimental errors. We obtain lower bounds on the fidelities of the state and measurement operators that are linear in the errors. We propose to analyze experimental outcomes in terms of a contextuality witness W, which satisfies 〈W〉 ≤ 3 for any classical probabilistic model of the data. A violation of the inequality witnesses quantum contextuality, and the closeness to the maximum ideal value 〈W〉 = 5 indicates the degree of confidence in the detection of Majorana fermions.