Fractional Conformal Map, Qubit Dynamics and the Leggett-Garg Inequality
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| Format: | Preprint |
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2024
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| _version_ | 1866917414455738368 |
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| author | Paul, Sourav Varma, Anant Vijay Das, Sourin |
| author_facet | Paul, Sourav Varma, Anant Vijay Das, Sourin |
| contents | Any pure state of a qubit can be geometrically represented as a point on the extended complex plane through stereographic projection. By employing successive conformal maps on the extended complex plane, we can generate an effective discrete-time evolution of the pure states of the qubit. This work focuses on a subset of analytic maps known as fractional linear conformal maps. We show that these maps serve as a unifying framework for a diverse range of quantum-inspired conceivable dynamics, including (i) unitary dynamics,(ii) non-unitary but linear dynamics and (iii) non-unitary and non-linear dynamics where linearity (non-linearity) refers to the action of the discrete time evolution operator on the Hilbert space. We provide a characterization of these maps in terms of Leggett-Garg Inequality complemented with No-signaling in Time (NSIT) and Arrow of Time (AoT) conditions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_10602 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional Conformal Map, Qubit Dynamics and the Leggett-Garg Inequality Paul, Sourav Varma, Anant Vijay Das, Sourin Quantum Physics Mathematical Physics Any pure state of a qubit can be geometrically represented as a point on the extended complex plane through stereographic projection. By employing successive conformal maps on the extended complex plane, we can generate an effective discrete-time evolution of the pure states of the qubit. This work focuses on a subset of analytic maps known as fractional linear conformal maps. We show that these maps serve as a unifying framework for a diverse range of quantum-inspired conceivable dynamics, including (i) unitary dynamics,(ii) non-unitary but linear dynamics and (iii) non-unitary and non-linear dynamics where linearity (non-linearity) refers to the action of the discrete time evolution operator on the Hilbert space. We provide a characterization of these maps in terms of Leggett-Garg Inequality complemented with No-signaling in Time (NSIT) and Arrow of Time (AoT) conditions. |
| title | Fractional Conformal Map, Qubit Dynamics and the Leggett-Garg Inequality |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2401.10602 |