Pre- and post-selection paradoxes in quantum walks

Kopyciuk, T.; Lewandowski, Mikołaj; Kurzyński, Paweł

doi:10.1088/1367-2630/ab4cf8

Cited by 4 publications

(4 citation statements)

References 44 publications

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“…Paradox Pre-and post-selection can lead to paradoxes [19], such as the three-box one [20]. In our case the paradox originates from the following counterfactual reasoning [16]. Imagine that at time t = 0 the system was pre-selected in the state |pre(0) and at time t = 2 it was post-selected in the state |post(2) .…”

Section: Modelmentioning

confidence: 96%

“…We do this by designing a Bell-like inequality [12] and showing that experimentally obtained measurement data violates it. The inequality is based on a recent logical pre-and post-selection (LPPS) paradox designed by some of the authors [16]. Notice that LPPS paradoxes were shown to be proofs of contextuality [17,18], hence if some system admits such a paradox, it is nonclassical in a sense that it is contextual [13].…”

Section: Introductionmentioning

confidence: 99%

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Nonclassical oscillations in pre- and post-selected quantum walks

Chen

Meng

et al. 2021

Phys. Rev. A

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Quantum walks are counterparts of classical random walks. They spread faster, which can be exploited in information processing tasks, and constitute a versatile simulation platform for many quantum systems. Yet, some of their properties can be emulated with classical light. This rises a question: which aspects of the model are truly nonclassical? We address it by carrying out a photonic experiment based on a pre-and post-selection paradox. The paradox implies that if somebody could choose to ask, either if the particle is at position x = 0 at even time steps, or at position x = d (d > 1) at odd time steps, the answer would be positive, no matter the question asked. Therefore, the particle seems to undergo long distance oscillations despite the fact that the model allows to jump one position at a time. We translate this paradox into a Bell-like inequality and experimentally confirm its violation up to eight standard deviations.

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Section: Modelmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Nonclassical oscillations in pre- and post-selected quantum walks

Chen

Meng

et al. 2021

Phys. Rev. A

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“…Both cases are quite different to what we discussed in the previous section. The latter case, in particular, has also been discussed in the context of several quantum paradoxes (e.g., the Quantum Cheshire Cat and the Quantum violations of the pigeonhole principle [88][89][90]), dealt with by the technique known as pre-and post-selections [91]. Clearly, the importance of temporal nonlocality is not limited to quantum physical systems and the idea that the "flow" of time is the result of correlations between "subsequent" moments of time which are entangled (or correlated) in non-local manner has been re-surging in different forms on many different occasions (e.g., [5,83,92,93] and references therein).…”

Section: Nonlocality In Timementioning

confidence: 99%

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Sytnyk

Melnik

2021

MCA

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Nonlocal models are ubiquitous in all branches of science and engineering, with a rapidly expanding range of mathematical and computational applications due to the ability of such models to capture effects and phenomena that traditional models cannot. While spatial nonlocalities have received considerable attention in the research community, the same cannot be said about nonlocality in time, in particular when nonlocal initial conditions are present. This paper aims at filling this gap, providing an overview of the current status of nonlocal models and focusing on the mathematical treatment of such models when nonlocal initial conditions are at the heart of the problem. Specifically, our representative example is given for a nonlocal-in-time problem for the abstract Schrödinger equation. By exploiting the linear nature of nonlocal conditions, we derive an exact representation of the solution operator under assumptions that the spectrum of Hamiltonian is contained in the horizontal strip of the complex plane. The derived representation permits us to establish the necessary and sufficient conditions for the problem’s well-posedness and the existence of its solution under different regularities. Furthermore, we present new sufficient conditions for the existence of the solution that extend the existing results in this field to the case when some nonlocal parameters are unbounded. Two further examples demonstrate the developed methodology and highlight the importance of its computer algebra component in the reduction procedures and parameter estimations for nonlocal models. Finally, a connection of the considered models and developed analysis is discussed in the context of other reduction techniques, concentrating on the most promising from the viewpoint of data-driven modelling environments, and providing directions for further generalizations.

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“…Quantum walks are also very useful to build quantum algorithms [5][6][7][8], and a comparison with the corresponding classical random walks is crucial to assess the possible quantum enhancement due to the faster spreading of probability distributions. As a consequence, the differences between a classical and a quantum walk have been analyzed quite extensively, with short-and long-time behavior studied in both scenarios [9][10][11][12][13][14]. Signatures of the nonclassicality of the evolution involve the ballistic propagation of the quantum walker, compared to the classical diffusive analog [15], and their measurement-induced disturbance or the presence of nonclassical correlations, i.e., discord, in bipartite systems [16].…”

Section: Introductionmentioning

confidence: 99%

Quantum-classical dynamical distance and quantumness of quantum walks

2020

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We introduce a fidelity-based measure, D QC (t), to quantify the differences in the dynamics of classical versus quantum walks over a graph. We provide universal, graph-independent, analytic expressions of this quantumclassical dynamical distance, showing that at short times D QC (t) is proportional to the coherence of the walker, i.e., a genuine quantum feature, whereas at long times it depends only on the size of the graph. At intermediate times, D QC (t) does depend on the graph topology through its algebraic connectivity. Our results show that the difference in the dynamical behavior of classical and quantum walks is entirely due to the emergence of quantum features at short times. In the long-time limit, quantumness and the different nature of the generators of the dynamics, e.g., the open-system nature of classical walks and the unitary nature of quantum walks, are instead contributing equally.

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Pre- and post-selection paradoxes in quantum walks

Cited by 4 publications

References 44 publications

Nonclassical oscillations in pre- and post-selected quantum walks

Nonclassical oscillations in pre- and post-selected quantum walks

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Quantum-classical dynamical distance and quantumness of quantum walks

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