Examining the quantum fisher information in the interaction of a dirac system with a squeezed generalized amplitude damping channel

The inherent association between real quantum systems and their surrounding environment invariably results in decoherence, leading to the loss of entanglement. This diminution in entanglement coincides with a decline in the fidelity of transmitted information using the entangled quantum resource. This study scrutinizes the impact of the squeezed generalized amplitude damping (SGAD) channel on quantum Fisher information (QFI) parameters. The SGAD channel model, a versatile framework, is also employed to simulate other dissipative channels, including amplitude damping (AD) and generalized amplitude damping (GAD). Kraus operators facilitate the modeling of noisy channels. The results reveal that, within the SGAD channel, the QFI remains impervious to the squeezing variables (r and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Φ</mml:mi></mml:math> ). In the GAD channel, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>F</mml:mi> <mml:msub><mml:mi>θ</mml:mi> <mml:mrow><mml:mi>GAD</mml:mi></mml:mrow> </mml:msub> </mml:mrow> </mml:math> undergoes enhancement to a constant value with an upswing in temperature (T), while the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ϕ</mml:mi></mml:math> parameter in the GAD channel, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>F</mml:mi> <mml:msub><mml:mi>ϕ</mml:mi> <mml:mrow><mml:mi>GAD</mml:mi></mml:mrow> </mml:msub> </mml:mrow> </mml:math> , akin to the SGAD channel, surges around T = 2 before complete loss ensues. Concerning the AD channel, the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>θ</mml:mi></mml:math> component of the QFI initially experiences decoherence with an augmentation in the AD noise parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>λ</mml:mi></mml:math> ). Subsequently, it is restored to its initial value with a further escalation in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>λ</mml:mi></mml:math> . Conversely, the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ϕ</mml:mi></mml:math> component of the QFI in the AD channel experiences decoherence with an elevation in the AD noise parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>λ</mml:mi></mml:math> ).