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International Journal of Physics

Analyzing the Decoherence on Biphoton and Schrödinger Cat States through Wigner Function

Simanshu Kumar, Nandan S Bisht

Published Aug 3, 2025• 0 citations
Publisher

Abstract

This study lights on the phenomenon of quantum decoherence when Biphoton and Schrödinger cat states are evolve. The primary focus of the work is to explore and analyze the phenomenon of decoherence by virtue of the insightful representations on the way of deriving the Wigner function for the considered states. A crucial aspect of this work involves shedding light on the behaviour of Biphoton and Schrödinger cat states with the same spatial modes and similar theoretical tomography. By considering the influence of an external environment, we further extend our exploration of decoherence, aiming to understand how environment as a factor, impact the stability and coherence of these quantum states.

DOI
10.12691/ijp-13-3-5

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This study lights on the phenomenon of quantum decoherence when Biphoton and Schrödinger cat states are evolve. The primary focus of the work is to explore and analyze the phenomenon of decoherence by virtue of the insightful representations on the way of deriving the Wigner function for the considered states. A crucial aspect of this work involves shedding light on the behaviour of Biphoton and Schrödinger cat states with the same spatial modes and similar theoretical tomography. By considering the influence of an external environment, we further extend our exploration of decoherence, aiming to understand how environment as a factor, impact the stability and coherence of these quantum states.
Abstract Since the beginning of quantum physics, the relation between the properties of the microscopic quantum and the macroscopic classical world has been an important source for the development of the theory, and has led to new insights on the role of the environment in the transition from quantum to classical physics. Decoherence affects both coherence and entanglement of open systems. Quantum optics and cavity quantum electrodynamics have allowed detailed investigations of this phenomenon, within the framework of microwaves and light waves. In this paper, I present a personal account of theoretical and experimental developments that have led to the probing of the subtle frontier between quantum and classical phenomena.
Wigner function has been widely used in quantum systems. However, most of the related works focus on analysing coherentstates of quantum systems. Few discuss the impact of decoherence, i.e. collision, arising from the environment. Decoherence is crucial as the interactions between systems and the environment may drive quantum systems into classical ones, losing their novel quantum properties. Here, we consider the collision related Wigner function and employ the concept of the energy functional approach to derive the fluctuation-dissipation relation for the present problem. Herein, we investigate the effect of linear and nonlinear potentials on decoherence. We find that nonlinear potentials tend to alleviatethe effect of decoherence. More strikingly, nonlinear potentials can sometimes temporarily promote coherence but induce more energy loss, resulting in more decoherence in the later stage. The present outcomes pave the way to quantify the effect of nonlinearity and hence covariance on quantum decoherence.
Quantum decoherence, a fundamental challenge in quantum information processing, represents the loss of quantum coherence due to interaction with the environment. This paper explores a novel mathematical framework for understanding and quantifying this phenomenon, proposing a 'Quantum Decoherence Metric' – a rigorously defined function that captures the rate of decoherence and offers a precise tool for analysis. This work addresses a longstanding difficulty in modeling and analyzing decoherence, aiming for a more mathematically solid and controllable approach. The core mechanism involves the creation of a metric specifically designed to quantify the degradation of quantum states. This development builds upon existing theoretical concepts, providing a quantitative lens through which to examine and potentially mitigate decoherence effects. The resulting framework offers a significant step towards a deeper understanding of quantum systems and their stability.
We challenge the standard picture of decohering Schrödinger cat states as an ensemble average obeying a Lindblad master equation, brought about locally from an irreversible interaction with an environment. We generate self-consistent collections of pure system states correlated with specific environmental records, corresponding to the function of the wave-particle correlator first introduced in Carmichael et al. [ Phys. Rev. Lett. 85 (2000)]. In the spirit of Carmichael et al. [in Coherent States: Past, Present and Future , World Scientific, 1994], we find that the complementary unravelings evince a pronounced disparity when the “position” and “momentum” of the damped cavity mode — an explicitly open quantum system — are measured. Intensity-field correlations may largely deviate from a monotonic decay, while Wigner functions of the cavity state display contrasting manifestations of quantum interference when conditioned on photon counts sampling a continuous photocurrent. In turn, the conditional photodetection events mark the contextual diffusion of both the net charge generated at the homodyne detector, and the electromagnetic field amplitude in the resonator.
Quantum Schrodinger cat states are of great interest in quantum communications and quantum optics. These states are used in various scientific fields such as quantum computing, quantum error correction and high-precision measurements. The analysis of the Schrodinger cat states coherence is an important task for their complete practical application. Our developed approach makes it possible to estimate the coherence of the quantum Schrodinger cat state of arbitrary dimension, as well as to find the interference visibility of the state: an important optical characteristic. The obtained simple quantitative relationship between coherence and the Schmidt number, as well as the developed approach of reducing the multidimensional quantum cat state to a two-mode analog allow us to analyze macroscopic states formed by a large number of modes. Several explicit formulas for the reduced states that arise after measuring of some modes of the considered multimode system are obtained. The research results have significant application and can be used in the development of high-dimensional quantum information processing systems.
Much of the discussion of decoherence has been in terms of a particle moving in one dimension that is placed in an initial superposition state (a Schrödinger "cat" state) corresponding to two widely separated wave packets. Decoherence refers to the destruction of the interference term in the quantum probability function. Here, we stress that a quantitative measure of decoherence depends not only on the specific system being studied but also on whether one is considering coordinate, momentum or phase space. We show that this is best illustrated by considering Wigner phase space where the measure is again different. Analytic results for the time development of the Wigner distribution function for a two-Gaussian Schrodinger "cat" state have been obtained in the high-temperature limit (where decoherence can occur even for negligible dissipation) which facilitates a simple demonstration of our remarks.