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arXiv:1505.01982 · Physical Review A

State-recycling method for testing quantum contextuality

Marek Wajs, Su‐Yong Lee, Paweł Kurzyński, Dagomir Kaszlikowski

Published May 4, 2016• 4 citations
arXivHTMLPDF

Abstract

We introduce a method to test the state-independent contextuality using a single copy of a system and without a state preparation. It can be implemented in realistic setups, like ion traps, or in other scenarios in which measurements are nondestructive. In particular, we show how to apply our idea to the Peres-Mermin state-independent contextuality test designed for nine observables of two spin-$1/2$ particles. Each measurement round is performed on a postmeasurement state from the previous round. The sequence of measurements can be described as a Markov chain, and we observe that after a few rounds the system arrives at a stationary state to which the contextuality of the system can be attributed. However, it has to be noted that it does not depend on the initial state of the system and therefore it is not a property of a particular state preparation. Finally, we show that our approach to test contextuality admits noisy measurements as it implies the self-correction of possible detection errors present in any real experiments.

DOI
10.1103/physreva.93.052104

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We introduce a method to test the state-independent contextuality using a single copy of a system and without a state preparation. It can be implemented in realistic setups, like ion traps, or in other scenarios in which measurements are nondestructive. In particular, we show how to apply our idea to the Peres-Mermin state-independent contextuality test designed for nine observables of two spin-1/21/21/2 particles. Each measurement round is performed on a postmeasurement state from the previous round. The sequence of measurements can be described as a Markov chain, and we observe that after a few rounds the system arrives at a stationary state to which the contextuality of the system can be attributed. However, it has to be noted that it does not depend on the initial state of the system and therefore it is not a property of a particular state preparation. Finally, we show that our approach to test contextuality admits noisy measurements as it implies the self-correction of possible detection errors present in any real experiments.
KS-contextuality is a crucial feature of quantum theory. Previous research demonstrated the vanishing of NNN-cycle KS-contextuality in setups where multiple independent observers measure sequentially on the same system, which we call Public Systems. This phenomenon can be explained as the additional observers' measurements degrading the state and depleting the quantum resource. This explanation would imply that state-independent contextuality should survive in such a system. In this paper, we show that this is not the case. We achieved this result by simulating an observer trying to violate the Peres-Mermin noncontextuality inequality in a Public System. Additionally, we provide an analytical description of our setup, explaining the loss of contextuality even in the state-independent case. Ultimately, these results show that state-independent contextuality is not independent of what happens to the system in-between the measurements of a context.
Abstract Self-testing allows for characterising quantum systems under minimal assumptions. However, existing schemes rely on quantum non-locality and cannot be applied to systems that are not entangled. Here, we introduce a robust method that achieves self-testing of individual systems by taking advantage of contextuality. The scheme is based on the simplest contextuality witness for the simplest contextual quantum system—the Klyachko-Can-Binicioglu-Shumovsky inequality for the qutrit. We establish a lower bound on the fidelity of the state and the measurements as a function of the value of the witness under a pragmatic assumption on the measurements. We apply the method in an experiment on a single trapped 40Ca+ and using randomly chosen measurements and perfect detection efficiency. Using the observed statistics, we obtain the first experimental demonstration of self-testing of a single quantum system with negligible deviations from the assumptions.
Simulating quantum contextuality with classical systems requires memory. A fundamental yet open question is what is the minimum memory needed and, therefore, the precise sense in which quantum systems outperform classical ones. Here, we make rigorous the notion of classically simulating quantum state-independent contextuality (QSIC) in the case of a single quantum system submitted to an infinite sequence of measurements randomly chosen from a finite QSIC set. We obtain the minimum memory needed to simulate arbitrary QSIC sets via classical systems under the assumption that the simulation should not contain any oracular information. In particular, we show that, while classically simulating two qubits tested with the Peres-Mermin set requires log_{2}24≈4.585 bits, simulating a single qutrit tested with the Yu-Oh set requires, at least, 5.740 bits.
Quantum contextuality refers to the impossibility of assigning a predefined, intrinsic value to a physical property of a system independently of the context in which the property is measured. It is, perhaps, the most fundamental feature of quantum mechanics. The many states with different spin that particle physics provides are the ideal setting for testing contextuality. We verify that the polarization states of single spin-1 massive particles produced at colliders are contextual. We test W + gauge bosons produced in top-quark decays, J / ψ and K * ( 892 ) 0 mesons in B -meson decays and ϕ mesons in χ c 0 and χ c 1 charmonium decays by reinterpreting the data and the analyses of the ATLAS, LHCb, Belle II and BESIII experimental collaborations, respectively. The polarization states of these four particles show contextuality with a significance larger than 5 σ . We also discuss the presence of quantum contextuality in spin states of bipartite systems formed by spin- 1 / 2 particles. We test Λ and Σ baryons reinterpreting two BESIII data analyses, and pairs of top quarks utilizing a recent analysis of the CMS Collaboration. Quantum contextuality is present with a significance exceeding 5 σ also in these cases. In addition, we study the feasibility of testing quantum contextuality by means of Z boson production in association with the Higgs boson, Z and W bosons pairs created in Higgs boson decays and with pairs of τ leptons. For the latter, we use Monte Carlo simulations that mimic the settings of SuperKEKB and of future lepton colliders. Experiments at high energies, though not designed for the purpose, perform surprisingly well in testing for quantum contextuality.
The emergence of classicality is fundamentally driven by the interaction between a quantum system and its environment. Foundational open-system approaches, notably the Caldeira-Leggett model, successfully captured how these interactions lead to macroscopic effects like quantum dissipation and decoherence. However, these approaches often leave the precise definitions of classicality and quantumness ambiguous. In quantum information theory, this boundary is a heavily scrutinized question, and Kochen-Specker contextuality emerges as a hallmark of nonclassicality. It is therefore natural to investigate whether decoherence can actually suppress this property. Taking this path creates an apparent conundrum, once there exist two distinct manifestations of quantum contextuality: state-dependent and state-independent ones. While state-dependent contextuality naturally vanishes under state degradation, state-independent contextuality could persist for any quantum state, since it shows up even for the maximally mixed state! In this paper, we resolve this apparent paradox by analyzing sequential measurement implementations of the paradigmatic Klyachko, Can, Binicioğlu, and Shumovsky (KCBS) and Peres-Mermin prepare-and-measure scenarios under the influence of depolarizing channels. By introducing noise both prior to and in between measurements, and by analyzing the resulting sequential correlators in both the Schrödinger and Heisenberg pictures, we show how open-system dynamics suppress the correlations required to witness contextuality, leading to classicalization.
Contextuality provides a unifying paradigm for nonclassical aspects of quantum probabilities and resources of quantum information. Unfortunately, most forms of quantum contextuality remain experimentally unexplored due to the difficulty of performing sequences of projective measurements on individual quantum systems. Here we show that two-point correlations between binary compatible observables are sufficient to reveal any form of contextuality. This allows us to design simple experiments that are more robust against imperfections and easier to analyze, thus opening the door for observing interesting forms of contextuality, including those requiring quantum systems of high dimensions. In addition, it allows us to connect contextuality to communication complexity scenarios and reformulate a recent result relating contextuality and quantum computation.