Noise effects on purity and quantum entanglement in terms of physical implementability

TL;DR

This paper introduces a novel way to quantify quantum noise effects by examining the physical implementability of the inverse noise channel, linking it to decoherence and entanglement loss in quantum systems.

Contribution

It proposes a new measure based on the implementability of the inverse noise channel, establishing inequalities that relate this measure to purity and entanglement degradation.

Findings

Derived inequalities connecting noise inverse implementability to purity loss.

Numerical validation on common two-qubit noise models.

Provides theoretical insights for quantum circuit design.

Abstract

Quantum decoherence due to imperfect manipulation of quantum devices is a key issue in the noisy intermediate-scale quantum (NISQ) era. Standard analyses in quantum information and quantum computation use error rates to parameterize quantum noise channels. However, there is no explicit relation between the decoherence effect induced by a noise channel and its error rate. In this work, we propose to characterize the decoherence effect of a noise channel by the physical implementability of its inverse, which is a universal parameter quantifying the difficulty to simulate the noise inverse with accessible quantum channels. We establish two concise inequalities connecting the decrease of the state purity and logarithmic negativity after a noise channel to the physical implementability of the noise inverse, which is required to be decomposed as mutually orthogonal unitaries or product channels respectively. Our results are numerically demonstrated on several commonly adopted two-qubit noise models. We believe that these relations contribute to the theoretical research on the entanglement properties of noise channels and provide guiding principles for quantum circuit design.