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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Online-Zugang: | https://arxiv.org/abs/2312.16281 |
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| _version_ | 1866911933086564352 |
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| author | Hotta, Masahiro Murk, Sebastian |
| author_facet | Hotta, Masahiro Murk, Sebastian |
| contents | Leggett-Garg inequalities place bounds on the temporal correlations of a system based on the principles of macroscopic realism $\textit{per se}$ and noninvasive measurability. Their conventional formulation relies on the ensemble-averaged products of observables measured at different instants of time. However, a complete description that enables a precise understanding and captures all physically relevant features requires the study of probability distributions associated with noncommuting observables. In this article, we propose a scheme to describe the dynamics of generic $N$-level quantum systems ("qudits") via a probability vector representation of the Schrödinger equation and define a precise notion of no-signaling in time (NSIT) for the probability distributions of noncommuting observables. This provides a systematic way of identifying the interferences responsible for nonclassical behavior. In addition, we introduce an interference witness measure to quantify violations of NSIT for arbitrary general probabilistic states. For single-qubit systems, we pinpoint the pivotal relation that establishes a connection between the disturbance of observables incurred during a measurement and the resulting NSIT violation. For large-$N$ systems where a manual determination is infeasible, the classification of states as either NSIT-conforming or NSIT-violating may be performed by a machine learning algorithm. We present a proof-of-principle implementation of such an algorithm in which the classifier function is prepared via supervised learning using pseudorandomly generated training data sets composed of states whose corresponding classifications are known $\textit{a priori}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16281 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Probability vector representation of the Schrödinger equation and Leggett-Garg-type experiments Hotta, Masahiro Murk, Sebastian Quantum Physics Leggett-Garg inequalities place bounds on the temporal correlations of a system based on the principles of macroscopic realism $\textit{per se}$ and noninvasive measurability. Their conventional formulation relies on the ensemble-averaged products of observables measured at different instants of time. However, a complete description that enables a precise understanding and captures all physically relevant features requires the study of probability distributions associated with noncommuting observables. In this article, we propose a scheme to describe the dynamics of generic $N$-level quantum systems ("qudits") via a probability vector representation of the Schrödinger equation and define a precise notion of no-signaling in time (NSIT) for the probability distributions of noncommuting observables. This provides a systematic way of identifying the interferences responsible for nonclassical behavior. In addition, we introduce an interference witness measure to quantify violations of NSIT for arbitrary general probabilistic states. For single-qubit systems, we pinpoint the pivotal relation that establishes a connection between the disturbance of observables incurred during a measurement and the resulting NSIT violation. For large-$N$ systems where a manual determination is infeasible, the classification of states as either NSIT-conforming or NSIT-violating may be performed by a machine learning algorithm. We present a proof-of-principle implementation of such an algorithm in which the classifier function is prepared via supervised learning using pseudorandomly generated training data sets composed of states whose corresponding classifications are known $\textit{a priori}$. |
| title | Probability vector representation of the Schrödinger equation and Leggett-Garg-type experiments |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2312.16281 |