Fractional Conformal Map, Qubit Dynamics and the Leggett-Garg Inequality
- URL: http://arxiv.org/abs/2401.10602v1
- Date: Fri, 19 Jan 2024 10:20:57 GMT
- Title: Fractional Conformal Map, Qubit Dynamics and the Leggett-Garg Inequality
- Authors: Sourav Paul, Anant Vijay Varma, Sourin Das
- Abstract summary: 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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
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