The claim of Meyer, Kent and Clifton (MKC) that finite precision measurement nullifies the Kochen-Specker theorem is criticised. It is argued that, although MKC have nullified the Kochen-Specker theorem strictly so-called, there are other, related propositions which are not nullified. The argument given is an elaboration of some of Mermin's critical remarks. Although MKC allow for the fact that the observables to be measured cannot be precisely specified, they continue to assume that the observables which are actually measured are strictly commuting. As Mermin points out, this assumption is unjustified. Consequently, the analysis of MKC is incomplete. To make it complete one needs to investigate the predictions their models make regarding approximate joint measurements of non-commuting observables. Such an investigation is carried out, using methods previously developed in connection with approximate joint measurements of position and momentum. It is shown that a form of contextuality then re-emerges.
Contextuality is a signature of operational nonclassicality in the outcome statistics of an experiment. This notion of nonclassicality applies to a breadth of physical phenomena. Here, we establish its relation to two fundamental nonclassical entities in quantum theory; measurement incompatibility and steering. We show that each is necessary and sufficient the failure of operational contextuality. We exploit the established connection to contextuality to provide a novel approach to problems in measurement incompatibility and steering.
A set of quantum measurements exhibits quantum contextuality when any consistent value assignment to the measurement outcomes leads to a contradiction with quantum theory. In the original Kochen-Specker-type of argument the measurement projectors are assumed to be rays, that is, of unit rank. Only recently a contextuality scenario has been identified where state-independent contextuality requires measurements with projectors of rank two. Using the disjunctive graph product, we provide a systematic method to construct contextuality scenarios which require non-unit rank. We construct explicit ex…
In quantum physics, the notion of contextuality has a variety of interpretations which are typically associated with the names of their inventors, say Bohr, Bell, Kochen and Specker, and recently Dzhafarov. In fact, Bohr was the first who pointed to contextuality of quantum measurements as a part of formulation of his principle of complementarity. (Instead of "contextuality", he considered dependence on "experimental conditions.") Unfortunately, the contextuality counterpart of the complementarity principle was overshadowed by the issue of incompatibility of observables. And the interest for c…
The conspiracy of ontic states responding to measurements contextually to comply with noncontextual quantum mechanical probabilities is analyzed for general ontological models. A general physical picture of ontological space structure and how ontic states are disturbed by measurement contexts is presented. A common assumption in ontological models called lambda-sufficiency is analyzed and argued to be inconsistent with measurement contextuality for ontological models with certain symmetry in ontic space with respect to quantum states and measurements.
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.
Contextuality - the obstruction to describing quantum mechanics in a classical statistical way - has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality as a computational resource, as follows. If local measurements on a multi-qubit state can be used to evaluate non-linear boolean functions with only linear control processing, then this computation constitutes a proof of strong contextuality - the possible local measurement outcomes cannot all be pre-assigned. However, this connection is restricted to the spe…
Contextuality is a necessary resource for universal quantum computation and non-contextual quantum mechanics can be simulated efficiently by classical computers in many cases. Orders of Planck's constant, $\hbar$, can also be used to characterize the classical-quantum divide by expanding quantities of interest in powers of $\hbar$---all orders higher than $\hbar^0$ can be interpreted as quantum corrections to the order $\hbar^0$ term. We show that contextual measurements in finite-dimensional systems have formulations within the Wigner-Weyl-Moyal (WWM) formalism that require higher than order …
Okay, Roberts, Bartlett and Raussendorf recently introduced a new cohomological approach to contextuality in measurement based quantum computation. We give an abstract description of their obstruction and the algebraic structure it exploits, using the sheaf theoretic framework of Abramsky and Brandenburger. At this level of generality we contrast their approach to the Cech cohomology obstruction of Abramsky, Mansfield and Barbosa and give a direct proof that Cech cohomology is at least as powerful.
Multiple observers who independently harvest nonclassical correlations from a single physical system share the system's ability to enable quantum correlations. We show that any number of independent observers can share the preparation contextual outcome statistics enabled by state ensembles in quantum theory. Furthermore, we show that even in the presence of any amount of white noise, there exists quantum ensembles that enable such shared preparation contextuality. The findings are experimentally realised by applying sequential unsharp measurements to an optical qubit ensemble which reveals th…
Contextuality is considered as an intrinsic signature of non-classicality, and a crucial resource for achieving unique advantages of quantum information processing. However, recently there have been debates on whether classical fields may also demonstrate contextuality. Here we experimentally configure a contextuality test for optical fields, adopting various definitions of measurement events, and analyse how the definitions affect the emergence of non-classical correlations. The heralded single photon state, a typical non-classical light field, manifests contextuality in our setup, while cont…
Quantum contextuality from measurement invasiveness
Università degli Studi di Milano（米兰大学）；ICFO – Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（巴塞罗那光子科学研究所，巴塞罗那科学技术研究院）；Istituto Nazionale di Fisica Nucleare, Sezione di Milano（意大利国家核物理研究所，米兰分部）
We investigate the connection between steering and contextuality in general probabilistic theories. We show that for a class of bipartite states the steerability of the state by given set of measurements is equivalent to non-existence of preparation noncontextual hidden variable model for certain restricted theory constructed from the given state and measurements. The connection between steering and contextuality is provided by the concept of incompatibility in restricted theories, which we also investigate.
If noncontextuality is defined as the robustness of a system's response to a measurement against other simultaneous measurements, then the Kochen-Specker arguments do not provide an algebraic proof for quantum contextuality. Namely, for the argument to be effective, (i) each operator must be uniquely associated with a measurement and (ii) commuting operators must represent simultaneous measurements. However, in all Kochen-Specker arguments discussed in the literature either (i) or (ii) is not met. Arguments meeting (i) contain at least one subset of mutually commuting operators which do not re…
Measurement incompatibility is the most basic resource that distinguishes quantum from classical physics. Contextuality is the critical resource behind the power of some models of quantum computation and is also a necessary ingredient for many applications in quantum information. A fundamental problem is thus identifying when incompatibility produces contextuality. Here, we show that, given a structure of incompatibility characterized by a graph in which nonadjacent vertices represent incompatible ideal measurements, the necessary and sufficient condition for the existence of a quantum realiza…
Linear-optical test of quantum contextuality with sequential measurements
National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学固体微结构物理国家重点实验室、智能光学传感与操控重点实验室、工程与应用科学学院和物理学院、先进微结构协同创新中心）；Physics Department, Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学高等研究院物理系）；Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien（维也纳量子科学与技术中心、原子研究所、维也纳工业大学）；School of Quantum Physics and Matter, Institute for Research in Fundamental Sciences (IPM)（基本科学研究院量子物理与物质学院）；Wallenberg Centre for Quantum Technology, Department of Microtechnology and Nanoscience, Chalmers University of Technology（查尔姆斯理工大学微技术与纳米科学部瓦伦堡量子技术中心）
In [Phys. Rev. Lett. 114, 250401 (2015)] the sharing of non-locality by multiple observers was demonstrated through the quantum violation of Clauser-Horne-Shimony-Halt inequality. In this paper we provide a scheme for sharing of non-locality and non-trivial preparation contextuality sequentially through the quantum violation of a family of Bell's inequalities where Alice and Bob perform $2^{n-1}$ and $n$ numbers of measurements of dichotomic observables respectively. For this, we consider that Alice always performs projective measurement and multiple Bobs sequentially perform unsharp measureme…
In this work we analyse the notion of measurement non-contextuality (MNC) and identify contextual scenarios which involve sequential measurements of only a single measurement device. We show that any non-contextual ontological model fails to explain the statistics of outcomes of a single carefully constructed positive operator valued measure (POVM) executed sequentially on a quantum system. The context of measurement arises from the different configurations in which the device can be used. We develop an inequality from the non-contextual (NC) ontic model, and construct a quantum situation invo…
The non-classicality of single quantum systems can be formalised using the notion of contextuality. But can contextuality be convincingly demonstrated in an experiment, without reference to the quantum formalism? The operational approach to contextuality due to Spekkens requires finding operationally equivalent preparation procedures. Previously these have been obtained by demanding indistinguishability under a set of measurements taken to be tomographically complete. In the language of generalised probability theories, this requires the ability to explore all the dimensions of the system's st…
We uncover a form of quantum contextuality that connects maximal contextuality to boson indistinguihability in a similar way maximal nonlocality with respect to the Clauser-Horne-Shimony-Holt Bell inequality is connected to maximal entanglement. Unlike previous forms of photonic contextuality, this form cannot be simulated with classical light, as it relies on indistinguishability and higher-order interference. Ideal measurements on the bosonic system can be performed by means of dispersive coupling with an ancillary qubit. This allows us delaying at will the ending of each measurement and tar…
A theory is universal contextual if its prediction cannot be reproduced by an ontological model satisfying both preparation and measurement noncontextuality assumptions. In this report, we first generalize the logical proofs of quantum preparation and measurement contextuality for qubit system for any odd number of preparations and measurements. Based on the logical proof, we derive testable universally non-contextual inequalities violated by quantum theory. We then propose a class of two-party communication games and show that the average success probability of winning such games is solely li…
International Centre for Theory of Quantum Technologies, University of Gdańsk（格但斯克大学量子技术理论国际中心）；Perimeter Institute for Theoretical Physics（基础物理研究所）；Basic Research Community for Physics e.V.（基础物理社区协会）
Contextuality describes the nontrivial dependence of measurement outcomes on particular choices of jointly measurable observables. In this work we review and generalize the bundle diagram representation introduced in [S. Abramsky et al., 24th EACSL Annual Conference on Computer Science Logic, 41, 211-228, (2015)] in order to graphically demonstrate the contextuality of diverse empirical models.
Postselection following weak measurements has long been investigated for its peculiar manifestation of quantum signatures. In particular, the postselected events can give rise to anomalous values lying outside the spectrum of the measured quantity, and may provide enhanced Fisher information. Furthermore, the Pusey inequality highlights that, for extremely weak measurements, non-contextual models can account for the outcome probabilities. It is then interesting to investigate whether these are linked in a unified framework. Here we discuss on the existence of a possible connection in the case …
Quantum measurements cannot be thought of as revealing preexisting results, even when they do not disturb any other measurement in the same trial. This feature is called contextuality and is crucial for the quantum advantage in computing. Here, we report the first observation of quantum contextuality simultaneously free of the detection, sharpness and compatibility loopholes. The detection and sharpness loopholes are closed by adopting a hybrid two-ion system and highly efficient fluorescence measurements offering a detection efficiency of $100\%$ and a measurement repeatability $>98\%$. The c…
Connection between the contextuality breaking and incompatibility breaking qubit channels
Indian Institute of Technology Dharwad（达尔瓦德印度理工学院）；Patna Science College, Patna University（巴特那大学巴特那理学院）；S. N. Bose National Center for Basic Sciences（S.N. 玻色基础科学国家中心）
We report on the realization and application of non-destructive three-qubit parity measurements on nuclear spin qubits in diamond. We use high-fidelity quantum logic to map the parity of the joint state of three nuclear spin qubits onto an electronic spin qubit that acts as an ancilla, followed by single-shot non-destructive readout of the ancilla combined with an electron spin echo to ensure outcome-independent evolution of the nuclear spins. Through the sequential application of three such parity measurements, we demonstrate the generation of genuine multipartite entangled states out of the …
Results of measurements give legitimacy to a physical theory. What if acquiring these results in the first place necessitates what the same theory considers to be an interaction? In this note, we assume that theories account for interactions so that they are empirically traceable, and that observations necessarily go with such an interaction with the observed system. We investigate consequences of this assumption: The unfolding language game, inspired by "quantum logic," leads to a class of contextual and probabilistic theories. Contextuality becomes a means to render interactions, thus also m…
