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

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.

Automated summary

Quantum decoherence caused by imperfect manipulation of quantum devices is a crucial issue in the NISQ era. The traditional method of using error rates to parameterize quantum noise channels does not provide an explicit relationship between the decoherence effect and the error rate. This study proposes characterizing the decoherence effect of a noise channel based on the physical implementability of its inverse, which quantifies the difficulty of simulating the noise inverse using accessible quantum channels. Two concise inequalities are established to connect the decrease in state purity and logarithmic negativity after a noise channel to the physical implementability of the noise inverse, which should be decomposed as mutually orthogonal unitaries or product channels. Numerical demonstrations are conducted on commonly adopted two-qubit noise models, and the results contribute to the theoretical research on the entanglement properties of noise channels and provide guiding principles for quantum circuit design.